From 57f0f42d3c6c001ddcd2cfc9aedb1b52af5de7af Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 14:27:22 +0100 Subject: [PATCH 01/33] remove title and add subject-area --- _data/core.yml | 2589 +++++++++++++++++++++++++----------------------- 1 file changed, 1348 insertions(+), 1241 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index 79b1c671..d2dc4478 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -211,1264 +211,1371 @@ defaultfixity: concepts: - - ## From chapter 4 of MathML3 - - ## - concept: TODO numbers representations - + ## ================ 4.4.1 functions and inverses ==================== - - title: functions and inverses - intents: - - concept: closed-interval - arity: 2 - property: function - en: closed interval between $1 and $2 - fr: intervalle fermé entre $1 et $2 - - - concept: closed-open-interval - arity: 2 - property: function - en: interval between $1 (included) and $2 - fr: intervalle ouvert à droite entre $1 et $2 - - - concept: open-closed-interval - arity: 2 - property: function - en: interval between $1 and $2, included - fr: intervalle ouvert à gauche... - - - concept: open-interval - arity: 2 - property: function - en: open interval between $1 and $2 - fr: intervalle ouvert - - - concept: inverse - arity: 1 - property: function* - en: inverse of $1 - comments: - - "`inverse` can be used for function inverses, matrix inverses, etc." - - - concept: inverse - arity: 1 - property: postfix - en: $1 inverse - - - concept: domain - arity: 1 - property: function - en: domain of $1 - fr: domaine de définition de $1 - - - concept: codomain - arity: 1 - property: function - en: codomain of $1 - fr: ensemble d'arrivée de $1 - - - concept: image - arity: 1 - property: function* - en: image of $1 - fr: image de $1 - - - concept: fraction - arity: 2 - property: function - en: fraction $1 over $2 end fraction - - - concept: mixed-fraction - arity: 2 - property: function - en: $1 and $2 - comments: - - "$1 is a positive integer and $2 is a fraction with positive numerical components. - The second argument can be an `mfrac` (normal or beveled) or can be a linear fraction using `/`" - - - concept: quotient - arity: 2 - property: function - en: integer part of $1 divided by $2 - fr: quotient de $1 par $2 - - - concept: evaluated-at - arity: 2 - property: infix - en: $1 evaluated-at $2 - comments: - - "Two common notations are - x2|3 - and - - - - x2 - | - - x=3 - - - " - - concept: remainder - arity: 2 - property: function - en: the remainder of $1 divided by $2 - fr: reste de la divsion de $1 par $2 - - - concept: max - arity: ">=1" - property: function - en: "max of $1, ..." - - - concept: min - arity: ">=1" - property: function - en: "min of $1, ..." - - - concept: power - arity: 2 - property: infix - conditions: - - condition: "$2=2" - en: "$1 squared" - fr: "$1 carré" - - condition: "$2=3" - en: "$1 cubed" - fr: "$1 cube" - - condition: "" - en: "$1 to the $2th power" - fr: "$1 à la $2" - - - - concept: root - arity: 2 - property: function - conditions: - - condition: "$2=2" - en: "square root of $1" - - condition: "$2=3" - en: "cube root of $1" - - condition: "$2=4" - en: "fourth root of $1" - - condition: "" - en: "$2th root of $1" - - - concept: greatest-common-divisor - arity: ">=2" - property: function - en: greatest common divisor of $1, $2, ... - fr: plus grand commun diviseur de $1, $2, ... - - - concept: least-common-multiple - arity: ">=2" - property: function - en: lest common multiple of $1, $2, ... - fr: plus grand commun diviseur de $1, $2, ... - - - concept: absolute-value - arity: 1 - property: function - en: absolute value of $1 - fr: valeur absolue de $1 - de: Betrag von $1 - - - concept: complex-conjugate - arity: 1 - property: function - en: complex conjugate of $1 - fr: $1 conjugé - - - concept: complex-arg - arity: 1 - property: function - en: arg of $1 - - - concept: real-part - arity: 1 - property: function - en: - - real part of $1 - - imaginary part of $1 - - - concept: imaginary-part - arity: 1 - property: function - en: imaginary part of $1 - - - concept: polar-coordinate - arity: 2 - property: function - en: "polar coordinate $1 comma $2" - comment: - - "The first argument is the radius, the second argument is the polar angle, the third arguments is the azimuthal angle." - - "Example: (r, θ)" - - - concept: spherical-coordinate - arity: 3 - property: function - en: "spherical coordinate $1 comma $2, comma $3" - comment: - - "The first argument is the radius, the second argument is the angle." - - "Example: (r,Φ,θ)" - - - concept: cartesian-coordinate - arity: ">=2" - property: function - en: "cartesian coordinate $1 comma $2 ..." - comment: - - "Example: (1,2)" - - - concept: coordinate - arity: ">=2" - property: function - en: "coordinate $1 comma $2 ..." - comment: - - "This a generic coordinate that doesn't specify the coordinate system. It takes 2 or more arguments." - - "Example: (1,2)" - - - concept: floor - arity: 1 - property: function - en: floor of $1 - - - concept: ceiling - arity: 1 - property: function - en: ceiling of $1 - - - concept: round - arity: 1 - property: function - en: rounded-value of $1 - comments: - - "This sometimes uses the notation - ⌊x⌉ - or - [x]" - - - concept: fractional-part - arity: 1 - property: function - en: fractional part of $1 - - ## ====================== 4.4.4 Calculus ============================ - - title: calculus - intents: - - concept: definite-integral - arity: 1 - property: ??? - en: "integral over $1" - comments: - - "integral sign is not an argument" - - - concept: definite-integral - arity: 2 - property: ??? - en: "integral from $1 to $2" - comments: - - "integral sign is not an argument" - - - - concept: derivative - arity: 3 - property: ??? - en: - - "(verbose) the $3 derivative of $1 with respect to $2" - - "(terse) d <$3 if $3 != 1> $1 by d $2 <$3 if $3 != 1>" - comments: - - "the terse reading only makes sense for Leibniz notation such as - d2ydx2 - or - d2dx2f(x). - It does not make sense for other notations such as - f''(x) - " - - "The first of these examples might be marked up as" - - | - ``` - - - d2 - y - + - concept: closed-interval + subject-area: functions and inverses + arity: 2 + property: function + en: closed interval between $1 and $2 + fr: intervalle fermé entre $1 et $2 + + - concept: closed-open-interval + subject-area: functions and inverses + arity: 2 + property: function + en: interval between $1 (included) and $2 + fr: intervalle ouvert à droite entre $1 et $2 + + - concept: open-closed-interval + subject-area: functions and inverses + arity: 2 + property: function + en: interval between $1 and $2, included + fr: intervalle ouvert à gauche... + + - concept: open-interval + subject-area: functions and inverses + arity: 2 + property: function + en: open interval between $1 and $2 + fr: intervalle ouvert + + - concept: inverse + subject-area: functions and inverses + arity: 1 + property: function* + en: inverse of $1 + comments: + - "`inverse` can be used for function inverses, matrix inverses, etc." + + - concept: inverse + subject-area: functions and inverses + arity: 1 + property: postfix + en: $1 inverse + + - concept: domain + subject-area: functions and inverses + arity: 1 + property: function + en: domain of $1 + fr: domaine de définition de $1 + + - concept: codomain + subject-area: functions and inverses + arity: 1 + property: function + en: codomain of $1 + fr: ensemble d'arrivée de $1 + + - concept: image + subject-area: functions and inverses + arity: 1 + property: function* + en: image of $1 + fr: image de $1 + + - concept: fraction + subject-area: functions and inverses + arity: 2 + property: function + en: fraction $1 over $2 end fraction + + - concept: mixed-fraction + subject-area: functions and inverses + arity: 2 + property: function + en: $1 and $2 + comments: + - "$1 is a positive integer and $2 is a fraction with positive numerical components. + The second argument can be an `mfrac` (normal or beveled) or can be a linear fraction using `/`" + + - concept: quotient + subject-area: functions and inverses + arity: 2 + property: function + en: integer part of $1 divided by $2 + fr: quotient de $1 par $2 + + - concept: evaluated-at + subject-area: functions and inverses + arity: 2 + property: infix + en: $1 evaluated-at $2 + comments: + - "Two common notations are + x2|3 + and + + - d - x2 + x2 + | - - ``` - - - - concept: partial-derivative - arity: ">=3" - property: ??? - en: - - "partial $1 partial $2 <$3 if $3 != 1> [partial $4 <$5 if $5 != 1> ...]" - comments: - - | + x=3 + + + " + - concept: remainder + subject-area: functions and inverses + arity: 2 + property: function + en: the remainder of $1 divided by $2 + fr: reste de la divsion de $1 par $2 + + - concept: max + subject-area: functions and inverses + arity: ">=1" + property: function + en: "max of $1, ..." + + - concept: min + subject-area: functions and inverses + arity: ">=1" + property: function + en: "min of $1, ..." + + - concept: power + subject-area: functions and inverses + arity: 2 + property: infix + conditions: + - condition: "$2=2" + en: "$1 squared" + fr: "$1 carré" + - condition: "$2=3" + en: "$1 cubed" + fr: "$1 cube" + - condition: "" + en: "$1 to the $2th power" + fr: "$1 à la $2" + + + - concept: root + subject-area: functions and inverses + arity: 2 + property: function + conditions: + - condition: "$2=2" + en: "square root of $1" + - condition: "$2=3" + en: "cube root of $1" + - condition: "$2=4" + en: "fourth root of $1" + - condition: "" + en: "$2th root of $1" + + - concept: greatest-common-divisor + subject-area: functions and inverses + arity: ">=2" + property: function + en: greatest common divisor of $1, $2, ... + fr: plus grand commun diviseur de $1, $2, ... + + - concept: least-common-multiple + subject-area: functions and inverses + arity: ">=2" + property: function + en: lest common multiple of $1, $2, ... + fr: plus grand commun diviseur de $1, $2, ... + + - concept: absolute-value + subject-area: functions and inverses + arity: 1 + property: function + en: absolute value of $1 + fr: valeur absolue de $1 + de: Betrag von $1 + + - concept: complex-conjugate + subject-area: functions and inverses + arity: 1 + property: function + en: complex conjugate of $1 + fr: $1 conjugé + + - concept: complex-arg + subject-area: functions and inverses + arity: 1 + property: function + en: arg of $1 + + - concept: real-part + subject-area: functions and inverses + arity: 1 + property: function + en: + - real part of $1 + - imaginary part of $1 + + - concept: imaginary-part + subject-area: functions and inverses + arity: 1 + property: function + en: imaginary part of $1 + + - concept: polar-coordinate + subject-area: functions and inverses + arity: 2 + property: function + en: "polar coordinate $1 comma $2" + comment: + - "The first argument is the radius, the second argument is the polar angle, the third arguments is the azimuthal angle." + - "Example: (r, θ)" + + - concept: spherical-coordinate + subject-area: functions and inverses + arity: 3 + property: function + en: "spherical coordinate $1 comma $2, comma $3" + comment: + - "The first argument is the radius, the second argument is the angle." + - "Example: (r,Φ,θ)" + + - concept: cartesian-coordinate + subject-area: functions and inverses + arity: ">=2" + property: function + en: "cartesian coordinate $1 comma $2 ..." + comment: + - "Example: (1,2)" + + - concept: coordinate + subject-area: functions and inverses + arity: ">=2" + property: function + en: "coordinate $1 comma $2 ..." + comment: + - "This a generic coordinate that doesn't specify the coordinate system. It takes 2 or more arguments." + - "Example: (1,2)" + + - concept: floor + subject-area: functions and inverses + arity: 1 + property: function + en: floor of $1 + + - concept: ceiling + subject-area: functions and inverses + arity: 1 + property: function + en: ceiling of $1 + + - concept: round + subject-area: functions and inverses + arity: 1 + property: function + en: rounded-value of $1 + comments: + - "This sometimes uses the notation + ⌊x⌉ + or + [x]" + + - concept: fractional-part + subject-area: functions and inverses + arity: 1 + property: function + en: fractional part of $1 + + ## ====================== 4.4.4 Calculus ============================ + - concept: definite-integral + subject-area: calculus + arity: 1 + property: ??? + en: "integral over $1" + comments: + - "integral sign is not an argument" + + - concept: definite-integral + subject-area: calculus + arity: 2 + property: ??? + en: "integral from $1 to $2" + comments: + - "integral sign is not an argument" + + + - concept: derivative + subject-area: calculus + arity: 3 + property: ??? + en: + - "(verbose) the $3 derivative of $1 with respect to $2" + - "(terse) d <$3 if $3 != 1> $1 by d $2 <$3 if $3 != 1>" + comments: + - "the terse reading only makes sense for Leibniz notation such as + d2ydx2 + or + d2dx2f(x). + It does not make sense for other notations such as + f''(x) + " + - "The first of these examples might be marked up as" + - | ``` - + - ∂3 - sin(x)y + d2 + y - ∂2 - x∂y + d + x2 ``` - - - concept: limit - arity: 1 - property: prefix - en: "limit as $1" - comments: - - "limit is not an argument, but intent should be on `msub` or `munder`" - - "There are several arrows used for limits. " - - "Example: - - lim - x↗0 - - - might be spoken as \"limit as x tends to from below 0\" and marked up as:" - - | - ``` - - lim - - x - ↗ - 0 - - - ``` - - "Another notation that might be spoken similarly is - limx→0- - " - - - concept: tends-to - arity: 2 - property: infix - en: "$1 tends to $2" - comments: - - "see \"limit\" example" - - - concept: tends-to-from-above - arity: 2 - property: infix - en: "$1 tends to from above $2" - comments: - - "see \"limit\" example" - - - concept: tends-to-from-below - arity: 2 - property: infix - en: "$1 tends to from below $2" - comments: - - "see \"limit\" example" - + + + - concept: partial-derivative + subject-area: calculus + arity: ">=3" + property: ??? + en: + - "partial $1 partial $2 <$3 if $3 != 1> [partial $4 <$5 if $5 != 1> ...]" + comments: + - | + ``` + + + ∂3 + sin(x)y + + + ∂2 + x∂y + + + ``` + + - concept: limit + subject-area: calculus + arity: 1 + property: prefix + en: "limit as $1" + comments: + - "limit is not an argument, but intent should be on `msub` or `munder`" + - "There are several arrows used for limits. " + - "Example: + + lim + x↗0 + + + might be spoken as \"limit as x tends to from below 0\" and marked up as:" + - | + ``` + + lim + + x + ↗ + 0 + + + ``` + - "Another notation that might be spoken similarly is + limx→0- + " + + - concept: tends-to + subject-area: calculus + arity: 2 + property: infix + en: "$1 tends to $2" + comments: + - "see \"limit\" example" + + - concept: tends-to-from-above + subject-area: calculus + arity: 2 + property: infix + en: "$1 tends to from above $2" + comments: + - "see \"limit\" example" + + - concept: tends-to-from-below + subject-area: calculus + arity: 2 + property: infix + en: "$1 tends to from below $2" + comments: + - "see \"limit\" example" + ## ====================== 4.4.5 Sets ============================ - - title: Sets - intents: - - concept: set - arity: 1 - property: function - en: "set of $1" - comments: - - | - the argument to `set` is typically an `mrow`. For example: - + - concept: set + subject-area: sets + arity: 1 + property: function + en: "set of $1" + comments: + - | + the argument to `set` is typically an `mrow`. For example: + + ``` + + + { + + 2 + , + 4 + , + 6 + , + 8 + + } + + + ``` + + - concept: set-difference + subject-area: sets + arity: 2 + property: function + en: "set difference of $1 and $2" + comments: + - "This can be spoken in many ways. See other entry for infix speech." + - "There are several notations that are used and their order of appearance differs: + A-B, A\\B" + + - concept: set-difference + subject-area: sets + arity: 2 + property: infix + en: "\"$1 minus $2\" or \"$2 subtracted from $1\"" + comments: + - "This can be spoken in many ways. See other entry for functional speech." + - "See functional form for some notational usages." + + - concept: complement + subject-area: sets + arity: 1 + property: function + en: "complement of $1" + comments: + - "This can be spoken in many ways. See other entry for functional speech." + - "Two notations used for complement are: + AC, A'" + + - concept: empty-set + subject-area: sets + arity: 0 + en: "empty set" + comments: + - "Three notations used for empty set are: { }, ∅, and ∅" + + + - concept: cardinality + subject-area: sets + arity: 1 + property: function + comments: + - "often used with matchfix single vertical bars" + + - concept: list + subject-area: sets + arity: ">=0" + en: "list of $1, ..." + + - concept: tuple + subject-area: sets + arity: ">=0" + en: "tuple of $1, ..." + + ## ====================== 4.4.6 sequence and series ============================ + - concept: sum + subject-area: sequences and series + arity: 1 + property: function + en: "sum of $1" + comments: + - usually on `` + + - concept: sum + subject-area: sequences and series + arity: 2 + property: function + en: "sum over $1 of $2" + comments: + - usually on `` or `` + + - concept: sum + subject-area: sequences and series + arity: 3 + property: function + en: "sum from $1 to $2 of $3" + comments: + - usually on `` or `` + + - concept: product + subject-area: sequences and series + arity: 1 + property: function + en: "product of $1" + comments: + - usually on `` + + - concept: product + subject-area: sequences and series + arity: 2 + property: function + en: "product over $1 of $2" + comments: + - usually on `` or `` + + - concept: product + subject-area: sequences and series + arity: 3 + property: function + en: "product from $1 to $2 of $3" + comments: + - usually on `` or `` + + + ## ====================== 4.4.7 elementary classical functions ====================== + - concept: sine + subject-area: elementary classical functions + arity: 1 + property: function + en: "sine $1" + fr: "sinus $1" + comments: + - used as 'sin', 'sen' + + - concept: cosine + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) cosine $1" + - "(terse) cos $1" + + - concept: tangent + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) tangent $1" + - "(terse) tan $1" + comments: + - used as 'tan', 'tg' + + - concept: secant + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) secant $1" + - "(terse) seech $1" + comments: + - used as 'sec' + + - concept: cosecant + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) cosecant $1" + - "(terse) co-seech $1" + comments: + - used as 'csc' + + - concept: cotangent + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) cotangent $1" + - "(terse) co-tan $1" + comments: + - used as 'cot' + + + ## inverse trig functions + - concept: arcsine + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) arcsine $1" + comments: + - "used as 'arcsin', 'arc sin'" + - "this is distinct from sin inverse (sin-1)" + + - concept: arccosine + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) arccosine $1" + comments: + - "used as 'arccos', 'arc cos'" + + - concept: arctangent + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) arctangent $1" + comments: + - "used as 'arctan', 'arc tan'" + + - concept: arcsecant + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) arcsecant $1" + comments: + - "used as 'arcsec', 'arc sec'" + + - concept: arccosecant + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) arc-cosecant $1" + comments: + - "used as 'arccos', 'arc cos'" + + - concept: arccotangent + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "(verbose) arc-cotangent $1" + comments: + - "used as 'arccos', 'arc cos'" + + ## hyperbolic trig functions + - concept: hyperbolic-sine + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "youtube" + - "used as 'sinh'" + en: + - "short form 'shine $1'" + fr: + - "sinus hyperbolique $1" + + + - concept: hyperbolic-cosine + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "youtube" + - "used as 'cosh'" + en: + - "short form 'cosh $1'" + fr: + - "cosh $1" + - "kosh $1" + + - concept: hyperbolic-tangent + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "youtube" + - "used as 'tanh'" + en: + - "short form American 'tanch $1'" + - "short form British 'than $1'" + + - concept: hyperbolic-secant + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "youtube" + - "used as 'sech'" + en: + - "short form American 'sech $1'" + - "short form British 'shek $1'" + + - concept: hyperbolic-cosecant + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "youtube" + - "used as 'cosech'" + en: + - "short form American 'cosech $1'" + - "short form British 'coshek $1'" + + + - concept: hyperbolic-cotangent + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "youtube" + - "used as 'coth'" + en: + - "short form American 'coth $1'" + - "short form British 'coath $1'" + + + + ## inverse hyperbolic trig functions + - concept: arc-hyperbolic-sine + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "used as 'asinh'" + en: + - "short form 'arc shine $1'" + fr: + - "sinus hyperbolique $1" + + + - concept: arc-hyperbolic-cosine + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "used as 'acosh'" + en: + - "short form 'arc cosh $1'" + fr: + - "cosh $1" + - "kosh $1" + + - concept: arc-hyperbolic-tangent + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "used as 'atanh'" + en: + - "short form American 'arc tanch $1'" + - "short form British 'arc than $1'" + + - concept: arc-hyperbolic-secant + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "used as 'asech'" + en: + - "short form American 'arc sech $1'" + - "short form British 'arc shek $1'" + + - concept: arc-hyperbolic-cosecant + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "used as 'acsch'" + en: + - "short form American 'arc cosech $1'" + - "short form British 'arc coshek $1'" + + + - concept: arc-hyperbolic-cotangent + subject-area: elementary classical functions + arity: 1 + property: function + comments: + - "used as 'acoth'" + en: + - "short form American 'arc coth $1'" + - "short form British 'arc coath $1'" + + + ## exponential related functions + - concept: exponential + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "exponential of $1" + + - concept: natural-logarithm + subject-area: elementary classical functions + arity: 1 + property: function + en: + - "natural log of $1" + - "log of $1" + + - concept: logarithm + subject-area: elementary classical functions + arity: 1 + property: function + en: "log of $1" + + - concept: logarithm + subject-area: elementary classical functions + arity: 2 + property: function + en: "log base $2 of $1" + + + + + ## ====================== 4.4.8 Statistics ====================== + - concept: mean + subject-area: Statistics and Probability + arity: 1 + property: function + en: "mean of $1" + comments: + - "This might be display as x¯" + + - concept: standard-deviation + subject-area: Statistics and Probability + arity: 1 + property: function + en: "standard deviation of $1" + + - concept: variance + subject-area: Statistics and Probability + arity: 1 + property: function + en: "variance of $1" + + - concept: median + subject-area: Statistics and Probability + arity: 1 + property: function + en: "median of $1" + + - concept: mode + subject-area: Statistics and Probability + arity: 1 + property: function + en: "mode of $1" + + + + - concept: conditional-probability + subject-area: Statistics and Probability + arity: 2 + property: function + en: "probability of $1 given $2" + comments: + - | + The intent should be on the `mrow` that includes the "P" + ``` - - { - - 2 - , - 4 - , - 6 - , - 8 + + P + ( + + A + | + B - } + ) ``` - - - concept: set-difference - arity: 2 - property: function - en: "set difference of $1 and $2" - comments: - - "This can be spoken in many ways. See other entry for infix speech." - - "There are several notations that are used and their order of appearance differs: - A-B, A\\B" - - - concept: set-difference - arity: 2 - property: infix - en: "\"$1 minus $2\" or \"$2 subtracted from $1\"" - comments: - - "This can be spoken in many ways. See other entry for functional speech." - - "See functional form for some notational usages." - - - concept: complement - arity: 1 - property: function - en: "complement of $1" - comments: - - "This can be spoken in many ways. See other entry for functional speech." - - "Two notations used for complement are: - AC, A'" - - - concept: empty-set - arity: 0 - en: "empty set" - comments: - - "Three notations used for empty set are: { }, ∅, and ∅" - - - - concept: cardinality - arity: 1 - property: function - comments: - - "often used with matchfix single vertical bars" - - - concept: list - arity: ">=0" - en: "list of $1, ..." - - - concept: tuple - arity: ">=0" - en: "tuple of $1, ..." - - ## ====================== 4.4.6 sequence and series ============================ - - title: sequence and series - intents: - - concept: sum - arity: 1 - property: function - en: "sum of $1" - comments: - - usually on `` - - - concept: sum - arity: 2 - property: function - en: "sum over $1 of $2" - comments: - - usually on `` or `` - - - concept: sum - arity: 3 - property: function - en: "sum from $1 to $2 of $3" - comments: - - usually on `` or `` - - - concept: product - arity: 1 - property: function - en: "product of $1" - comments: - - usually on `` - - - concept: product - arity: 2 - property: function - en: "product over $1 of $2" - comments: - - usually on `` or `` - - - concept: product - arity: 3 - property: function - en: "product from $1 to $2 of $3" - comments: - - usually on `` or `` - - - ## ====================== 4.4.7 elementary classical functions ====================== - - title: elementary classical functions - intents: - - concept: sine - arity: 1 - property: function - en: "sine $1" - fr: "sinus $1" - comments: - - used as 'sin', 'sen' - - - concept: cosine - arity: 1 - property: function - en: - - "(verbose) cosine $1" - - "(terse) cos $1" - - - concept: tangent - arity: 1 - property: function - en: - - "(verbose) tangent $1" - - "(terse) tan $1" - comments: - - used as 'tan', 'tg' - - - concept: secant - arity: 1 - property: function - en: - - "(verbose) secant $1" - - "(terse) seech $1" - comments: - - used as 'sec' - - - concept: cosecant - arity: 1 - property: function - en: - - "(verbose) cosecant $1" - - "(terse) co-seech $1" - comments: - - used as 'csc' - - - concept: cotangent - arity: 1 - property: function - en: - - "(verbose) cotangent $1" - - "(terse) co-tan $1" - comments: - - used as 'cot' - - - ## inverse trig functions - - concept: arcsine - arity: 1 - property: function - en: - - "(verbose) arcsine $1" - comments: - - "used as 'arcsin', 'arc sin'" - - "this is distinct from sin inverse (sin-1)" - - - concept: arccosine - arity: 1 - property: function - en: - - "(verbose) arccosine $1" - comments: - - "used as 'arccos', 'arc cos'" - - - concept: arctangent - arity: 1 - property: function - en: - - "(verbose) arctangent $1" - comments: - - "used as 'arctan', 'arc tan'" - - - concept: arcsecant - arity: 1 - property: function - en: - - "(verbose) arcsecant $1" - comments: - - "used as 'arcsec', 'arc sec'" - - - concept: arccosecant - arity: 1 - property: function - en: - - "(verbose) arc-cosecant $1" - comments: - - "used as 'arccos', 'arc cos'" - - - concept: arccotangent - arity: 1 - property: function - en: - - "(verbose) arc-cotangent $1" - comments: - - "used as 'arccos', 'arc cos'" - - ## hyperbolic trig functions - - concept: hyperbolic-sine - arity: 1 - property: function - comments: - - "youtube" - - "used as 'sinh'" - en: - - "short form 'shine $1'" - fr: - - "sinus hyperbolique $1" - - - - concept: hyperbolic-cosine - arity: 1 - property: function - comments: - - "youtube" - - "used as 'cosh'" - en: - - "short form 'cosh $1'" - fr: - - "cosh $1" - - "kosh $1" - - - concept: hyperbolic-tangent - arity: 1 - property: function - comments: - - "youtube" - - "used as 'tanh'" - en: - - "short form American 'tanch $1'" - - "short form British 'than $1'" - - - concept: hyperbolic-secant - arity: 1 - property: function - comments: - - "youtube" - - "used as 'sech'" - en: - - "short form American 'sech $1'" - - "short form British 'shek $1'" - - - concept: hyperbolic-cosecant - arity: 1 - property: function - comments: - - "youtube" - - "used as 'cosech'" - en: - - "short form American 'cosech $1'" - - "short form British 'coshek $1'" - - - - concept: hyperbolic-cotangent - arity: 1 - property: function - comments: - - "youtube" - - "used as 'coth'" - en: - - "short form American 'coth $1'" - - "short form British 'coath $1'" - - - - ## inverse hyperbolic trig functions - - concept: arc-hyperbolic-sine - arity: 1 - property: function - comments: - - "used as 'asinh'" - en: - - "short form 'arc shine $1'" - fr: - - "sinus hyperbolique $1" - - - - concept: arc-hyperbolic-cosine - arity: 1 - property: function - comments: - - "used as 'acosh'" - en: - - "short form 'arc cosh $1'" - fr: - - "cosh $1" - - "kosh $1" - - - concept: arc-hyperbolic-tangent - arity: 1 - property: function - comments: - - "used as 'atanh'" - en: - - "short form American 'arc tanch $1'" - - "short form British 'arc than $1'" - - - concept: arc-hyperbolic-secant - arity: 1 - property: function - comments: - - "used as 'asech'" - en: - - "short form American 'arc sech $1'" - - "short form British 'arc shek $1'" - - - concept: arc-hyperbolic-cosecant - arity: 1 - property: function - comments: - - "used as 'acsch'" - en: - - "short form American 'arc cosech $1'" - - "short form British 'arc coshek $1'" - - - - concept: arc-hyperbolic-cotangent - arity: 1 - property: function - comments: - - "used as 'acoth'" - en: - - "short form American 'arc coth $1'" - - "short form British 'arc coath $1'" - - - ## exponential related functions - - concept: exponential - arity: 1 - property: function - en: - - "exponential of $1" - - - concept: natural-logarithm - arity: 1 - property: function - en: - - "natural log of $1" - - "log of $1" - - - concept: logarithm - arity: 1 - property: function - en: "log of $1" - - - concept: logarithm - arity: 2 - property: function - en: "log base $2 of $1" - - - - - ## ====================== 4.4.8 Statistics ====================== - - title: Statistics and Probability - intents: - - concept: mean - arity: 1 - property: function - en: "mean of $1" - comments: - - "This might be display as x¯" - - - concept: standard-deviation - arity: 1 - property: function - en: "standard deviation of $1" - - - concept: variance - arity: 1 - property: function - en: "variance of $1" - - - concept: median - arity: 1 - property: function - en: "median of $1" - - - concept: mode - arity: 1 - property: function - en: "mode of $1" - - - - - concept: conditional-probability - arity: 2 - property: function - en: "probability of $1 given $2" - comments: - - | - The intent should be on the `mrow` that includes the "P" - - ``` - - - P - ( - - A - | - B - - ) - - - ``` - - ## ====================== 4.4.9 Linear Algebra ====================== - - title: Linear Algebra - intents: - - concept: vector - arity: 1 - property: function - - - concept: matrix - arity: 1 - property: function - comments: - - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly - - - concept: determinant - arity: 1 - property: function - comments: - - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly - - - concept: adjugate - arity: 1 - property: function - comments: - - "sometimes used when computing an inverse matrix" - - - concept: magnitude - arity: 1 - property: function - comments: - - "often used with matchfix single or double vertical bars" - - - concept: norm - arity: 1 - property: function - comments: - - "often used with matchfix double vertical bars" - - - concept: span - arity: 1 - property: function - comments: - - "often used with matchfix angle brackets" - - - concept: unit-vector - arity: 1 - property: prefix - comments: - - "Example: x^" - en: "unit vector x" - - - concept: identity-matrix - arity: 0 - comments: - - "This is typically represented as 'I' or bold-faced '𝐈'" - en: "identity matrix" - - - concept: transpose - arity: 1 - property: postfix - en: "$1 transpose" - fr: "$1 transposée" - - - concept: transpose - arity: 1 - property: function - default: false - en: "transpose of $1" - fr: "transposée de $1" - - - concept: dimensional-product - arity: ">=2" - property: infix - default: false - en: "$1 by $2 ..." - comments: - - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name. - A common use would be describe the size of a matrix. For example m×n." - - - ## ====================== 4.4.10 Constants and Sets ====================== - - title: Constants and Sets - intents: - - concept: set-of-integers - arity: 0 - en: - - "(verbose) set of all integers" - - "(terse) Z" - fr: "Z" - - - concept: set-of-reals - arity: 0 - en: - - "(verbose) set of all real numbers" - - "(terse) R" - - - concept: set-of-rationals - arity: 0 - en: - - "(verbose) set of all rational numbers" - - "(terse) R" - - - concept: set-of-natural-numbers - arity: 0 - en: - - "(verbose) set of all natural numbers" - - "(terse) N" - - - concept: set-of-complex-numbers - arity: 0 - en: - - "(verbose) set of all complex numbers" - - "(terse) C" - - - concept: set-of-primes - arity: 0 - en: - - "(verbose) set of all prime numbers" - - "(terse) P" - - - concept: exponential-e - arity: 0 - en: "e" - fr: "e" - - - concept: imaginary-i - arity: 0 - en: "i" - fr: "i" - - - concept: differential-d - arity: 0 - en: "d" - fr: "d" - - - concept: golden-ratio - arity: 0 - en: "golden ratio" - fr: "d" - comments: - - "Often denoted as φ" - - - + + ## ====================== 4.4.9 Linear Algebra ====================== + - concept: vector + subject-area: Linear Algebra + arity: 1 + property: function + + - concept: matrix + subject-area: Linear Algebra + arity: 1 + property: function + comments: + - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly + + - concept: determinant + subject-area: Linear Algebra + arity: 1 + property: function + comments: + - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly + + - concept: adjugate + subject-area: Linear Algebra + arity: 1 + property: function + comments: + - "sometimes used when computing an inverse matrix" + + - concept: magnitude + subject-area: Linear Algebra + arity: 1 + property: function + comments: + - "often used with matchfix single or double vertical bars" + + - concept: norm + subject-area: Linear Algebra + arity: 1 + property: function + comments: + - "often used with matchfix double vertical bars" + + - concept: span + subject-area: Linear Algebra + arity: 1 + property: function + comments: + - "often used with matchfix angle brackets" + + - concept: unit-vector + subject-area: Linear Algebra + arity: 1 + property: prefix + comments: + - "Example: x^" + en: "unit vector x" + + - concept: identity-matrix + subject-area: Linear Algebra + arity: 0 + comments: + - "This is typically represented as 'I' or bold-faced '𝐈'" + en: "identity matrix" + + - concept: transpose + subject-area: Linear Algebra + arity: 1 + property: postfix + en: "$1 transpose" + fr: "$1 transposée" + + - concept: transpose + subject-area: Linear Algebra + arity: 1 + property: function + default: false + en: "transpose of $1" + fr: "transposée de $1" + + - concept: dimensional-product + subject-area: Linear Algebra + arity: ">=2" + property: infix + default: false + en: "$1 by $2 ..." + comments: + - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name. + A common use would be describe the size of a matrix. For example m×n." + + + ## ====================== 4.4.10 Constants and Sets ====================== + - concept: set-of-integers + subject-area: Constants and Sets + arity: 0 + en: + - "(verbose) set of all integers" + - "(terse) Z" + fr: "Z" + + - concept: set-of-reals + subject-area: Constants and Sets + arity: 0 + en: + - "(verbose) set of all real numbers" + - "(terse) R" + + - concept: set-of-rationals + subject-area: Constants and Sets + arity: 0 + en: + - "(verbose) set of all rational numbers" + - "(terse) R" + + - concept: set-of-natural-numbers + subject-area: Constants and Sets + arity: 0 + en: + - "(verbose) set of all natural numbers" + - "(terse) N" + + - concept: set-of-complex-numbers + subject-area: Constants and Sets + arity: 0 + en: + - "(verbose) set of all complex numbers" + - "(terse) C" + + - concept: set-of-primes + subject-area: Constants and Sets + arity: 0 + en: + - "(verbose) set of all prime numbers" + - "(terse) P" + + - concept: exponential-e + subject-area: Constants and Sets + arity: 0 + en: "e" + fr: "e" + + - concept: imaginary-i + subject-area: Constants and Sets + arity: 0 + en: "i" + fr: "i" + + - concept: differential-d + subject-area: Constants and Sets + arity: 0 + en: "d" + fr: "d" + + - concept: golden-ratio + subject-area: Constants and Sets + arity: 0 + en: "golden ratio" + fr: "d" + comments: + - "Often denoted as φ" + + + ## other areas ======================================================= - - - title: Geometry - intents: - - concept: line-segment - arity: 2 - property: prefix - en: - - "line segment $1 $2" - comments: - - "Example: (`mover`): AB_" - - - concept: directed-line-segment - arity: 2 - property: prefix - en: - - "directed line segment $1 $2" - comments: - - "Example: (`mover`): AB→" - - - concept: line - arity: 2 - property: prefix - en: - - "line $1 $2" - comments: - - "Example: (`mover`): AB↔" - - - concept: ray - arity: 2 - property: prefix - en: - - "ray $1 $2" - comments: - - "Example: (`mover`): AB→" - - - concept: arc - arity: 2 - property: prefix - en: - - "arc $1 $2" - comments: - - "Example: (`mover`): AB⌒" - - - concept: length - arity: 1 - property: function - en: - - "length of $1" - comments: - - "It may be necessary to 'nest' the intent as shown here for the example: - - A - B - " - - "The markup for this is:" - - | - ``` - - A - B - - ``` - - - concept: area - arity: 1 - property: function - en: - - "area of $1" - comments: - - "There are many notations. Here's one: - [ABCD]" - - "The markup for this is:" - - | - ``` - - [ - - A - B - C - D - ] - + + - concept: line-segment + subject-area: Geometry + arity: 2 + property: prefix + en: + - "line segment $1 $2" + comments: + - "Example: (`mover`): AB_" + + - concept: directed-line-segment + subject-area: Geometry + arity: 2 + property: prefix + en: + - "directed line segment $1 $2" + comments: + - "Example: (`mover`): AB→" + + - concept: line + subject-area: Geometry + arity: 2 + property: prefix + en: + - "line $1 $2" + comments: + - "Example: (`mover`): AB↔" + + - concept: ray + subject-area: Geometry + arity: 2 + property: prefix + en: + - "ray $1 $2" + comments: + - "Example: (`mover`): AB→" + + - concept: arc + subject-area: Geometry + arity: 2 + property: prefix + en: + - "arc $1 $2" + comments: + - "Example: (`mover`): AB⌒" + + - concept: length + subject-area: Geometry + arity: 1 + property: function + en: + - "length of $1" + comments: + - "It may be necessary to 'nest' the intent as shown here for the example: + + A + B + " + - "The markup for this is:" + - | + ``` + + A + B + + ``` + + - concept: area + subject-area: Geometry + arity: 1 + property: function + en: + - "area of $1" + comments: + - "There are many notations. Here's one: + [ABCD]" + - "The markup for this is:" + - | + ``` + + [ + + A + B + C + D + ] - ``` - - "It may be necessary to 'nest' the intent as shown in the `length` intent" - - concept: point - arity: ">=1" - property: ??? - en: - - "point $1 [comma $2 ...]" - comment: - - "Example: (1,2,3)" - - - concept: volume - arity: 1 - property: function - en: - - "volume of $1" - comments: - - "See comments for `length` and `volume` for examples of how this might be marked up" - - - title: Fill in the blank - intents: - - concept: blank - arity: 0 - en: - - "blank" - comments: - - "blanks can be represented in many ways in MathML. Some examples:" - - "`__`" - - "`?`" - - "`□`" - - "``" - - "``
``
``" - - - title: Separators - intents: - - concept: time-separator - arity: 2 - property: infix - en: $1 $2 - comments: - - "separates hours and minutes and is typically silent" - - "Example: 2:31" - - - - title: General Concepts - intents: - - concept: fenced-group - arity: 1 - property: function - en: "fenced-group of $1" - comments: - - "this includes parens, brackets, and braces" - - - concept: ordered-pair - arity: 2 - property: function - en: "the pair $1 and $2" - - - concept: indexed-by - arity: 2 - property: infix - en: "$1 indexed by $2" - comments: - - "this is typically a subscript and might also be spoken as '$1 sub $2'" - - - concept: highlight - arity: 1 - property: postfix - en: "$1 highlighted" - comments: - - "this typically would be used inside of a larger expression and not on its own" - - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" - - - concept: least-common-denominator - arity: ">=2" - property: function - en: "least common denominator of $1, $2, ..." - - - concept: rate - arity: 2 - property: infix - en: "$1 per $2" - comments: - - "Typically used with units" - - "Used with `mfrac` or `/`" - - - concept: translation - arity: 2 - property: function - en: "translation by $1 comma $2" - comments: - - "Example: T(1,3)" - - - concept: constraint - arity: 2 - property: infix - en: "fraction 2 over x minus 1 with constraint x not equal to 1" - comments: - - "Example: 2x-1, x≠1" - - - concept: binomial-coefficient - arity: 2 - property: infix - en: "$1 choose $2" - comments: - - "There are many notations used for the binomial coefficient. Here are some of them: - - ( - - n - k - - ) - , - - - C - k - n - - , - - - C - k - - n - - " - - - concept: pochhammer - arity: 2 - property: function - en: "$2 permutation of $1" - comments: - - "There are many notations for this: some of them are - - Pkn - ,  - Pkn - ,  - Pkn - ,  - Pn,k - ,  - P(n,k) - ,  - nk - " - - "The first of these would be marked up as:" - - | - ``` - - P - k - n - - ``` - - - concept: permutation-cycle - arity: ">=2" - property: function - en: "permutation cycle of $1 $2 ..." - comments: - - "A common notation for a permutation cycle is ( - 132 - )" - - "This would be marked up as:" - - | - ``` - ( - - 1 - 3 - 2 - - ) - ``` - - - concept: embellished-name - arity: 2 - property: infix - en: "$1 with annotation $2" - comments: - - "used with `mover` or `munder`" - + + ``` + - "It may be necessary to 'nest' the intent as shown in the `length` intent" + - concept: point + subject-area: Geometry + arity: ">=1" + property: ??? + en: + - "point $1 [comma $2 ...]" + comment: + - "Example: (1,2,3)" + + - concept: volume + subject-area: Geometry + arity: 1 + property: function + en: + - "volume of $1" + comments: + - "See comments for `length` and `volume` for examples of how this might be marked up" + + - concept: blank + subject-area: Fill in the blank + arity: 0 + en: + - "blank" + comments: + - "blanks can be represented in many ways in MathML. Some examples:" + - "`__`" + - "`?`" + - "`□`" + - "``" + - "``
``
``" + + - concept: time-separator + subject-area: Separators + arity: 2 + property: infix + en: $1 $2 + comments: + - "separates hours and minutes and is typically silent" + - "Example: 2:31" + + + - concept: fenced-group + subject-area: General Concepts + arity: 1 + property: function + en: "fenced-group of $1" + comments: + - "this includes parens, brackets, and braces" + + - concept: ordered-pair + subject-area: General Concepts + arity: 2 + property: function + en: "the pair $1 and $2" + + - concept: indexed-by + subject-area: General Concepts + arity: 2 + property: infix + en: "$1 indexed by $2" + comments: + - "this is typically a subscript and might also be spoken as '$1 sub $2'" + + - concept: highlight + subject-area: General Concepts + arity: 1 + property: postfix + en: "$1 highlighted" + comments: + - "this typically would be used inside of a larger expression and not on its own" + - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" + + - concept: least-common-denominator + arity: ">=2" + property: function + en: "least common denominator of $1, $2, ..." + + - concept: rate + subject-area: General Concepts + arity: 2 + property: infix + en: "$1 per $2" + comments: + - "Typically used with units" + - "Used with `mfrac` or `/`" + + - concept: translation + subject-area: General Concepts + arity: 2 + property: function + en: "translation by $1 comma $2" + comments: + - "Example: T(1,3)" + + - concept: constraint + subject-area: General Concepts + arity: 2 + property: infix + en: "fraction 2 over x minus 1 with constraint x not equal to 1" + comments: + - "Example: 2x-1, x≠1" + + - concept: binomial-coefficient + subject-area: General Concepts + arity: 2 + property: infix + en: "$1 choose $2" + comments: + - "There are many notations used for the binomial coefficient. Here are some of them: + + ( + + n + k + + ) + , + + + C + k + n + + , + + + C + k + + n + + " + + - concept: pochhammer + subject-area: General Concepts + arity: 2 + property: function + en: "$2 permutation of $1" + comments: + - "There are many notations for this: some of them are + + Pkn + ,  + Pkn + ,  + Pkn + ,  + Pn,k + ,  + P(n,k) + ,  + nk + " + - "The first of these would be marked up as:" + - | + ``` + + P + k + n + + ``` + + - concept: permutation-cycle + subject-area: General Concepts + arity: ">=2" + property: function + en: "permutation cycle of $1 $2 ..." + comments: + - "A common notation for a permutation cycle is ( + 132 + )" + - "This would be marked up as:" + - | + ``` + ( + + 1 + 3 + 2 + + ) + ``` + + - concept: embellished-name + subject-area: General Concepts + arity: 2 + property: infix + en: "$1 with annotation $2" + comments: + - "used with `mover` or `munder`" - - title: Grouping - intents: - - concept: fenced-group - arity: 1 - property: function - en: "fenced-group of $1" - comments: - - "this includes parens, brackets, and braces" - - - concept: annotation - arity: 2 - property: function - en: "$1 which is $2" - comments: - - "used with `mover` or `munder`" - - "Example: H2O⏟water" - - - concept: braced-group - arity: 1 - property: function - en: "grouped $1 end-grouped" - comments: - - "used with `mover` or `munder`" - - "Example: 13-16⏟" - - - concept: repeating-decimal - arity: 1 - property: function - en: "repeating decimal $1" - comments: - - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits." - - "Example: 122=0.045_" - - "This right hand side of this might be might be marked up as:" - - | - ``` - 0.0 - - 45 - _ - - ``` - - "or using the elementary math elements in MathML full as" - - | - ``` - - - 0.045 - - ``` + + - concept: fenced-group + subject-area: Grouping + arity: 1 + property: function + en: "fenced-group of $1" + comments: + - "this includes parens, brackets, and braces" + + - concept: annotation + subject-area: Grouping + arity: 2 + property: function + en: "$1 which is $2" + comments: + - "used with `mover` or `munder`" + - "Example: H2O⏟water" + + - concept: braced-group + subject-area: Grouping + arity: 1 + property: function + en: "grouped $1 end-grouped" + comments: + - "used with `mover` or `munder`" + - "Example: 13-16⏟" + + - concept: repeating-decimal + subject-area: Grouping + arity: 1 + property: function + en: "repeating decimal $1" + comments: + - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits." + - "Example: 122=0.045_" + - "This right hand side of this might be might be marked up as:" + - | + ``` + 0.0 + + 45 + _ + + ``` + - "or using the elementary math elements in MathML full as" + - | + ``` + + + 0.045 + + ``` From ec0efd2e2be6513860e44481510c14533bb0ce7a Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 14:32:32 +0100 Subject: [PATCH 02/33] adjust loop --- intent-core-concepts/index.md | 7 ++----- 1 file changed, 2 insertions(+), 5 deletions(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index f2e2adc5..d51a3a56 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -165,9 +165,6 @@ if c.link

-{%- for section in site.data.core.concepts -%} - -### {{section.title}} @@ -182,7 +179,7 @@ if c.link -{%- for c in section.intents -%} +{%- for c in site.data.core.concepts -%} {%- assign clss = forloop.index| modulo:2 -%} {%- assign arityr = c.arity | replace: ">=", "⩾" -%} {%- assign arityu = c.arity | replace: ">=", "GEQ" -%} @@ -256,7 +253,7 @@ if c.link
-{%- endfor -%} + ### Key From 0bc516c1d5210106047f6b3613df6554d3ae3dbb Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 15:15:12 +0100 Subject: [PATCH 03/33] sorting --- _data/core.yml | 13 +++++++------ intent-core-concepts/index.md | 8 +++++++- 2 files changed, 14 insertions(+), 7 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index d2dc4478..17bbe603 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -213,12 +213,6 @@ defaultfixity: concepts: ## ================ 4.4.1 functions and inverses ==================== - - concept: closed-interval - subject-area: functions and inverses - arity: 2 - property: function - en: closed interval between $1 and $2 - fr: intervalle fermé entre $1 et $2 - concept: closed-open-interval subject-area: functions and inverses @@ -1579,3 +1573,10 @@ concepts: 0.045 ``` + + - concept: closed-interval + subject-area: functions and inverses + arity: 2 + property: function + en: closed interval between $1 and $2 + fr: intervalle fermé entre $1 et $2 diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index d51a3a56..fb9519fe 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -165,6 +165,8 @@ if c.link

+{% assign cpts = site.data.languages | sort "subject-area" %} +{% assign subjt = "" %} @@ -179,7 +181,11 @@ if c.link -{%- for c in site.data.core.concepts -%} +{%- for c in cpts -%} +{%- if c.subject-area != subjt -%} +{%- assign subjt = c.subject-area -%}} + +{%- endif -%} {%- assign clss = forloop.index| modulo:2 -%} {%- assign arityr = c.arity | replace: ">=", "⩾" -%} {%- assign arityu = c.arity | replace: ">=", "GEQ" -%} From 21dc39fce263e5597ff13de77641d7186411b133 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 15:17:59 +0100 Subject: [PATCH 04/33] colon liquid syntax --- intent-core-concepts/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index fb9519fe..39b1c3b9 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -165,7 +165,7 @@ if c.link

-{% assign cpts = site.data.languages | sort "subject-area" %} +{% assign cpts = site.data.languages | sort: "subject-area" %} {% assign subjt = "" %}
{{subjt}}
From 04d9a6491d88a5d252b16e96781966f275e8ef94 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 15:22:53 +0100 Subject: [PATCH 05/33] concepts list --- intent-core-concepts/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 39b1c3b9..307e3b51 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -165,7 +165,7 @@ if c.link

-{% assign cpts = site.data.languages | sort: "subject-area" %} +{% assign cpts = site.data.core.concepts | sort: "subject-area" %} {% assign subjt = "" %}
From c1f77d83008123f12ca7cbf77f968fc9a6eb4987 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 15:28:08 +0100 Subject: [PATCH 06/33] test 1 --- _data/core.yml | 1 + intent-core-concepts/index.md | 9 +++++++++ 2 files changed, 10 insertions(+) diff --git a/_data/core.yml b/_data/core.yml index 17bbe603..7cf7d72a 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -1401,6 +1401,7 @@ concepts: - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" - concept: least-common-denominator + subject-area: functions and inverses arity: ">=2" property: function en: "least common denominator of $1, $2, ..." diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 307e3b51..1cea947e 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -165,9 +165,18 @@ if c.link

+

AAA + {% assign cpts = site.data.core.concepts | sort: "subject-area" %} + +

+ +

BBB + {% assign subjt = "" %} +

+
From 9d003731293dac283031683f3697d5857f619683 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 15:31:38 +0100 Subject: [PATCH 07/33] test 2 --- intent-core-concepts/index.md | 11 +---------- 1 file changed, 1 insertion(+), 10 deletions(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 1cea947e..d0a585c4 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -165,18 +165,9 @@ if c.link

-

AAA - {% assign cpts = site.data.core.concepts | sort: "subject-area" %} - -

- -

BBB - {% assign subjt = "" %} -

-
@@ -192,7 +183,7 @@ if c.link {%- for c in cpts -%} {%- if c.subject-area != subjt -%} -{%- assign subjt = c.subject-area -%}} +{%- assign subjt = c.subject-area -%} {%- endif -%} {%- assign clss = forloop.index| modulo:2 -%} From 1b306fddead22e83da8bbab4406615952dc4cfce Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 17:03:27 +0100 Subject: [PATCH 08/33] don't sort for core --- _data/core.yml | 15 ++++++++------- intent-core-concepts/index.md | 5 +++++ 2 files changed, 13 insertions(+), 7 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index 7cf7d72a..84b78a24 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -235,7 +235,14 @@ concepts: en: open interval between $1 and $2 fr: intervalle ouvert - - concept: inverse + - concept: closed-interval + subject-area: functions and inverses + arity: 2 + property: function + en: closed interval between $1 and $2 + fr: intervalle fermé entre $1 et $2 + +- concept: inverse subject-area: functions and inverses arity: 1 property: function* @@ -1575,9 +1582,3 @@ concepts: ``` - - concept: closed-interval - subject-area: functions and inverses - arity: 2 - property: function - en: closed interval between $1 and $2 - fr: intervalle fermé entre $1 et $2 diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index d0a585c4..e41a9337 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -165,7 +165,12 @@ if c.link

+{% comment %} {% assign cpts = site.data.core.concepts | sort: "subject-area" %} +{% endcomment %% +{% assign cpts = site.data.core.concepts %} + + {% assign subjt = "" %}
{{subjt}}
From 97946f4425b8c9607c9f963689e9165ca3bf7cc2 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 17:11:00 +0100 Subject: [PATCH 09/33] align headings --- intent-core-concepts/index.md | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index e41a9337..23067d2c 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -34,6 +34,7 @@ tr:target >td:first-child {border-left:solid thick black} span.cb {margin-right: 2em; white-space:nowrap} .markdown-body table tr.row0, .markdown-body table th.row0 {background-color:#F6F8FA} .markdown-body table tr.row1 {background-color:#FEFFFE} +.markdown-body table tr.subj {background-color:beige;font-size:110%;text-align:left;} a.link {font-weight:500} a.self {color: black; font-weight:500} @@ -189,7 +190,7 @@ if c.link {%- for c in cpts -%} {%- if c.subject-area != subjt -%} {%- assign subjt = c.subject-area -%} - + {%- endif -%} {%- assign clss = forloop.index| modulo:2 -%} {%- assign arityr = c.arity | replace: ">=", "⩾" -%} From fb38f560c1cddeb0e5fe8e50cd3bf1729ab0a99a Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 17:13:21 +0100 Subject: [PATCH 10/33] restore indent --- _data/core.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/_data/core.yml b/_data/core.yml index 84b78a24..3cb9cba0 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -242,7 +242,7 @@ concepts: en: closed interval between $1 and $2 fr: intervalle fermé entre $1 et $2 -- concept: inverse + - concept: inverse subject-area: functions and inverses arity: 1 property: function* From 44b964a8bd0056cc092983ed8906785a4b8e282e Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 17:20:50 +0100 Subject: [PATCH 11/33] comment syntax --- intent-core-concepts/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 23067d2c..02424147 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -168,7 +168,7 @@ if c.link {% comment %} {% assign cpts = site.data.core.concepts | sort: "subject-area" %} -{% endcomment %% +{% endcomment %} {% assign cpts = site.data.core.concepts %} From 8dc525c0c6f6cbfc227cd3526e1ce191b693a85b Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 17:24:52 +0100 Subject: [PATCH 12/33] least common denominator --- _data/core.yml | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index 3cb9cba0..dcdeadf5 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -381,6 +381,12 @@ concepts: en: lest common multiple of $1, $2, ... fr: plus grand commun diviseur de $1, $2, ... + - concept: least-common-denominator + subject-area: functions and inverses + arity: ">=2" + property: function + en: "least common denominator of $1, $2, ..." + - concept: absolute-value subject-area: functions and inverses arity: 1 @@ -1407,11 +1413,6 @@ concepts: - "this typically would be used inside of a larger expression and not on its own" - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" - - concept: least-common-denominator - subject-area: functions and inverses - arity: ">=2" - property: function - en: "least common denominator of $1, $2, ..." - concept: rate subject-area: General Concepts From 76bde047f9ba9a542fc32489761bc75f464dee3f Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 17:41:16 +0100 Subject: [PATCH 13/33] arguments field --- _data/core.yml | 140 ++++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 139 insertions(+), 1 deletion(-) diff --git a/_data/core.yml b/_data/core.yml index dcdeadf5..9b786de9 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -1,7 +1,7 @@ ## Defaults: ### - property infix => arity 2 ### - property prefix => arity 1 -### - property suffix => arity 1((((( +### - property suffix => arity 1 ### - property set, number => arity 0 @@ -217,6 +217,7 @@ concepts: - concept: closed-open-interval subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: interval between $1 (included) and $2 fr: intervalle ouvert à droite entre $1 et $2 @@ -224,6 +225,7 @@ concepts: - concept: open-closed-interval subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: interval between $1 and $2, included fr: intervalle ouvert à gauche... @@ -231,6 +233,7 @@ concepts: - concept: open-interval subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: open interval between $1 and $2 fr: intervalle ouvert @@ -238,6 +241,7 @@ concepts: - concept: closed-interval subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: closed interval between $1 and $2 fr: intervalle fermé entre $1 et $2 @@ -245,6 +249,7 @@ concepts: - concept: inverse subject-area: functions and inverses arity: 1 + arguments: [a1] property: function* en: inverse of $1 comments: @@ -253,12 +258,14 @@ concepts: - concept: inverse subject-area: functions and inverses arity: 1 + arguments: [a1] property: postfix en: $1 inverse - concept: domain subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: domain of $1 fr: domaine de définition de $1 @@ -266,6 +273,7 @@ concepts: - concept: codomain subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: codomain of $1 fr: ensemble d'arrivée de $1 @@ -273,6 +281,7 @@ concepts: - concept: image subject-area: functions and inverses arity: 1 + arguments: [a1] property: function* en: image of $1 fr: image de $1 @@ -280,12 +289,14 @@ concepts: - concept: fraction subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: fraction $1 over $2 end fraction - concept: mixed-fraction subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: $1 and $2 comments: @@ -295,6 +306,7 @@ concepts: - concept: quotient subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: integer part of $1 divided by $2 fr: quotient de $1 par $2 @@ -302,6 +314,7 @@ concepts: - concept: evaluated-at subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: infix en: $1 evaluated-at $2 comments: @@ -321,6 +334,7 @@ concepts: - concept: remainder subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: the remainder of $1 divided by $2 fr: reste de la divsion de $1 par $2 @@ -328,18 +342,21 @@ concepts: - concept: max subject-area: functions and inverses arity: ">=1" + arguments: [a1,...] property: function en: "max of $1, ..." - concept: min subject-area: functions and inverses arity: ">=1" + arguments: [a1,...] property: function en: "min of $1, ..." - concept: power subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: infix conditions: - condition: "$2=2" @@ -356,6 +373,7 @@ concepts: - concept: root subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function conditions: - condition: "$2=2" @@ -370,6 +388,7 @@ concepts: - concept: greatest-common-divisor subject-area: functions and inverses arity: ">=2" + arguments: [a1,a2,...] property: function en: greatest common divisor of $1, $2, ... fr: plus grand commun diviseur de $1, $2, ... @@ -377,6 +396,7 @@ concepts: - concept: least-common-multiple subject-area: functions and inverses arity: ">=2" + arguments: [a1,a2,...] property: function en: lest common multiple of $1, $2, ... fr: plus grand commun diviseur de $1, $2, ... @@ -384,12 +404,14 @@ concepts: - concept: least-common-denominator subject-area: functions and inverses arity: ">=2" + arguments: [a1,a2,...] property: function en: "least common denominator of $1, $2, ..." - concept: absolute-value subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: absolute value of $1 fr: valeur absolue de $1 @@ -398,6 +420,7 @@ concepts: - concept: complex-conjugate subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: complex conjugate of $1 fr: $1 conjugé @@ -405,12 +428,14 @@ concepts: - concept: complex-arg subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: arg of $1 - concept: real-part subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: - real part of $1 @@ -419,12 +444,14 @@ concepts: - concept: imaginary-part subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: imaginary part of $1 - concept: polar-coordinate subject-area: functions and inverses arity: 2 + arguments: [a1,a2] property: function en: "polar coordinate $1 comma $2" comment: @@ -434,6 +461,7 @@ concepts: - concept: spherical-coordinate subject-area: functions and inverses arity: 3 + arguments: [a1,a2,a3] property: function en: "spherical coordinate $1 comma $2, comma $3" comment: @@ -443,6 +471,7 @@ concepts: - concept: cartesian-coordinate subject-area: functions and inverses arity: ">=2" + arguments: [a1,a2,...] property: function en: "cartesian coordinate $1 comma $2 ..." comment: @@ -451,6 +480,7 @@ concepts: - concept: coordinate subject-area: functions and inverses arity: ">=2" + arguments: [a1,a2,...] property: function en: "coordinate $1 comma $2 ..." comment: @@ -460,18 +490,21 @@ concepts: - concept: floor subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: floor of $1 - concept: ceiling subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: ceiling of $1 - concept: round subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: rounded-value of $1 comments: @@ -483,6 +516,7 @@ concepts: - concept: fractional-part subject-area: functions and inverses arity: 1 + arguments: [a1] property: function en: fractional part of $1 @@ -490,6 +524,7 @@ concepts: - concept: definite-integral subject-area: calculus arity: 1 + arguments: [a1] property: ??? en: "integral over $1" comments: @@ -498,6 +533,7 @@ concepts: - concept: definite-integral subject-area: calculus arity: 2 + arguments: [a1,a2] property: ??? en: "integral from $1 to $2" comments: @@ -507,6 +543,7 @@ concepts: - concept: derivative subject-area: calculus arity: 3 + arguments: [a1,a2,a3] property: ??? en: - "(verbose) the $3 derivative of $1 with respect to $2" @@ -538,6 +575,7 @@ concepts: - concept: partial-derivative subject-area: calculus arity: ">=3" + arguments: [a1,a2,a3,...] property: ??? en: - "partial $1 partial $2 <$3 if $3 != 1> [partial $4 <$5 if $5 != 1> ...]" @@ -559,6 +597,7 @@ concepts: - concept: limit subject-area: calculus arity: 1 + arguments: [a1] property: prefix en: "limit as $1" comments: @@ -589,6 +628,7 @@ concepts: - concept: tends-to subject-area: calculus arity: 2 + arguments: [a1,a2] property: infix en: "$1 tends to $2" comments: @@ -597,6 +637,7 @@ concepts: - concept: tends-to-from-above subject-area: calculus arity: 2 + arguments: [a1,a2] property: infix en: "$1 tends to from above $2" comments: @@ -605,6 +646,7 @@ concepts: - concept: tends-to-from-below subject-area: calculus arity: 2 + arguments: [a1,a2] property: infix en: "$1 tends to from below $2" comments: @@ -614,6 +656,7 @@ concepts: - concept: set subject-area: sets arity: 1 + arguments: [a1] property: function en: "set of $1" comments: @@ -641,6 +684,7 @@ concepts: - concept: set-difference subject-area: sets arity: 2 + arguments: [a1,a2] property: function en: "set difference of $1 and $2" comments: @@ -651,6 +695,7 @@ concepts: - concept: set-difference subject-area: sets arity: 2 + arguments: [a1,a2] property: infix en: "\"$1 minus $2\" or \"$2 subtracted from $1\"" comments: @@ -660,6 +705,7 @@ concepts: - concept: complement subject-area: sets arity: 1 + arguments: [a1] property: function en: "complement of $1" comments: @@ -670,6 +716,7 @@ concepts: - concept: empty-set subject-area: sets arity: 0 + arguments: [] en: "empty set" comments: - "Three notations used for empty set are: { }, ∅, and ∅" @@ -678,6 +725,7 @@ concepts: - concept: cardinality subject-area: sets arity: 1 + arguments: [a1] property: function comments: - "often used with matchfix single vertical bars" @@ -685,17 +733,20 @@ concepts: - concept: list subject-area: sets arity: ">=0" + arguments: [a1,...] en: "list of $1, ..." - concept: tuple subject-area: sets arity: ">=0" + arguments: [a1,...] en: "tuple of $1, ..." ## ====================== 4.4.6 sequence and series ============================ - concept: sum subject-area: sequences and series arity: 1 + arguments: [a1] property: function en: "sum of $1" comments: @@ -704,6 +755,7 @@ concepts: - concept: sum subject-area: sequences and series arity: 2 + arguments: [a1,a2] property: function en: "sum over $1 of $2" comments: @@ -712,6 +764,7 @@ concepts: - concept: sum subject-area: sequences and series arity: 3 + arguments: [a1,a2,a3] property: function en: "sum from $1 to $2 of $3" comments: @@ -720,6 +773,7 @@ concepts: - concept: product subject-area: sequences and series arity: 1 + arguments: [a1] property: function en: "product of $1" comments: @@ -728,6 +782,7 @@ concepts: - concept: product subject-area: sequences and series arity: 2 + arguments: [a1,a2] property: function en: "product over $1 of $2" comments: @@ -736,6 +791,7 @@ concepts: - concept: product subject-area: sequences and series arity: 3 + arguments: [a1,a2,a3] property: function en: "product from $1 to $2 of $3" comments: @@ -746,6 +802,7 @@ concepts: - concept: sine subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: "sine $1" fr: "sinus $1" @@ -755,6 +812,7 @@ concepts: - concept: cosine subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) cosine $1" @@ -763,6 +821,7 @@ concepts: - concept: tangent subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) tangent $1" @@ -773,6 +832,7 @@ concepts: - concept: secant subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) secant $1" @@ -783,6 +843,7 @@ concepts: - concept: cosecant subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) cosecant $1" @@ -793,6 +854,7 @@ concepts: - concept: cotangent subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) cotangent $1" @@ -805,6 +867,7 @@ concepts: - concept: arcsine subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) arcsine $1" @@ -815,6 +878,7 @@ concepts: - concept: arccosine subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) arccosine $1" @@ -824,6 +888,7 @@ concepts: - concept: arctangent subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) arctangent $1" @@ -833,6 +898,7 @@ concepts: - concept: arcsecant subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) arcsecant $1" @@ -842,6 +908,7 @@ concepts: - concept: arccosecant subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) arc-cosecant $1" @@ -851,6 +918,7 @@ concepts: - concept: arccotangent subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "(verbose) arc-cotangent $1" @@ -861,6 +929,7 @@ concepts: - concept: hyperbolic-sine subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "youtube" @@ -874,6 +943,7 @@ concepts: - concept: hyperbolic-cosine subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "youtube" @@ -887,6 +957,7 @@ concepts: - concept: hyperbolic-tangent subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "youtube" @@ -898,6 +969,7 @@ concepts: - concept: hyperbolic-secant subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "youtube" @@ -909,6 +981,7 @@ concepts: - concept: hyperbolic-cosecant subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "youtube" @@ -921,6 +994,7 @@ concepts: - concept: hyperbolic-cotangent subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "youtube" @@ -935,6 +1009,7 @@ concepts: - concept: arc-hyperbolic-sine subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "used as 'asinh'" @@ -947,6 +1022,7 @@ concepts: - concept: arc-hyperbolic-cosine subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "used as 'acosh'" @@ -959,6 +1035,7 @@ concepts: - concept: arc-hyperbolic-tangent subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "used as 'atanh'" @@ -969,6 +1046,7 @@ concepts: - concept: arc-hyperbolic-secant subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "used as 'asech'" @@ -979,6 +1057,7 @@ concepts: - concept: arc-hyperbolic-cosecant subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "used as 'acsch'" @@ -990,6 +1069,7 @@ concepts: - concept: arc-hyperbolic-cotangent subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function comments: - "used as 'acoth'" @@ -1002,6 +1082,7 @@ concepts: - concept: exponential subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "exponential of $1" @@ -1009,6 +1090,7 @@ concepts: - concept: natural-logarithm subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: - "natural log of $1" @@ -1017,12 +1099,14 @@ concepts: - concept: logarithm subject-area: elementary classical functions arity: 1 + arguments: [a1] property: function en: "log of $1" - concept: logarithm subject-area: elementary classical functions arity: 2 + arguments: [a1,a2] property: function en: "log base $2 of $1" @@ -1033,6 +1117,7 @@ concepts: - concept: mean subject-area: Statistics and Probability arity: 1 + arguments: [a1] property: function en: "mean of $1" comments: @@ -1041,24 +1126,28 @@ concepts: - concept: standard-deviation subject-area: Statistics and Probability arity: 1 + arguments: [a1] property: function en: "standard deviation of $1" - concept: variance subject-area: Statistics and Probability arity: 1 + arguments: [a1] property: function en: "variance of $1" - concept: median subject-area: Statistics and Probability arity: 1 + arguments: [a1] property: function en: "median of $1" - concept: mode subject-area: Statistics and Probability arity: 1 + arguments: [a1] property: function en: "mode of $1" @@ -1067,6 +1156,7 @@ concepts: - concept: conditional-probability subject-area: Statistics and Probability arity: 2 + arguments: [a1,a2] property: function en: "probability of $1 given $2" comments: @@ -1092,11 +1182,13 @@ concepts: - concept: vector subject-area: Linear Algebra arity: 1 + arguments: [a1] property: function - concept: matrix subject-area: Linear Algebra arity: 1 + arguments: [a1] property: function comments: - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly @@ -1104,6 +1196,7 @@ concepts: - concept: determinant subject-area: Linear Algebra arity: 1 + arguments: [a1] property: function comments: - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly @@ -1111,6 +1204,7 @@ concepts: - concept: adjugate subject-area: Linear Algebra arity: 1 + arguments: [a1] property: function comments: - "sometimes used when computing an inverse matrix" @@ -1118,6 +1212,7 @@ concepts: - concept: magnitude subject-area: Linear Algebra arity: 1 + arguments: [a1] property: function comments: - "often used with matchfix single or double vertical bars" @@ -1125,6 +1220,7 @@ concepts: - concept: norm subject-area: Linear Algebra arity: 1 + arguments: [a1] property: function comments: - "often used with matchfix double vertical bars" @@ -1132,6 +1228,7 @@ concepts: - concept: span subject-area: Linear Algebra arity: 1 + arguments: [a1] property: function comments: - "often used with matchfix angle brackets" @@ -1139,6 +1236,7 @@ concepts: - concept: unit-vector subject-area: Linear Algebra arity: 1 + arguments: [a1] property: prefix comments: - "Example: x^" @@ -1147,6 +1245,7 @@ concepts: - concept: identity-matrix subject-area: Linear Algebra arity: 0 + arguments: [] comments: - "This is typically represented as 'I' or bold-faced '𝐈'" en: "identity matrix" @@ -1154,6 +1253,7 @@ concepts: - concept: transpose subject-area: Linear Algebra arity: 1 + arguments: [a1] property: postfix en: "$1 transpose" fr: "$1 transposée" @@ -1161,6 +1261,7 @@ concepts: - concept: transpose subject-area: Linear Algebra arity: 1 + arguments: [a1] property: function default: false en: "transpose of $1" @@ -1169,6 +1270,7 @@ concepts: - concept: dimensional-product subject-area: Linear Algebra arity: ">=2" + arguments: [a1,a2,...] property: infix default: false en: "$1 by $2 ..." @@ -1181,6 +1283,7 @@ concepts: - concept: set-of-integers subject-area: Constants and Sets arity: 0 + arguments: [] en: - "(verbose) set of all integers" - "(terse) Z" @@ -1189,6 +1292,7 @@ concepts: - concept: set-of-reals subject-area: Constants and Sets arity: 0 + arguments: [] en: - "(verbose) set of all real numbers" - "(terse) R" @@ -1196,6 +1300,7 @@ concepts: - concept: set-of-rationals subject-area: Constants and Sets arity: 0 + arguments: [] en: - "(verbose) set of all rational numbers" - "(terse) R" @@ -1203,6 +1308,7 @@ concepts: - concept: set-of-natural-numbers subject-area: Constants and Sets arity: 0 + arguments: [] en: - "(verbose) set of all natural numbers" - "(terse) N" @@ -1210,6 +1316,7 @@ concepts: - concept: set-of-complex-numbers subject-area: Constants and Sets arity: 0 + arguments: [] en: - "(verbose) set of all complex numbers" - "(terse) C" @@ -1217,6 +1324,7 @@ concepts: - concept: set-of-primes subject-area: Constants and Sets arity: 0 + arguments: [] en: - "(verbose) set of all prime numbers" - "(terse) P" @@ -1224,24 +1332,28 @@ concepts: - concept: exponential-e subject-area: Constants and Sets arity: 0 + arguments: [] en: "e" fr: "e" - concept: imaginary-i subject-area: Constants and Sets arity: 0 + arguments: [] en: "i" fr: "i" - concept: differential-d subject-area: Constants and Sets arity: 0 + arguments: [] en: "d" fr: "d" - concept: golden-ratio subject-area: Constants and Sets arity: 0 + arguments: [] en: "golden ratio" fr: "d" comments: @@ -1254,6 +1366,7 @@ concepts: - concept: line-segment subject-area: Geometry arity: 2 + arguments: [a1,a2] property: prefix en: - "line segment $1 $2" @@ -1263,6 +1376,7 @@ concepts: - concept: directed-line-segment subject-area: Geometry arity: 2 + arguments: [a1,a2] property: prefix en: - "directed line segment $1 $2" @@ -1272,6 +1386,7 @@ concepts: - concept: line subject-area: Geometry arity: 2 + arguments: [a1,a2] property: prefix en: - "line $1 $2" @@ -1281,6 +1396,7 @@ concepts: - concept: ray subject-area: Geometry arity: 2 + arguments: [a1,a2] property: prefix en: - "ray $1 $2" @@ -1290,6 +1406,7 @@ concepts: - concept: arc subject-area: Geometry arity: 2 + arguments: [a1,a2] property: prefix en: - "arc $1 $2" @@ -1299,6 +1416,7 @@ concepts: - concept: length subject-area: Geometry arity: 1 + arguments: [a1] property: function en: - "length of $1" @@ -1320,6 +1438,7 @@ concepts: - concept: area subject-area: Geometry arity: 1 + arguments: [a1] property: function en: - "area of $1" @@ -1344,6 +1463,7 @@ concepts: - concept: point subject-area: Geometry arity: ">=1" + arguments: [a1,...] property: ??? en: - "point $1 [comma $2 ...]" @@ -1353,6 +1473,7 @@ concepts: - concept: volume subject-area: Geometry arity: 1 + arguments: [a1] property: function en: - "volume of $1" @@ -1362,6 +1483,7 @@ concepts: - concept: blank subject-area: Fill in the blank arity: 0 + arguments: [] en: - "blank" comments: @@ -1375,6 +1497,7 @@ concepts: - concept: time-separator subject-area: Separators arity: 2 + arguments: [a1,a2] property: infix en: $1 $2 comments: @@ -1385,6 +1508,7 @@ concepts: - concept: fenced-group subject-area: General Concepts arity: 1 + arguments: [a1] property: function en: "fenced-group of $1" comments: @@ -1393,12 +1517,14 @@ concepts: - concept: ordered-pair subject-area: General Concepts arity: 2 + arguments: [a1,a2] property: function en: "the pair $1 and $2" - concept: indexed-by subject-area: General Concepts arity: 2 + arguments: [a1,a2] property: infix en: "$1 indexed by $2" comments: @@ -1407,6 +1533,7 @@ concepts: - concept: highlight subject-area: General Concepts arity: 1 + arguments: [a1] property: postfix en: "$1 highlighted" comments: @@ -1417,6 +1544,7 @@ concepts: - concept: rate subject-area: General Concepts arity: 2 + arguments: [a1,a2] property: infix en: "$1 per $2" comments: @@ -1426,6 +1554,7 @@ concepts: - concept: translation subject-area: General Concepts arity: 2 + arguments: [a1,a2] property: function en: "translation by $1 comma $2" comments: @@ -1434,6 +1563,7 @@ concepts: - concept: constraint subject-area: General Concepts arity: 2 + arguments: [a1,a2] property: infix en: "fraction 2 over x minus 1 with constraint x not equal to 1" comments: @@ -1442,6 +1572,7 @@ concepts: - concept: binomial-coefficient subject-area: General Concepts arity: 2 + arguments: [a1,a2] property: infix en: "$1 choose $2" comments: @@ -1473,6 +1604,7 @@ concepts: - concept: pochhammer subject-area: General Concepts arity: 2 + arguments: [a1,a2] property: function en: "$2 permutation of $1" comments: @@ -1503,6 +1635,7 @@ concepts: - concept: permutation-cycle subject-area: General Concepts arity: ">=2" + arguments: [a1,a2,...] property: function en: "permutation cycle of $1 $2 ..." comments: @@ -1525,6 +1658,7 @@ concepts: - concept: embellished-name subject-area: General Concepts arity: 2 + arguments: [a1,a2] property: infix en: "$1 with annotation $2" comments: @@ -1534,6 +1668,7 @@ concepts: - concept: fenced-group subject-area: Grouping arity: 1 + arguments: [a1] property: function en: "fenced-group of $1" comments: @@ -1542,6 +1677,7 @@ concepts: - concept: annotation subject-area: Grouping arity: 2 + arguments: [a1,a2] property: function en: "$1 which is $2" comments: @@ -1551,6 +1687,7 @@ concepts: - concept: braced-group subject-area: Grouping arity: 1 + arguments: [a1] property: function en: "grouped $1 end-grouped" comments: @@ -1560,6 +1697,7 @@ concepts: - concept: repeating-decimal subject-area: Grouping arity: 1 + arguments: [a1] property: function en: "repeating decimal $1" comments: From dc43d32f5d05d5fbf527c6cc68ca8c01ec0ec177 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 18:50:28 +0100 Subject: [PATCH 14/33] show arguments --- intent-core-concepts/index.md | 10 +++++++++- 1 file changed, 9 insertions(+), 1 deletion(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 02424147..18e848c2 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -233,7 +233,15 @@ if c.link {%- else -%} - + {%- for language in site.data.languages -%} {%- for language in site.data.languages -%} + {%- endif -%} {%- assign clss = forloop.index| modulo:2 -%} {%- assign arityr = c.arity | replace: ">=", "⩾" -%} From 46f927134596f83dfc42455dd696fa4ed222e71a Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 14:12:10 +0100 Subject: [PATCH 23/33] open index 3 --- intent-open-concepts/index.md | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/intent-open-concepts/index.md b/intent-open-concepts/index.md index aec05517..d7854899 100644 --- a/intent-open-concepts/index.md +++ b/intent-open-concepts/index.md @@ -165,8 +165,8 @@ Additional contributions are welcome: {%- for language in site.data.languages -%} {%- for language in site.data.languages -%} {%- if forloop.first -%}{%- endif -%} -{%- if forloop.first -%}{%- endif -%} +{%- if forloop.first -%}{%- endif -%} {%- if forloop.first -%}{%- endif -%} {%- for language in site.data.languages -%} {%- if forloop.first -%}{%- endif -%} {%- if forloop.first -%}{%- endif -%} +]{%- endif -%} {%- if forloop.first -%}{%- endif -%} {%- for language in site.data.languages -%} {%- for language in site.data.languages -%} From 1f03ff53c0355c86fefdbeb81ccfcc230dac446e Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Mon, 31 Aug 2026 20:40:37 +0100 Subject: [PATCH 32/33] show argument list in open --- intent-open-concepts/index.md | 17 +++++++++++++++-- 1 file changed, 15 insertions(+), 2 deletions(-) diff --git a/intent-open-concepts/index.md b/intent-open-concepts/index.md index d7854899..1605bd63 100644 --- a/intent-open-concepts/index.md +++ b/intent-open-concepts/index.md @@ -32,6 +32,7 @@ title: Open Concept List p.langs {margin:1em; padding:1em;background-color: #EEE} tr:target >td:first-child {border-left:solid thick black} span.cb {margin-right: 2em; white-space:nowrap} +span.nw {white-space:nowrap} .markdown-body table {font-size:85%} .markdown-body table tr.row0, .markdown-body table th.row0 {background-color:#F6F8FA} .markdown-body table tr.row1 {background-color:#FEFFFE} @@ -160,7 +161,13 @@ Additional contributions are welcome: {%- for cond in c.conditions -%} {%- if forloop.first -%}{%- endif -%} -{%- if forloop.first -%}{%- endif -%} +{%- if forloop.first -%}{%- endif -%} {%- if forloop.first -%}{%- endif -%} {%- for language in site.data.languages -%} - + {%- for language in site.data.languages -%}
{{subjt}}
{{subjt}}
{{c.concept}}{{arityr}} +{{arityr}}
+[ +{%- for arg in c.arguments -% +{{arg}} +{%- unless forloop.last -%},{% endunless -%} +{%- endfor -%} +] +		 {{c.property}}{%- unless c.default == false or c.arity == 0-%}*{%- endunless -%} From 9994a990685a1fa3aac3a33322bd4f44319fc8d9 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 18:51:47 +0100 Subject: [PATCH 15/33] show arguments --- intent-core-concepts/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 18e848c2..b6d336b9 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -236,7 +236,7 @@ if c.link {{arityr}}
[ -{%- for arg in c.arguments -% +{%- for arg in c.arguments -%} {{arg}} {%- unless forloop.last -%},{% endunless -%} {%- endfor -%} From 444e43a472a272f8e473cd753392d0bec14d33f2 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 18:59:29 +0100 Subject: [PATCH 16/33] replace $ by a --- _data/core.yml | 334 +++++++++++++++++----------------- intent-core-concepts/index.md | 2 +- 2 files changed, 168 insertions(+), 168 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index 9b786de9..fc1bbbf6 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -219,15 +219,15 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: interval between $1 (included) and $2 - fr: intervalle ouvert à droite entre $1 et $2 + en: interval between a1 (included) and a2 + fr: intervalle ouvert à droite entre a1 et a2 - concept: open-closed-interval subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: interval between $1 and $2, included + en: interval between a1 and a2, included fr: intervalle ouvert à gauche... - concept: open-interval @@ -235,7 +235,7 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: open interval between $1 and $2 + en: open interval between a1 and a2 fr: intervalle ouvert - concept: closed-interval @@ -243,15 +243,15 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: closed interval between $1 and $2 - fr: intervalle fermé entre $1 et $2 + en: closed interval between a1 and a2 + fr: intervalle fermé entre a1 et a2 - concept: inverse subject-area: functions and inverses arity: 1 arguments: [a1] property: function* - en: inverse of $1 + en: inverse of a1 comments: - "`inverse` can be used for function inverses, matrix inverses, etc." @@ -260,47 +260,47 @@ concepts: arity: 1 arguments: [a1] property: postfix - en: $1 inverse + en: a1 inverse - concept: domain subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: domain of $1 - fr: domaine de définition de $1 + en: domain of a1 + fr: domaine de définition de a1 - concept: codomain subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: codomain of $1 - fr: ensemble d'arrivée de $1 + en: codomain of a1 + fr: ensemble d'arrivée de a1 - concept: image subject-area: functions and inverses arity: 1 arguments: [a1] property: function* - en: image of $1 - fr: image de $1 + en: image of a1 + fr: image de a1 - concept: fraction subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: fraction $1 over $2 end fraction + en: fraction a1 over a2 end fraction - concept: mixed-fraction subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: $1 and $2 + en: a1 and a2 comments: - - "$1 is a positive integer and $2 is a fraction with positive numerical components. + - "a1 is a positive integer and a2 is a fraction with positive numerical components. The second argument can be an `mfrac` (normal or beveled) or can be a linear fraction using `/`" - concept: quotient @@ -308,15 +308,15 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: integer part of $1 divided by $2 - fr: quotient de $1 par $2 + en: integer part of a1 divided by a2 + fr: quotient de a1 par a2 - concept: evaluated-at subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: infix - en: $1 evaluated-at $2 + en: a1 evaluated-at a2 comments: - "Two common notations are x2|3 @@ -336,22 +336,22 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: the remainder of $1 divided by $2 - fr: reste de la divsion de $1 par $2 + en: the remainder of a1 divided by a2 + fr: reste de la divsion de a1 par a2 - concept: max subject-area: functions and inverses arity: ">=1" arguments: [a1,...] property: function - en: "max of $1, ..." + en: "max of a1, ..." - concept: min subject-area: functions and inverses arity: ">=1" arguments: [a1,...] property: function - en: "min of $1, ..." + en: "min of a1, ..." - concept: power subject-area: functions and inverses @@ -359,15 +359,15 @@ concepts: arguments: [a1,a2] property: infix conditions: - - condition: "$2=2" - en: "$1 squared" - fr: "$1 carré" - - condition: "$2=3" - en: "$1 cubed" - fr: "$1 cube" + - condition: "a2=2" + en: "a1 squared" + fr: "a1 carré" + - condition: "a2=3" + en: "a1 cubed" + fr: "a1 cube" - condition: "" - en: "$1 to the $2th power" - fr: "$1 à la $2" + en: "a1 to the a2th power" + fr: "a1 à la a2" - concept: root @@ -376,61 +376,61 @@ concepts: arguments: [a1,a2] property: function conditions: - - condition: "$2=2" - en: "square root of $1" - - condition: "$2=3" - en: "cube root of $1" - - condition: "$2=4" - en: "fourth root of $1" + - condition: "a2=2" + en: "square root of a1" + - condition: "a2=3" + en: "cube root of a1" + - condition: "a2=4" + en: "fourth root of a1" - condition: "" - en: "$2th root of $1" + en: "a2th root of a1" - concept: greatest-common-divisor subject-area: functions and inverses arity: ">=2" arguments: [a1,a2,...] property: function - en: greatest common divisor of $1, $2, ... - fr: plus grand commun diviseur de $1, $2, ... + en: greatest common divisor of a1, a2, ... + fr: plus grand commun diviseur de a1, a2, ... - concept: least-common-multiple subject-area: functions and inverses arity: ">=2" arguments: [a1,a2,...] property: function - en: lest common multiple of $1, $2, ... - fr: plus grand commun diviseur de $1, $2, ... + en: lest common multiple of a1, a2, ... + fr: plus grand commun diviseur de a1, a2, ... - concept: least-common-denominator subject-area: functions and inverses arity: ">=2" arguments: [a1,a2,...] property: function - en: "least common denominator of $1, $2, ..." + en: "least common denominator of a1, a2, ..." - concept: absolute-value subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: absolute value of $1 - fr: valeur absolue de $1 - de: Betrag von $1 + en: absolute value of a1 + fr: valeur absolue de a1 + de: Betrag von a1 - concept: complex-conjugate subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: complex conjugate of $1 - fr: $1 conjugé + en: complex conjugate of a1 + fr: a1 conjugé - concept: complex-arg subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: arg of $1 + en: arg of a1 - concept: real-part subject-area: functions and inverses @@ -438,22 +438,22 @@ concepts: arguments: [a1] property: function en: - - real part of $1 - - imaginary part of $1 + - real part of a1 + - imaginary part of a1 - concept: imaginary-part subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: imaginary part of $1 + en: imaginary part of a1 - concept: polar-coordinate subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: "polar coordinate $1 comma $2" + en: "polar coordinate a1 comma a2" comment: - "The first argument is the radius, the second argument is the polar angle, the third arguments is the azimuthal angle." - "Example: (r, θ)" @@ -463,7 +463,7 @@ concepts: arity: 3 arguments: [a1,a2,a3] property: function - en: "spherical coordinate $1 comma $2, comma $3" + en: "spherical coordinate a1 comma a2, comma a3" comment: - "The first argument is the radius, the second argument is the angle." - "Example: (r,Φ,θ)" @@ -473,7 +473,7 @@ concepts: arity: ">=2" arguments: [a1,a2,...] property: function - en: "cartesian coordinate $1 comma $2 ..." + en: "cartesian coordinate a1 comma a2 ..." comment: - "Example: (1,2)" @@ -482,7 +482,7 @@ concepts: arity: ">=2" arguments: [a1,a2,...] property: function - en: "coordinate $1 comma $2 ..." + en: "coordinate a1 comma a2 ..." comment: - "This a generic coordinate that doesn't specify the coordinate system. It takes 2 or more arguments." - "Example: (1,2)" @@ -492,21 +492,21 @@ concepts: arity: 1 arguments: [a1] property: function - en: floor of $1 + en: floor of a1 - concept: ceiling subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: ceiling of $1 + en: ceiling of a1 - concept: round subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: rounded-value of $1 + en: rounded-value of a1 comments: - "This sometimes uses the notation ⌊x⌉ @@ -518,7 +518,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: fractional part of $1 + en: fractional part of a1 ## ====================== 4.4.4 Calculus ============================ - concept: definite-integral @@ -526,7 +526,7 @@ concepts: arity: 1 arguments: [a1] property: ??? - en: "integral over $1" + en: "integral over a1" comments: - "integral sign is not an argument" @@ -535,7 +535,7 @@ concepts: arity: 2 arguments: [a1,a2] property: ??? - en: "integral from $1 to $2" + en: "integral from a1 to a2" comments: - "integral sign is not an argument" @@ -546,8 +546,8 @@ concepts: arguments: [a1,a2,a3] property: ??? en: - - "(verbose) the $3 derivative of $1 with respect to $2" - - "(terse) d <$3 if $3 != 1> $1 by d $2 <$3 if $3 != 1>" + - "(verbose) the a3 derivative of a1 with respect to a2" + - "(terse) d a1 by d a2 " comments: - "the terse reading only makes sense for Leibniz notation such as d2ydx2 @@ -578,7 +578,7 @@ concepts: arguments: [a1,a2,a3,...] property: ??? en: - - "partial $1 partial $2 <$3 if $3 != 1> [partial $4 <$5 if $5 != 1> ...]" + - "partial a1 partial a2 [partial a4 ...]" comments: - | ``` @@ -599,7 +599,7 @@ concepts: arity: 1 arguments: [a1] property: prefix - en: "limit as $1" + en: "limit as a1" comments: - "limit is not an argument, but intent should be on `msub` or `munder`" - "There are several arrows used for limits. " @@ -630,7 +630,7 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "$1 tends to $2" + en: "a1 tends to a2" comments: - "see \"limit\" example" @@ -639,7 +639,7 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "$1 tends to from above $2" + en: "a1 tends to from above a2" comments: - "see \"limit\" example" @@ -648,7 +648,7 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "$1 tends to from below $2" + en: "a1 tends to from below a2" comments: - "see \"limit\" example" @@ -658,7 +658,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "set of $1" + en: "set of a1" comments: - | the argument to `set` is typically an `mrow`. For example: @@ -686,7 +686,7 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "set difference of $1 and $2" + en: "set difference of a1 and a2" comments: - "This can be spoken in many ways. See other entry for infix speech." - "There are several notations that are used and their order of appearance differs: @@ -697,7 +697,7 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "\"$1 minus $2\" or \"$2 subtracted from $1\"" + en: "\"a1 minus a2\" or \"a2 subtracted from a1\"" comments: - "This can be spoken in many ways. See other entry for functional speech." - "See functional form for some notational usages." @@ -707,7 +707,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "complement of $1" + en: "complement of a1" comments: - "This can be spoken in many ways. See other entry for functional speech." - "Two notations used for complement are: @@ -734,13 +734,13 @@ concepts: subject-area: sets arity: ">=0" arguments: [a1,...] - en: "list of $1, ..." + en: "list of a1, ..." - concept: tuple subject-area: sets arity: ">=0" arguments: [a1,...] - en: "tuple of $1, ..." + en: "tuple of a1, ..." ## ====================== 4.4.6 sequence and series ============================ - concept: sum @@ -748,7 +748,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "sum of $1" + en: "sum of a1" comments: - usually on `` @@ -757,7 +757,7 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "sum over $1 of $2" + en: "sum over a1 of a2" comments: - usually on `` or `` @@ -766,7 +766,7 @@ concepts: arity: 3 arguments: [a1,a2,a3] property: function - en: "sum from $1 to $2 of $3" + en: "sum from a1 to a2 of a3" comments: - usually on `` or `` @@ -775,7 +775,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "product of $1" + en: "product of a1" comments: - usually on `` @@ -784,7 +784,7 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "product over $1 of $2" + en: "product over a1 of a2" comments: - usually on `` or `` @@ -793,7 +793,7 @@ concepts: arity: 3 arguments: [a1,a2,a3] property: function - en: "product from $1 to $2 of $3" + en: "product from a1 to a2 of a3" comments: - usually on `` or `` @@ -804,8 +804,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "sine $1" - fr: "sinus $1" + en: "sine a1" + fr: "sinus a1" comments: - used as 'sin', 'sen' @@ -815,8 +815,8 @@ concepts: arguments: [a1] property: function en: - - "(verbose) cosine $1" - - "(terse) cos $1" + - "(verbose) cosine a1" + - "(terse) cos a1" - concept: tangent subject-area: elementary classical functions @@ -824,8 +824,8 @@ concepts: arguments: [a1] property: function en: - - "(verbose) tangent $1" - - "(terse) tan $1" + - "(verbose) tangent a1" + - "(terse) tan a1" comments: - used as 'tan', 'tg' @@ -835,8 +835,8 @@ concepts: arguments: [a1] property: function en: - - "(verbose) secant $1" - - "(terse) seech $1" + - "(verbose) secant a1" + - "(terse) seech a1" comments: - used as 'sec' @@ -846,8 +846,8 @@ concepts: arguments: [a1] property: function en: - - "(verbose) cosecant $1" - - "(terse) co-seech $1" + - "(verbose) cosecant a1" + - "(terse) co-seech a1" comments: - used as 'csc' @@ -857,8 +857,8 @@ concepts: arguments: [a1] property: function en: - - "(verbose) cotangent $1" - - "(terse) co-tan $1" + - "(verbose) cotangent a1" + - "(terse) co-tan a1" comments: - used as 'cot' @@ -870,7 +870,7 @@ concepts: arguments: [a1] property: function en: - - "(verbose) arcsine $1" + - "(verbose) arcsine a1" comments: - "used as 'arcsin', 'arc sin'" - "this is distinct from sin inverse (sin-1)" @@ -881,7 +881,7 @@ concepts: arguments: [a1] property: function en: - - "(verbose) arccosine $1" + - "(verbose) arccosine a1" comments: - "used as 'arccos', 'arc cos'" @@ -891,7 +891,7 @@ concepts: arguments: [a1] property: function en: - - "(verbose) arctangent $1" + - "(verbose) arctangent a1" comments: - "used as 'arctan', 'arc tan'" @@ -901,7 +901,7 @@ concepts: arguments: [a1] property: function en: - - "(verbose) arcsecant $1" + - "(verbose) arcsecant a1" comments: - "used as 'arcsec', 'arc sec'" @@ -911,7 +911,7 @@ concepts: arguments: [a1] property: function en: - - "(verbose) arc-cosecant $1" + - "(verbose) arc-cosecant a1" comments: - "used as 'arccos', 'arc cos'" @@ -921,7 +921,7 @@ concepts: arguments: [a1] property: function en: - - "(verbose) arc-cotangent $1" + - "(verbose) arc-cotangent a1" comments: - "used as 'arccos', 'arc cos'" @@ -935,9 +935,9 @@ concepts: - "youtube" - "used as 'sinh'" en: - - "short form 'shine $1'" + - "short form 'shine a1'" fr: - - "sinus hyperbolique $1" + - "sinus hyperbolique a1" - concept: hyperbolic-cosine @@ -949,10 +949,10 @@ concepts: - "youtube" - "used as 'cosh'" en: - - "short form 'cosh $1'" + - "short form 'cosh a1'" fr: - - "cosh $1" - - "kosh $1" + - "cosh a1" + - "kosh a1" - concept: hyperbolic-tangent subject-area: elementary classical functions @@ -963,8 +963,8 @@ concepts: - "youtube" - "used as 'tanh'" en: - - "short form American 'tanch $1'" - - "short form British 'than $1'" + - "short form American 'tanch a1'" + - "short form British 'than a1'" - concept: hyperbolic-secant subject-area: elementary classical functions @@ -975,8 +975,8 @@ concepts: - "youtube" - "used as 'sech'" en: - - "short form American 'sech $1'" - - "short form British 'shek $1'" + - "short form American 'sech a1'" + - "short form British 'shek a1'" - concept: hyperbolic-cosecant subject-area: elementary classical functions @@ -987,8 +987,8 @@ concepts: - "youtube" - "used as 'cosech'" en: - - "short form American 'cosech $1'" - - "short form British 'coshek $1'" + - "short form American 'cosech a1'" + - "short form British 'coshek a1'" - concept: hyperbolic-cotangent @@ -1000,8 +1000,8 @@ concepts: - "youtube" - "used as 'coth'" en: - - "short form American 'coth $1'" - - "short form British 'coath $1'" + - "short form American 'coth a1'" + - "short form British 'coath a1'" @@ -1014,9 +1014,9 @@ concepts: comments: - "used as 'asinh'" en: - - "short form 'arc shine $1'" + - "short form 'arc shine a1'" fr: - - "sinus hyperbolique $1" + - "sinus hyperbolique a1" - concept: arc-hyperbolic-cosine @@ -1027,10 +1027,10 @@ concepts: comments: - "used as 'acosh'" en: - - "short form 'arc cosh $1'" + - "short form 'arc cosh a1'" fr: - - "cosh $1" - - "kosh $1" + - "cosh a1" + - "kosh a1" - concept: arc-hyperbolic-tangent subject-area: elementary classical functions @@ -1040,8 +1040,8 @@ concepts: comments: - "used as 'atanh'" en: - - "short form American 'arc tanch $1'" - - "short form British 'arc than $1'" + - "short form American 'arc tanch a1'" + - "short form British 'arc than a1'" - concept: arc-hyperbolic-secant subject-area: elementary classical functions @@ -1051,8 +1051,8 @@ concepts: comments: - "used as 'asech'" en: - - "short form American 'arc sech $1'" - - "short form British 'arc shek $1'" + - "short form American 'arc sech a1'" + - "short form British 'arc shek a1'" - concept: arc-hyperbolic-cosecant subject-area: elementary classical functions @@ -1062,8 +1062,8 @@ concepts: comments: - "used as 'acsch'" en: - - "short form American 'arc cosech $1'" - - "short form British 'arc coshek $1'" + - "short form American 'arc cosech a1'" + - "short form British 'arc coshek a1'" - concept: arc-hyperbolic-cotangent @@ -1074,8 +1074,8 @@ concepts: comments: - "used as 'acoth'" en: - - "short form American 'arc coth $1'" - - "short form British 'arc coath $1'" + - "short form American 'arc coth a1'" + - "short form British 'arc coath a1'" ## exponential related functions @@ -1085,7 +1085,7 @@ concepts: arguments: [a1] property: function en: - - "exponential of $1" + - "exponential of a1" - concept: natural-logarithm subject-area: elementary classical functions @@ -1093,22 +1093,22 @@ concepts: arguments: [a1] property: function en: - - "natural log of $1" - - "log of $1" + - "natural log of a1" + - "log of a1" - concept: logarithm subject-area: elementary classical functions arity: 1 arguments: [a1] property: function - en: "log of $1" + en: "log of a1" - concept: logarithm subject-area: elementary classical functions arity: 2 arguments: [a1,a2] property: function - en: "log base $2 of $1" + en: "log base a2 of a1" @@ -1119,7 +1119,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "mean of $1" + en: "mean of a1" comments: - "This might be display as x¯" @@ -1128,28 +1128,28 @@ concepts: arity: 1 arguments: [a1] property: function - en: "standard deviation of $1" + en: "standard deviation of a1" - concept: variance subject-area: Statistics and Probability arity: 1 arguments: [a1] property: function - en: "variance of $1" + en: "variance of a1" - concept: median subject-area: Statistics and Probability arity: 1 arguments: [a1] property: function - en: "median of $1" + en: "median of a1" - concept: mode subject-area: Statistics and Probability arity: 1 arguments: [a1] property: function - en: "mode of $1" + en: "mode of a1" @@ -1158,7 +1158,7 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "probability of $1 given $2" + en: "probability of a1 given a2" comments: - | The intent should be on the `mrow` that includes the "P" @@ -1255,8 +1255,8 @@ concepts: arity: 1 arguments: [a1] property: postfix - en: "$1 transpose" - fr: "$1 transposée" + en: "a1 transpose" + fr: "a1 transposée" - concept: transpose subject-area: Linear Algebra @@ -1264,8 +1264,8 @@ concepts: arguments: [a1] property: function default: false - en: "transpose of $1" - fr: "transposée de $1" + en: "transpose of a1" + fr: "transposée de a1" - concept: dimensional-product subject-area: Linear Algebra @@ -1273,7 +1273,7 @@ concepts: arguments: [a1,a2,...] property: infix default: false - en: "$1 by $2 ..." + en: "a1 by a2 ..." comments: - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name. A common use would be describe the size of a matrix. For example m×n." @@ -1369,7 +1369,7 @@ concepts: arguments: [a1,a2] property: prefix en: - - "line segment $1 $2" + - "line segment a1 a2" comments: - "Example: (`mover`): AB_" @@ -1379,7 +1379,7 @@ concepts: arguments: [a1,a2] property: prefix en: - - "directed line segment $1 $2" + - "directed line segment a1 a2" comments: - "Example: (`mover`): AB→" @@ -1389,7 +1389,7 @@ concepts: arguments: [a1,a2] property: prefix en: - - "line $1 $2" + - "line a1 a2" comments: - "Example: (`mover`): AB↔" @@ -1399,7 +1399,7 @@ concepts: arguments: [a1,a2] property: prefix en: - - "ray $1 $2" + - "ray a1 a2" comments: - "Example: (`mover`): AB→" @@ -1409,7 +1409,7 @@ concepts: arguments: [a1,a2] property: prefix en: - - "arc $1 $2" + - "arc a1 a2" comments: - "Example: (`mover`): AB⌒" @@ -1419,7 +1419,7 @@ concepts: arguments: [a1] property: function en: - - "length of $1" + - "length of a1" comments: - "It may be necessary to 'nest' the intent as shown here for the example: @@ -1441,7 +1441,7 @@ concepts: arguments: [a1] property: function en: - - "area of $1" + - "area of a1" comments: - "There are many notations. Here's one: [ABCD]" @@ -1466,7 +1466,7 @@ concepts: arguments: [a1,...] property: ??? en: - - "point $1 [comma $2 ...]" + - "point a1 [comma a2 ...]" comment: - "Example: (1,2,3)" @@ -1476,7 +1476,7 @@ concepts: arguments: [a1] property: function en: - - "volume of $1" + - "volume of a1" comments: - "See comments for `length` and `volume` for examples of how this might be marked up" @@ -1499,7 +1499,7 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: $1 $2 + en: a1 a2 comments: - "separates hours and minutes and is typically silent" - "Example: 2:31" @@ -1510,7 +1510,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "fenced-group of $1" + en: "fenced-group of a1" comments: - "this includes parens, brackets, and braces" @@ -1519,23 +1519,23 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "the pair $1 and $2" + en: "the pair a1 and a2" - concept: indexed-by subject-area: General Concepts arity: 2 arguments: [a1,a2] property: infix - en: "$1 indexed by $2" + en: "a1 indexed by a2" comments: - - "this is typically a subscript and might also be spoken as '$1 sub $2'" + - "this is typically a subscript and might also be spoken as 'a1 sub a2'" - concept: highlight subject-area: General Concepts arity: 1 arguments: [a1] property: postfix - en: "$1 highlighted" + en: "a1 highlighted" comments: - "this typically would be used inside of a larger expression and not on its own" - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" @@ -1546,7 +1546,7 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "$1 per $2" + en: "a1 per a2" comments: - "Typically used with units" - "Used with `mfrac` or `/`" @@ -1556,7 +1556,7 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "translation by $1 comma $2" + en: "translation by a1 comma a2" comments: - "Example: T(1,3)" @@ -1574,7 +1574,7 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "$1 choose $2" + en: "a1 choose a2" comments: - "There are many notations used for the binomial coefficient. Here are some of them: @@ -1606,7 +1606,7 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "$2 permutation of $1" + en: "a2 permutation of a1" comments: - "There are many notations for this: some of them are @@ -1637,7 +1637,7 @@ concepts: arity: ">=2" arguments: [a1,a2,...] property: function - en: "permutation cycle of $1 $2 ..." + en: "permutation cycle of a1 a2 ..." comments: - "A common notation for a permutation cycle is ( 132 @@ -1660,7 +1660,7 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "$1 with annotation $2" + en: "a1 with annotation a2" comments: - "used with `mover` or `munder`" @@ -1670,7 +1670,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "fenced-group of $1" + en: "fenced-group of a1" comments: - "this includes parens, brackets, and braces" @@ -1679,7 +1679,7 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "$1 which is $2" + en: "a1 which is a2" comments: - "used with `mover` or `munder`" - "Example: H2O⏟water" @@ -1689,7 +1689,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "grouped $1 end-grouped" + en: "grouped a1 end-grouped" comments: - "used with `mover` or `munder`" - "Example: 13-16⏟" @@ -1699,7 +1699,7 @@ concepts: arity: 1 arguments: [a1] property: function - en: "repeating decimal $1" + en: "repeating decimal a1" comments: - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits." - "Example: 122=0.045_" diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index b6d336b9..1aed4cc1 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -190,7 +190,7 @@ if c.link {%- for c in cpts -%} {%- if c.subject-area != subjt -%} {%- assign subjt = c.subject-area -%} -
{{subjt}}
+
{{subjt}}
{%- endif -%} {%- assign clss = forloop.index| modulo:2 -%} {%- assign arityr = c.arity | replace: ">=", "⩾" -%} From 3215aaf37ddea39c362602ccc39ee9c6a249f59a Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 19:20:02 +0100 Subject: [PATCH 17/33] yaml indents --- _data/core.yml | 599 ++++++++++++++++++++++++++++++------------------- 1 file changed, 367 insertions(+), 232 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index fc1bbbf6..30460c88 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -219,39 +219,44 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: interval between a1 (included) and a2 - fr: intervalle ouvert à droite entre a1 et a2 + speech: + en: interval between a1 (included) and a2 + fr: intervalle ouvert à droite entre a1 et a2 - concept: open-closed-interval subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: interval between a1 and a2, included - fr: intervalle ouvert à gauche... + speech: + en: interval between a1 and a2, included + fr: intervalle ouvert à gauche... - concept: open-interval subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: open interval between a1 and a2 - fr: intervalle ouvert + speech: + en: open interval between a1 and a2 + fr: intervalle ouvert - concept: closed-interval subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: closed interval between a1 and a2 - fr: intervalle fermé entre a1 et a2 + speech: + en: closed interval between a1 and a2 + fr: intervalle fermé entre a1 et a2 - concept: inverse subject-area: functions and inverses arity: 1 arguments: [a1] property: function* - en: inverse of a1 + speech: + en: inverse of a1 comments: - "`inverse` can be used for function inverses, matrix inverses, etc." @@ -260,45 +265,51 @@ concepts: arity: 1 arguments: [a1] property: postfix - en: a1 inverse + speech: + en: a1 inverse - concept: domain subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: domain of a1 - fr: domaine de définition de a1 + speech: + en: domain of a1 + fr: domaine de définition de a1 - concept: codomain subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: codomain of a1 - fr: ensemble d'arrivée de a1 + speech: + en: codomain of a1 + fr: ensemble d'arrivée de a1 - concept: image subject-area: functions and inverses arity: 1 arguments: [a1] property: function* - en: image of a1 - fr: image de a1 + speech: + en: image of a1 + fr: image de a1 - concept: fraction subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: fraction a1 over a2 end fraction + speech: + en: fraction a1 over a2 end fraction - concept: mixed-fraction subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: a1 and a2 + speech: + en: a1 and a2 comments: - "a1 is a positive integer and a2 is a fraction with positive numerical components. The second argument can be an `mfrac` (normal or beveled) or can be a linear fraction using `/`" @@ -308,15 +319,17 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: integer part of a1 divided by a2 - fr: quotient de a1 par a2 + speech: + en: integer part of a1 divided by a2 + fr: quotient de a1 par a2 - concept: evaluated-at subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: infix - en: a1 evaluated-at a2 + speech: + en: a1 evaluated-at a2 comments: - "Two common notations are x2|3 @@ -336,22 +349,25 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: the remainder of a1 divided by a2 - fr: reste de la divsion de a1 par a2 + speech: + en: the remainder of a1 divided by a2 + fr: reste de la divsion de a1 par a2 - concept: max subject-area: functions and inverses arity: ">=1" arguments: [a1,...] property: function - en: "max of a1, ..." + speech: + en: "max of a1, ..." - concept: min subject-area: functions and inverses arity: ">=1" arguments: [a1,...] property: function - en: "min of a1, ..." + speech: + en: "min of a1, ..." - concept: power subject-area: functions and inverses @@ -360,14 +376,17 @@ concepts: property: infix conditions: - condition: "a2=2" - en: "a1 squared" - fr: "a1 carré" + speech: + en: "a1 squared" + fr: "a1 carré" - condition: "a2=3" - en: "a1 cubed" - fr: "a1 cube" + speech: + en: "a1 cubed" + fr: "a1 cube" - condition: "" - en: "a1 to the a2th power" - fr: "a1 à la a2" + speech: + en: "a1 to the a2th power" + fr: "a1 à la a2" - concept: root @@ -377,83 +396,96 @@ concepts: property: function conditions: - condition: "a2=2" - en: "square root of a1" + speech: + en: "square root of a1" - condition: "a2=3" - en: "cube root of a1" + speech: + en: "cube root of a1" - condition: "a2=4" - en: "fourth root of a1" + speech: + en: "fourth root of a1" - condition: "" - en: "a2th root of a1" + speech: + en: "a2th root of a1" - concept: greatest-common-divisor subject-area: functions and inverses arity: ">=2" arguments: [a1,a2,...] property: function - en: greatest common divisor of a1, a2, ... - fr: plus grand commun diviseur de a1, a2, ... + speech: + en: greatest common divisor of a1, a2, ... + fr: plus grand commun diviseur de a1, a2, ... - concept: least-common-multiple subject-area: functions and inverses arity: ">=2" arguments: [a1,a2,...] property: function - en: lest common multiple of a1, a2, ... - fr: plus grand commun diviseur de a1, a2, ... + speech: + en: lest common multiple of a1, a2, ... + fr: plus grand commun diviseur de a1, a2, ... - concept: least-common-denominator subject-area: functions and inverses arity: ">=2" arguments: [a1,a2,...] property: function - en: "least common denominator of a1, a2, ..." + speech: + en: "least common denominator of a1, a2, ..." - concept: absolute-value subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: absolute value of a1 - fr: valeur absolue de a1 - de: Betrag von a1 + speech: + en: absolute value of a1 + fr: valeur absolue de a1 + de: Betrag von a1 - concept: complex-conjugate subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: complex conjugate of a1 - fr: a1 conjugé + speech: + en: complex conjugate of a1 + fr: a1 conjugé - concept: complex-arg subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: arg of a1 + speech: + en: arg of a1 - concept: real-part subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: - - real part of a1 - - imaginary part of a1 + speech: + en: + - real part of a1 + - imaginary part of a1 - concept: imaginary-part subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: imaginary part of a1 + speech: + en: imaginary part of a1 - concept: polar-coordinate subject-area: functions and inverses arity: 2 arguments: [a1,a2] property: function - en: "polar coordinate a1 comma a2" + speech: + en: "polar coordinate a1 comma a2" comment: - "The first argument is the radius, the second argument is the polar angle, the third arguments is the azimuthal angle." - "Example: (r, θ)" @@ -463,7 +495,8 @@ concepts: arity: 3 arguments: [a1,a2,a3] property: function - en: "spherical coordinate a1 comma a2, comma a3" + speech: + en: "spherical coordinate a1 comma a2, comma a3" comment: - "The first argument is the radius, the second argument is the angle." - "Example: (r,Φ,θ)" @@ -473,7 +506,8 @@ concepts: arity: ">=2" arguments: [a1,a2,...] property: function - en: "cartesian coordinate a1 comma a2 ..." + speech: + en: "cartesian coordinate a1 comma a2 ..." comment: - "Example: (1,2)" @@ -482,7 +516,8 @@ concepts: arity: ">=2" arguments: [a1,a2,...] property: function - en: "coordinate a1 comma a2 ..." + speech: + en: "coordinate a1 comma a2 ..." comment: - "This a generic coordinate that doesn't specify the coordinate system. It takes 2 or more arguments." - "Example: (1,2)" @@ -492,21 +527,24 @@ concepts: arity: 1 arguments: [a1] property: function - en: floor of a1 + speech: + en: floor of a1 - concept: ceiling subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: ceiling of a1 + speech: + en: ceiling of a1 - concept: round subject-area: functions and inverses arity: 1 arguments: [a1] property: function - en: rounded-value of a1 + speech: + en: rounded-value of a1 comments: - "This sometimes uses the notation ⌊x⌉ @@ -518,7 +556,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: fractional part of a1 + speech: + en: fractional part of a1 ## ====================== 4.4.4 Calculus ============================ - concept: definite-integral @@ -526,7 +565,8 @@ concepts: arity: 1 arguments: [a1] property: ??? - en: "integral over a1" + speech: + en: "integral over a1" comments: - "integral sign is not an argument" @@ -535,7 +575,8 @@ concepts: arity: 2 arguments: [a1,a2] property: ??? - en: "integral from a1 to a2" + speech: + en: "integral from a1 to a2" comments: - "integral sign is not an argument" @@ -545,9 +586,10 @@ concepts: arity: 3 arguments: [a1,a2,a3] property: ??? - en: - - "(verbose) the a3 derivative of a1 with respect to a2" - - "(terse) d a1 by d a2 " + speech: + en: + - "(verbose) the a3 derivative of a1 with respect to a2" + - "(terse) d a1 by d a2 " comments: - "the terse reading only makes sense for Leibniz notation such as d2ydx2 @@ -577,8 +619,9 @@ concepts: arity: ">=3" arguments: [a1,a2,a3,...] property: ??? - en: - - "partial a1 partial a2 [partial a4 ...]" + speech: + en: + - "partial a1 partial a2 [partial a4 ...]" comments: - | ``` @@ -599,7 +642,8 @@ concepts: arity: 1 arguments: [a1] property: prefix - en: "limit as a1" + speech: + en: "limit as a1" comments: - "limit is not an argument, but intent should be on `msub` or `munder`" - "There are several arrows used for limits. " @@ -630,7 +674,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "a1 tends to a2" + speech: + en: "a1 tends to a2" comments: - "see \"limit\" example" @@ -639,7 +684,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "a1 tends to from above a2" + speech: + en: "a1 tends to from above a2" comments: - "see \"limit\" example" @@ -648,7 +694,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "a1 tends to from below a2" + speech: + en: "a1 tends to from below a2" comments: - "see \"limit\" example" @@ -658,7 +705,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "set of a1" + speech: + en: "set of a1" comments: - | the argument to `set` is typically an `mrow`. For example: @@ -686,7 +734,8 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "set difference of a1 and a2" + speech: + en: "set difference of a1 and a2" comments: - "This can be spoken in many ways. See other entry for infix speech." - "There are several notations that are used and their order of appearance differs: @@ -697,7 +746,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "\"a1 minus a2\" or \"a2 subtracted from a1\"" + speech: + en: "\"a1 minus a2\" or \"a2 subtracted from a1\"" comments: - "This can be spoken in many ways. See other entry for functional speech." - "See functional form for some notational usages." @@ -707,7 +757,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "complement of a1" + speech: + en: "complement of a1" comments: - "This can be spoken in many ways. See other entry for functional speech." - "Two notations used for complement are: @@ -717,7 +768,8 @@ concepts: subject-area: sets arity: 0 arguments: [] - en: "empty set" + speech: + en: "empty set" comments: - "Three notations used for empty set are: { }, ∅, and ∅" @@ -734,13 +786,15 @@ concepts: subject-area: sets arity: ">=0" arguments: [a1,...] - en: "list of a1, ..." + speech: + en: "list of a1, ..." - concept: tuple subject-area: sets arity: ">=0" arguments: [a1,...] - en: "tuple of a1, ..." + speech: + en: "tuple of a1, ..." ## ====================== 4.4.6 sequence and series ============================ - concept: sum @@ -748,7 +802,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "sum of a1" + speech: + en: "sum of a1" comments: - usually on `` @@ -757,7 +812,8 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "sum over a1 of a2" + speech: + en: "sum over a1 of a2" comments: - usually on `` or `` @@ -766,7 +822,8 @@ concepts: arity: 3 arguments: [a1,a2,a3] property: function - en: "sum from a1 to a2 of a3" + speech: + en: "sum from a1 to a2 of a3" comments: - usually on `` or `` @@ -775,7 +832,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "product of a1" + speech: + en: "product of a1" comments: - usually on `` @@ -784,7 +842,8 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "product over a1 of a2" + speech: + en: "product over a1 of a2" comments: - usually on `` or `` @@ -793,7 +852,8 @@ concepts: arity: 3 arguments: [a1,a2,a3] property: function - en: "product from a1 to a2 of a3" + speech: + en: "product from a1 to a2 of a3" comments: - usually on `` or `` @@ -804,8 +864,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: "sine a1" - fr: "sinus a1" + speech: + en: "sine a1" + fr: "sinus a1" comments: - used as 'sin', 'sen' @@ -814,18 +875,20 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) cosine a1" - - "(terse) cos a1" + speech: + en: + - "(verbose) cosine a1" + - "(terse) cos a1" - concept: tangent subject-area: elementary classical functions arity: 1 arguments: [a1] property: function - en: - - "(verbose) tangent a1" - - "(terse) tan a1" + speech: + en: + - "(verbose) tangent a1" + - "(terse) tan a1" comments: - used as 'tan', 'tg' @@ -834,9 +897,10 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) secant a1" - - "(terse) seech a1" + speech: + en: + - "(verbose) secant a1" + - "(terse) seech a1" comments: - used as 'sec' @@ -845,9 +909,10 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) cosecant a1" - - "(terse) co-seech a1" + speech: + en: + - "(verbose) cosecant a1" + - "(terse) co-seech a1" comments: - used as 'csc' @@ -856,9 +921,10 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) cotangent a1" - - "(terse) co-tan a1" + speech: + en: + - "(verbose) cotangent a1" + - "(terse) co-tan a1" comments: - used as 'cot' @@ -869,8 +935,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) arcsine a1" + speech: + en: + - "(verbose) arcsine a1" comments: - "used as 'arcsin', 'arc sin'" - "this is distinct from sin inverse (sin-1)" @@ -880,8 +947,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) arccosine a1" + speech: + en: + - "(verbose) arccosine a1" comments: - "used as 'arccos', 'arc cos'" @@ -890,8 +958,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) arctangent a1" + speech: + en: + - "(verbose) arctangent a1" comments: - "used as 'arctan', 'arc tan'" @@ -900,8 +969,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) arcsecant a1" + speech: + en: + - "(verbose) arcsecant a1" comments: - "used as 'arcsec', 'arc sec'" @@ -910,8 +980,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) arc-cosecant a1" + speech: + en: + - "(verbose) arc-cosecant a1" comments: - "used as 'arccos', 'arc cos'" @@ -920,8 +991,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "(verbose) arc-cotangent a1" + speech: + en: + - "(verbose) arc-cotangent a1" comments: - "used as 'arccos', 'arc cos'" @@ -934,10 +1006,11 @@ concepts: comments: - "youtube" - "used as 'sinh'" - en: - - "short form 'shine a1'" - fr: - - "sinus hyperbolique a1" + speech: + en: + - "short form 'shine a1'" + fr: + - "sinus hyperbolique a1" - concept: hyperbolic-cosine @@ -948,11 +1021,12 @@ concepts: comments: - "youtube" - "used as 'cosh'" - en: + speech: + en: - "short form 'cosh a1'" - fr: - - "cosh a1" - - "kosh a1" + fr: + - "cosh a1" + - "kosh a1" - concept: hyperbolic-tangent subject-area: elementary classical functions @@ -962,9 +1036,10 @@ concepts: comments: - "youtube" - "used as 'tanh'" - en: - - "short form American 'tanch a1'" - - "short form British 'than a1'" + speech: + en: + - "short form American 'tanch a1'" + - "short form British 'than a1'" - concept: hyperbolic-secant subject-area: elementary classical functions @@ -974,9 +1049,10 @@ concepts: comments: - "youtube" - "used as 'sech'" - en: - - "short form American 'sech a1'" - - "short form British 'shek a1'" + speech: + en: + - "short form American 'sech a1'" + - "short form British 'shek a1'" - concept: hyperbolic-cosecant subject-area: elementary classical functions @@ -986,9 +1062,10 @@ concepts: comments: - "youtube" - "used as 'cosech'" - en: - - "short form American 'cosech a1'" - - "short form British 'coshek a1'" + speech: + en: + - "short form American 'cosech a1'" + - "short form British 'coshek a1'" - concept: hyperbolic-cotangent @@ -999,9 +1076,10 @@ concepts: comments: - "youtube" - "used as 'coth'" - en: - - "short form American 'coth a1'" - - "short form British 'coath a1'" + speech: + en: + - "short form American 'coth a1'" + - "short form British 'coath a1'" @@ -1013,10 +1091,11 @@ concepts: property: function comments: - "used as 'asinh'" - en: - - "short form 'arc shine a1'" - fr: - - "sinus hyperbolique a1" + speech: + en: + - "short form 'arc shine a1'" + fr: + - "sinus hyperbolique a1" - concept: arc-hyperbolic-cosine @@ -1026,11 +1105,12 @@ concepts: property: function comments: - "used as 'acosh'" - en: - - "short form 'arc cosh a1'" - fr: - - "cosh a1" - - "kosh a1" + speech: + en: + - "short form 'arc cosh a1'" + fr: + - "cosh a1" + - "kosh a1" - concept: arc-hyperbolic-tangent subject-area: elementary classical functions @@ -1039,9 +1119,10 @@ concepts: property: function comments: - "used as 'atanh'" - en: - - "short form American 'arc tanch a1'" - - "short form British 'arc than a1'" + speech: + en: + - "short form American 'arc tanch a1'" + - "short form British 'arc than a1'" - concept: arc-hyperbolic-secant subject-area: elementary classical functions @@ -1050,9 +1131,10 @@ concepts: property: function comments: - "used as 'asech'" - en: - - "short form American 'arc sech a1'" - - "short form British 'arc shek a1'" + speech: + en: + - "short form American 'arc sech a1'" + - "short form British 'arc shek a1'" - concept: arc-hyperbolic-cosecant subject-area: elementary classical functions @@ -1061,9 +1143,10 @@ concepts: property: function comments: - "used as 'acsch'" - en: - - "short form American 'arc cosech a1'" - - "short form British 'arc coshek a1'" + speech: + en: + - "short form American 'arc cosech a1'" + - "short form British 'arc coshek a1'" - concept: arc-hyperbolic-cotangent @@ -1073,9 +1156,10 @@ concepts: property: function comments: - "used as 'acoth'" - en: - - "short form American 'arc coth a1'" - - "short form British 'arc coath a1'" + speech: + en: + - "short form American 'arc coth a1'" + - "short form British 'arc coath a1'" ## exponential related functions @@ -1084,7 +1168,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: + speech: + en: - "exponential of a1" - concept: natural-logarithm @@ -1092,7 +1177,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: + speech: + en: - "natural log of a1" - "log of a1" @@ -1101,14 +1187,16 @@ concepts: arity: 1 arguments: [a1] property: function - en: "log of a1" + speech: + en: "log of a1" - concept: logarithm subject-area: elementary classical functions arity: 2 arguments: [a1,a2] property: function - en: "log base a2 of a1" + speech: + en: "log base a2 of a1" @@ -1119,7 +1207,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "mean of a1" + speech: + en: "mean of a1" comments: - "This might be display as x¯" @@ -1128,28 +1217,32 @@ concepts: arity: 1 arguments: [a1] property: function - en: "standard deviation of a1" + speech: + en: "standard deviation of a1" - concept: variance subject-area: Statistics and Probability arity: 1 arguments: [a1] property: function - en: "variance of a1" + speech: + en: "variance of a1" - concept: median subject-area: Statistics and Probability arity: 1 arguments: [a1] property: function - en: "median of a1" + speech: + en: "median of a1" - concept: mode subject-area: Statistics and Probability arity: 1 arguments: [a1] property: function - en: "mode of a1" + speech: + en: "mode of a1" @@ -1158,7 +1251,8 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "probability of a1 given a2" + speech: + en: "probability of a1 given a2" comments: - | The intent should be on the `mrow` that includes the "P" @@ -1240,7 +1334,8 @@ concepts: property: prefix comments: - "Example: x^" - en: "unit vector x" + speech: + en: "unit vector x" - concept: identity-matrix subject-area: Linear Algebra @@ -1248,15 +1343,17 @@ concepts: arguments: [] comments: - "This is typically represented as 'I' or bold-faced '𝐈'" - en: "identity matrix" + speech: + en: "identity matrix" - concept: transpose subject-area: Linear Algebra arity: 1 arguments: [a1] property: postfix - en: "a1 transpose" - fr: "a1 transposée" + speech: + en: "a1 transpose" + fr: "a1 transposée" - concept: transpose subject-area: Linear Algebra @@ -1264,8 +1361,9 @@ concepts: arguments: [a1] property: function default: false - en: "transpose of a1" - fr: "transposée de a1" + speech: + en: "transpose of a1" + fr: "transposée de a1" - concept: dimensional-product subject-area: Linear Algebra @@ -1273,7 +1371,8 @@ concepts: arguments: [a1,a2,...] property: infix default: false - en: "a1 by a2 ..." + speech: + en: "a1 by a2 ..." comments: - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name. A common use would be describe the size of a matrix. For example m×n." @@ -1284,78 +1383,88 @@ concepts: subject-area: Constants and Sets arity: 0 arguments: [] - en: - - "(verbose) set of all integers" - - "(terse) Z" - fr: "Z" + speech: + en: + - "(verbose) set of all integers" + - "(terse) Z" + fr: "Z" - concept: set-of-reals subject-area: Constants and Sets arity: 0 arguments: [] - en: - - "(verbose) set of all real numbers" - - "(terse) R" + speech: + en: + - "(verbose) set of all real numbers" + - "(terse) R" - concept: set-of-rationals subject-area: Constants and Sets arity: 0 arguments: [] - en: - - "(verbose) set of all rational numbers" - - "(terse) R" + speech: + en: + - "(verbose) set of all rational numbers" + - "(terse) R" - concept: set-of-natural-numbers subject-area: Constants and Sets arity: 0 arguments: [] - en: - - "(verbose) set of all natural numbers" - - "(terse) N" + speech: + en: + - "(verbose) set of all natural numbers" + - "(terse) N" - concept: set-of-complex-numbers subject-area: Constants and Sets arity: 0 arguments: [] - en: - - "(verbose) set of all complex numbers" - - "(terse) C" + speech: + en: + - "(verbose) set of all complex numbers" + - "(terse) C" - concept: set-of-primes subject-area: Constants and Sets arity: 0 arguments: [] - en: - - "(verbose) set of all prime numbers" - - "(terse) P" + speech: + en: + - "(verbose) set of all prime numbers" + - "(terse) P" - concept: exponential-e subject-area: Constants and Sets arity: 0 arguments: [] - en: "e" - fr: "e" + speech: + en: "e" + fr: "e" - concept: imaginary-i subject-area: Constants and Sets arity: 0 arguments: [] - en: "i" - fr: "i" + speech: + en: "i" + fr: "i" - concept: differential-d subject-area: Constants and Sets arity: 0 arguments: [] - en: "d" - fr: "d" + speech: + en: "d" + fr: "d" - concept: golden-ratio subject-area: Constants and Sets arity: 0 arguments: [] - en: "golden ratio" - fr: "d" + speech: + en: "golden ratio" + fr: "d" comments: - "Often denoted as φ" @@ -1368,8 +1477,9 @@ concepts: arity: 2 arguments: [a1,a2] property: prefix - en: - - "line segment a1 a2" + speech: + en: + - "line segment a1 a2" comments: - "Example: (`mover`): AB_" @@ -1378,8 +1488,9 @@ concepts: arity: 2 arguments: [a1,a2] property: prefix - en: - - "directed line segment a1 a2" + speech: + en: + - "directed line segment a1 a2" comments: - "Example: (`mover`): AB→" @@ -1388,8 +1499,9 @@ concepts: arity: 2 arguments: [a1,a2] property: prefix - en: - - "line a1 a2" + speech: + en: + - "line a1 a2" comments: - "Example: (`mover`): AB↔" @@ -1398,8 +1510,9 @@ concepts: arity: 2 arguments: [a1,a2] property: prefix - en: - - "ray a1 a2" + speech: + en: + - "ray a1 a2" comments: - "Example: (`mover`): AB→" @@ -1408,8 +1521,9 @@ concepts: arity: 2 arguments: [a1,a2] property: prefix - en: - - "arc a1 a2" + speech: + en: + - "arc a1 a2" comments: - "Example: (`mover`): AB⌒" @@ -1418,8 +1532,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "length of a1" + speech: + en: + - "length of a1" comments: - "It may be necessary to 'nest' the intent as shown here for the example: @@ -1440,8 +1555,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "area of a1" + speech: + en: + - "area of a1" comments: - "There are many notations. Here's one: [ABCD]" @@ -1465,8 +1581,9 @@ concepts: arity: ">=1" arguments: [a1,...] property: ??? - en: - - "point a1 [comma a2 ...]" + speech: + en: + - "point a1 [comma a2 ...]" comment: - "Example: (1,2,3)" @@ -1475,8 +1592,9 @@ concepts: arity: 1 arguments: [a1] property: function - en: - - "volume of a1" + speech: + en: + - "volume of a1" comments: - "See comments for `length` and `volume` for examples of how this might be marked up" @@ -1484,8 +1602,9 @@ concepts: subject-area: Fill in the blank arity: 0 arguments: [] - en: - - "blank" + speech: + en: + - "blank" comments: - "blanks can be represented in many ways in MathML. Some examples:" - "`__`" @@ -1499,7 +1618,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: a1 a2 + speech: + en: a1 a2 comments: - "separates hours and minutes and is typically silent" - "Example: 2:31" @@ -1510,7 +1630,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "fenced-group of a1" + speech: + en: "fenced-group of a1" comments: - "this includes parens, brackets, and braces" @@ -1519,14 +1640,16 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "the pair a1 and a2" + speech: + en: "the pair a1 and a2" - concept: indexed-by subject-area: General Concepts arity: 2 arguments: [a1,a2] property: infix - en: "a1 indexed by a2" + speech: + en: "a1 indexed by a2" comments: - "this is typically a subscript and might also be spoken as 'a1 sub a2'" @@ -1535,7 +1658,8 @@ concepts: arity: 1 arguments: [a1] property: postfix - en: "a1 highlighted" + speech: + en: "a1 highlighted" comments: - "this typically would be used inside of a larger expression and not on its own" - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" @@ -1546,7 +1670,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "a1 per a2" + speech: + en: "a1 per a2" comments: - "Typically used with units" - "Used with `mfrac` or `/`" @@ -1556,7 +1681,8 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "translation by a1 comma a2" + speech: + en: "translation by a1 comma a2" comments: - "Example: T(1,3)" @@ -1565,7 +1691,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "fraction 2 over x minus 1 with constraint x not equal to 1" + speech: + en: "fraction 2 over x minus 1 with constraint x not equal to 1" comments: - "Example: 2x-1, x≠1" @@ -1574,7 +1701,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "a1 choose a2" + speech: + en: "a1 choose a2" comments: - "There are many notations used for the binomial coefficient. Here are some of them: @@ -1606,7 +1734,8 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "a2 permutation of a1" + speech: + en: "a2 permutation of a1" comments: - "There are many notations for this: some of them are @@ -1637,7 +1766,8 @@ concepts: arity: ">=2" arguments: [a1,a2,...] property: function - en: "permutation cycle of a1 a2 ..." + speech: + en: "permutation cycle of a1 a2 ..." comments: - "A common notation for a permutation cycle is ( 132 @@ -1660,7 +1790,8 @@ concepts: arity: 2 arguments: [a1,a2] property: infix - en: "a1 with annotation a2" + speech: + en: "a1 with annotation a2" comments: - "used with `mover` or `munder`" @@ -1670,7 +1801,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "fenced-group of a1" + speech: + en: "fenced-group of a1" comments: - "this includes parens, brackets, and braces" @@ -1679,7 +1811,8 @@ concepts: arity: 2 arguments: [a1,a2] property: function - en: "a1 which is a2" + speech: + en: "a1 which is a2" comments: - "used with `mover` or `munder`" - "Example: H2O⏟water" @@ -1689,7 +1822,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "grouped a1 end-grouped" + speech: + en: "grouped a1 end-grouped" comments: - "used with `mover` or `munder`" - "Example: 13-16⏟" @@ -1699,7 +1833,8 @@ concepts: arity: 1 arguments: [a1] property: function - en: "repeating decimal a1" + speech: + en: "repeating decimal a1" comments: - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits." - "Example: 122=0.045_" From 56bff272e2c3fd1905f9287e3d49483865feb642 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 20:06:39 +0100 Subject: [PATCH 18/33] colspan --- intent-core-concepts/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 1aed4cc1..1cdc8963 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -190,7 +190,7 @@ if c.link {%- for c in cpts -%} {%- if c.subject-area != subjt -%} {%- assign subjt = c.subject-area -%} -
{{subjt}}
+
{{subjt}}
{%- endif -%} {%- assign clss = forloop.index| modulo:2 -%} {%- assign arityr = c.arity | replace: ">=", "⩾" -%} From f5bbb5ebec8a81cb2868a7616733adaa759c3ef1 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Fri, 28 Aug 2026 20:09:36 +0100 Subject: [PATCH 19/33] speech[language] --- intent-core-concepts/index.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 1cdc8963..974e29db 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -205,8 +205,8 @@ if c.link {%- for language in site.data.languages -%} [{{cond.condition}}]: -{% if cond[language.language-code] -%} -{%- for l in cond[language.language-code] -%} +{% if cond.speech[language.language-code] -%} +{%- for l in cond.speech[language.language-code] -%} {{l}} {%- unless forloop.last -%}
{% endunless -%} {% endfor %} {%- else -%} @@ -245,8 +245,8 @@ if c.link 		{{c.property}}{%- unless c.default == false or c.arity == 0-%}*{%- endunless -%} -{%- if c[language.language-code] -%} -{%- for l in c[language.language-code] -%} +{%- if c.speech[language.language-code] -%} +{%- for l in c.speech[language.language-code] -%} {{l}} {%- unless forloop.last -%}
{% endunless -%} {% endfor %} {%- else -%} From fefbeee42a83efa11de6fcea0edf767eca6f43e4 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 13:54:11 +0100 Subject: [PATCH 20/33] restructure open yaml --- _data/open.yml | 27049 +++++++++++++++++++++++++---------------------- 1 file changed, 14532 insertions(+), 12517 deletions(-) diff --git a/_data/open.yml b/_data/open.yml index 59e7e620..5f2d46bd 100644 --- a/_data/open.yml +++ b/_data/open.yml @@ -1,12744 +1,14759 @@ concepts: - - title: Open Concepts - intents: - - - concept: abelian-category - arity: 0 + + - concept: abelian-category + arity: 0 + arguments: [] + speech: en: abelian category - property: symbol - area: "category theory" - mathml: - - "Ab" - urls: - - "https://mathworld.wolfram.com/AbelianCategory.html" - - "https://en.wikipedia.org/wiki/Abelian_category" - - "https://ncatlab.org/nlab/show/abelian+category" - - "https://www.encyclopediaofmath.org/index.php/Abelian_category" - - - concept: abelian-integral - arity: 1 - en: abelian integral of $1 - property: indexed - area: "complex analysis" - mathml: - - "∫f" - urls: - - "https://mathworld.wolfram.com/AbelianIntegral.html" - - "https://en.wikipedia.org/wiki/Abelian_integral" - - "https://www.encyclopediaofmath.org/index.php/Abelian_integral" - - - concept: abundance - arity: 1 - en: abundance of $1 - property: prefix - area: "number theory" - mathml: - - "A(x)" - urls: - - "https://mathworld.wolfram.com/Abundance.html" - - - concept: abundancy - arity: 1 - en: abundancy index of $1 - property: mixfix - area: "number theory" - mathml: - - "σ(n)/n" - notation: "sigma (n) / n" - urls: - - "https://mathworld.wolfram.com/Abundancy.html" - - "https://en.wikipedia.org/wiki/Friendly_number" - - - concept: ackermann-function - arity: 1 - en: ackermann function of $1 - property: function - area: "computability theory" - mathml: - - "A(x)" - urls: - - "https://en.wikipedia.org/wiki/Ackermann_function" - - "https://www.encyclopediaofmath.org/index.php/Ackermann_function" - - "https://mathworld.wolfram.com/AckermannFunction.html" - - - concept: ad - arity: 1 - en: a d $1 - property: postfix. prefix - area: "calendar units" - mathml: - - "AD 2024" - urls: - - "https://en.wikipedia.org/wiki/Anno_Domini" - - - concept: additive-inverse - arity: 1 - en: additive inverse of $1 - property: prefix - area: "abstract algebra" - mathml: - - "-n" - urls: - - "https://en.wikipedia.org/wiki/Additive_inverse" - alias: - - opposite - - sign-change - - negation - - - concept: adiabatic-invariant-first - arity: 0 + property: symbol + subject-area: "category theory" + mathml: + - "Ab" + urls: + - "https://mathworld.wolfram.com/AbelianCategory.html" + - "https://en.wikipedia.org/wiki/Abelian_category" + - "https://ncatlab.org/nlab/show/abelian+category" + - "https://www.encyclopediaofmath.org/index.php/Abelian_category" + + - concept: abelian-integral + arity: 1 + arguments: [a1] + speech: + en: abelian integral of a1 + property: indexed + subject-area: "complex analysis" + mathml: + - "∫f" + urls: + - "https://mathworld.wolfram.com/AbelianIntegral.html" + - "https://en.wikipedia.org/wiki/Abelian_integral" + - "https://www.encyclopediaofmath.org/index.php/Abelian_integral" + + - concept: abundance + arity: 1 + arguments: [a1] + speech: + en: abundance of a1 + property: prefix + subject-area: "number theory" + mathml: + - "A(x)" + urls: + - "https://mathworld.wolfram.com/Abundance.html" + + - concept: abundancy + arity: 1 + arguments: [a1] + speech: + en: abundancy index of a1 + property: mixfix + subject-area: "number theory" + mathml: + - "σ(n)/n" + notation: "sigma (n) / n" + urls: + - "https://mathworld.wolfram.com/Abundancy.html" + - "https://en.wikipedia.org/wiki/Friendly_number" + + - concept: ackermann-function + arity: 1 + arguments: [a1] + speech: + en: ackermann function of a1 + property: function + subject-area: "computability theory" + mathml: + - "A(x)" + urls: + - "https://en.wikipedia.org/wiki/Ackermann_function" + - "https://www.encyclopediaofmath.org/index.php/Ackermann_function" + - "https://mathworld.wolfram.com/AckermannFunction.html" + + - concept: ad + arity: 1 + arguments: [a1] + speech: + en: a d a1 + property: postfix. prefix + subject-area: "calendar units" + mathml: + - "AD 2024" + urls: + - "https://en.wikipedia.org/wiki/Anno_Domini" + + - concept: additive-inverse + arity: 1 + arguments: [a1] + speech: + en: additive inverse of a1 + property: prefix + subject-area: "abstract algebra" + mathml: + - "-n" + urls: + - "https://en.wikipedia.org/wiki/Additive_inverse" + alias: + - opposite + - sign-change + - negation + + - concept: adiabatic-invariant-first + arity: 0 + arguments: [] + speech: en: adiabatic invariant first - property: symbol - area: "plasma physics" - mathml: - - "μ" - urls: - - "https://mathworld.wolfram.com/AdiabaticInvariant.html" - - "https://en.wikipedia.org/wiki/Adiabatic_invariant" - - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant" - - - concept: adiabatic-invariant-second - arity: 0 + property: symbol + subject-area: "plasma physics" + mathml: + - "μ" + urls: + - "https://mathworld.wolfram.com/AdiabaticInvariant.html" + - "https://en.wikipedia.org/wiki/Adiabatic_invariant" + - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant" + + - concept: adiabatic-invariant-second + arity: 0 + arguments: [] + speech: en: adiabatic invariant second - property: symbol - area: "plasma physics" - mathml: - - "J" - urls: - - "https://mathworld.wolfram.com/AdiabaticInvariant.html" - - "https://en.wikipedia.org/wiki/Adiabatic_invariant" - - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant" - - - concept: adiabatic-invariant-third - arity: 0 + property: symbol + subject-area: "plasma physics" + mathml: + - "J" + urls: + - "https://mathworld.wolfram.com/AdiabaticInvariant.html" + - "https://en.wikipedia.org/wiki/Adiabatic_invariant" + - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant" + + - concept: adiabatic-invariant-third + arity: 0 + arguments: [] + speech: en: adiabatic invariant third - property: symbol - area: "plasma physics" - mathml: - - "Φ" - urls: - - "https://mathworld.wolfram.com/AdiabaticInvariant.html" - - "https://en.wikipedia.org/wiki/Adiabatic_invariant" - - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant" - - - concept: adjoint - arity: 1 - en: adjoint of $1 - property: - area: - mathml: - - "G′" - - "G†" - - "Adg" - urls: - - "https://mathworld.wolfram.com/Adjoint.html" - - "https://en.wikipedia.org/wiki/Adjoint" - - "https://ncatlab.org/nlab/show/adjoint" - - - concept: adjoint-action - arity: 1 - en: adjoint action of $1 - property: "function/msub" - area: "lie algebra" - mathml: - - "ad(f)" - - "adf" - urls: - - "https://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_algebra" - - "https://en.wikipedia.org/wiki/Adjoint_representation" - - "https://ncatlab.org/nlab/show/adjoint+action" - - "https://www.encyclopediaofmath.org/index.php/Adjoint_action" - alias: - - adjoint-endomorphism - - - concept: adjoint-representation - arity: 1 - en: adjoint representation of $1 - property: function - area: "lie algebra" - mathml: - - "Ad(x)" - urls: - - "https://mathworld.wolfram.com/AdjointRepresentation.html" - - "https://en.wikipedia.org/wiki/Adjoint_representation" - - "https://ncatlab.org/nlab/show/adjoint+representation" - - - concept: adjugate - arity: 1 - en: adjugate of $1 - property: function - area: "linear algebra" - mathml: - - "adj(x)" - urls: - - "https://en.wikipedia.org/wiki/Adjugate_matrix" - - - concept: affine-group - arity: 1 - en: affine group of $1 - property: function - area: "group theory" - mathml: - - "Aff(x)" - urls: - - "https://mathworld.wolfram.com/AffineGroup.html" - - "https://en.wikipedia.org/wiki/Affine_group" - - "https://www.encyclopediaofmath.org/index.php/Affine_group" - - - concept: affine-hull - arity: 1 - en: affine hull of $1 - property: function - area: "affine geometry" - mathml: - - "aff(x)" - urls: - - "https://mathworld.wolfram.com/AffineHull.html" - - "https://en.wikipedia.org/wiki/Affine_hull" - - "https://www.encyclopediaofmath.org/index.php/Affine_hull" - - - concept: affine-line - arity: 0 + property: symbol + subject-area: "plasma physics" + mathml: + - "Φ" + urls: + - "https://mathworld.wolfram.com/AdiabaticInvariant.html" + - "https://en.wikipedia.org/wiki/Adiabatic_invariant" + - "https://www.encyclopediaofmath.org/index.php/Adiabatic_invariant" + + - concept: adjoint + arity: 1 + arguments: [a1] + speech: + en: adjoint of a1 + property: + subject-area: + mathml: + - "G′" + - "G†" + - "Adg" + urls: + - "https://mathworld.wolfram.com/Adjoint.html" + - "https://en.wikipedia.org/wiki/Adjoint" + - "https://ncatlab.org/nlab/show/adjoint" + + - concept: adjoint-action + arity: 1 + arguments: [a1] + speech: + en: adjoint action of a1 + property: "function/msub" + subject-area: "lie algebra" + mathml: + - "ad(f)" + - "adf" + urls: + - "https://en.wikipedia.org/wiki/Adjoint_representation_of_a_Lie_algebra" + - "https://en.wikipedia.org/wiki/Adjoint_representation" + - "https://ncatlab.org/nlab/show/adjoint+action" + - "https://www.encyclopediaofmath.org/index.php/Adjoint_action" + alias: + - adjoint-endomorphism + + - concept: adjoint-representation + arity: 1 + arguments: [a1] + speech: + en: adjoint representation of a1 + property: function + subject-area: "lie algebra" + mathml: + - "Ad(x)" + urls: + - "https://mathworld.wolfram.com/AdjointRepresentation.html" + - "https://en.wikipedia.org/wiki/Adjoint_representation" + - "https://ncatlab.org/nlab/show/adjoint+representation" + + - concept: adjugate + arity: 1 + arguments: [a1] + speech: + en: adjugate of a1 + property: function + subject-area: "linear algebra" + mathml: + - "adj(x)" + urls: + - "https://en.wikipedia.org/wiki/Adjugate_matrix" + + - concept: affine-group + arity: 1 + arguments: [a1] + speech: + en: affine group of a1 + property: function + subject-area: "group theory" + mathml: + - "Aff(x)" + urls: + - "https://mathworld.wolfram.com/AffineGroup.html" + - "https://en.wikipedia.org/wiki/Affine_group" + - "https://www.encyclopediaofmath.org/index.php/Affine_group" + + - concept: affine-hull + arity: 1 + arguments: [a1] + speech: + en: affine hull of a1 + property: function + subject-area: "affine geometry" + mathml: + - "aff(x)" + urls: + - "https://mathworld.wolfram.com/AffineHull.html" + - "https://en.wikipedia.org/wiki/Affine_hull" + - "https://www.encyclopediaofmath.org/index.php/Affine_hull" + + - concept: affine-line + arity: 0 + arguments: [] + speech: en: affine line - property: symbol - area: "universal algebra?" - mathml: - - "𝔸" - urls: - - "https://ncatlab.org/nlab/show/affine+line" - - - concept: airy-function - arity: 1 - en: airy function of $1 - property: function - area: "special functions" - mathml: - - "AiX" - - "BiX" - urls: - - "https://mathworld.wolfram.com/AiryFunctions.html" - - "https://en.wikipedia.org/wiki/Airy_function" - - "https://dlmf.nist.gov/9.1" - - "https://dlmf.nist.gov/9.2#i" - - "https://dlmf.nist.gov/9.2#i" - - "https://ncatlab.org/nlab/show/Airy+function" - - "https://www.encyclopediaofmath.org/index.php/Airy_functions" - - - concept: albanese-variety - arity: 1 - en: albanese variety of $1 - property: function - area: "algebraic geometry" - mathml: - - "AX" - - "AlbX" - urls: - - "https://mathworld.wolfram.com/AlbaneseVariety.html" - - "https://en.wikipedia.org/wiki/Albanese_variety" - - "https://ncatlab.org/nlab/show/Albanese+variety" - - "https://www.encyclopediaofmath.org/index.php/Albanese_variety" - - - concept: aleph - arity: 0 + property: symbol + subject-area: "universal algebra?" + mathml: + - "𝔸" + urls: + - "https://ncatlab.org/nlab/show/affine+line" + + - concept: airy-function + arity: 1 + arguments: [a1] + speech: + en: airy function of a1 + property: function + subject-area: "special functions" + mathml: + - "AiX" + - "BiX" + urls: + - "https://mathworld.wolfram.com/AiryFunctions.html" + - "https://en.wikipedia.org/wiki/Airy_function" + - "https://dlmf.nist.gov/9.1" + - "https://dlmf.nist.gov/9.2#i" + - "https://dlmf.nist.gov/9.2#i" + - "https://ncatlab.org/nlab/show/Airy+function" + - "https://www.encyclopediaofmath.org/index.php/Airy_functions" + + - concept: albanese-variety + arity: 1 + arguments: [a1] + speech: + en: albanese variety of a1 + property: function + subject-area: "algebraic geometry" + mathml: + - "AX" + - "AlbX" + urls: + - "https://mathworld.wolfram.com/AlbaneseVariety.html" + - "https://en.wikipedia.org/wiki/Albanese_variety" + - "https://ncatlab.org/nlab/show/Albanese+variety" + - "https://www.encyclopediaofmath.org/index.php/Albanese_variety" + + - concept: aleph + arity: 0 + arguments: [] + speech: en: aleph - property: symbol - area: "set theory" - mathml: - - "ℵ" - urls: - - "https://mathworld.wolfram.com/Aleph.html" - - "https://ncatlab.org/nlab/show/aleph" - - "https://www.encyclopediaofmath.org/index.php/Aleph" - - - concept: algebraics - arity: 0 + property: symbol + subject-area: "set theory" + mathml: + - "ℵ" + urls: + - "https://mathworld.wolfram.com/Aleph.html" + - "https://ncatlab.org/nlab/show/aleph" + - "https://www.encyclopediaofmath.org/index.php/Aleph" + + - concept: algebraics + arity: 0 + arguments: [] + speech: en: algebraics - property: symbol - area: "number theory" - mathml: - - "𝔸" - urls: - - "https://mathworld.wolfram.com/Algebraics.html" - - - concept: algebraic-closure - arity: 1 - en: algebraic closure of $1 - property: mover/msup - area: "algebra" - mathml: - - "A¯" - - "Aalg" - urls: - - "https://mathworld.wolfram.com/AlgebraicClosure.html" - - "https://en.wikipedia.org/wiki/Algebraic_closure" - - "https://www.encyclopediaofmath.org/index.php/Algebraic_closure" - - - concept: almost-surely - arity: 1 - en: almost surely of $1 - property: - area: "probability theory" - mathml: - - "Em.s." - urls: - - "https://en.wikipedia.org/wiki/Almost_surely" - - - concept: alternating-factorial - arity: 1 - en: alternating factorial of $1 - property: function - area: "functions" - mathml: - - "af(x)" - urls: - - "https://en.wikipedia.org/wiki/Alternating_factorial" - - - concept: alternating-group - arity: 1 - en: alternating group of $1 - property: function - area: "group theory" - mathml: - - "AX" - - "AltX" - urls: - - "https://mathworld.wolfram.com/AlternatingGroup.html" - - "https://en.wikipedia.org/wiki/Alternating_group" - - "https://www.encyclopediaofmath.org/index.php/Alternating_group" - - - concept: alternation - arity: 2 - en: $1 alternation $2 - property: infix - area: "logic" - mathml: - - "X|Y" - urls: - - "https://en.wikipedia.org/wiki/Alternation_(formal_language_theory)" - - "https://en.wikipedia.org/wiki/%E2%88%A8" - - "https://en.wikipedia.org/wiki/Logical_disjunction" - - "https://www.encyclopediaofmath.org/index.php/Alternation" - alias: - - disjunction - - or - - - concept: alternative-denial - arity: 2 - en: $1 alternative denial $2 - property: infix, prefix - area: "propositional calculus" - mathml: - - "p|q" - - "p↑q" - - "Dpq" - urls: - - "https://mathworld.wolfram.com/AlternativeDenial.html" - - "https://en.wikipedia.org/wiki/Sheffer_stroke" - alias: - - sheffer-stroke - - nand - - - concept: amalgam - arity: 5 - en: amalgam of $1 $2 $3 $4 $5 - property: fenced, 5-tuple - area: "model theory" - mathml: - - "(A,f,B,g,C)" - urls: - - "https://en.wikipedia.org/wiki/Amalgamation_property" - - "https://ncatlab.org/nlab/show/amalgamation+property" - - - concept: amalgamated-product - arity: 3 - en: Free product with amalgamation of $1 and $3 with respect to $2 - property: indexed infix - area: "group theory" - mathml: - - "A⁎CB" - urls: - - "https://math.stackexchange.com/questions/828828/amalgamated-product" - - "https://en.wikipedia.org/wiki/Free_product" - - "https://home.iiserb.ac.in/~kashyap/Group/thesis_abhay.pdf" - alias: - - amalgamated-free-product - - free-product-with-amalgamation - - - concept: analytic-manifold - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "𝔸" + urls: + - "https://mathworld.wolfram.com/Algebraics.html" + + - concept: algebraic-closure + arity: 1 + arguments: [a1] + speech: + en: algebraic closure of a1 + property: mover/msup + subject-area: "algebra" + mathml: + - "A¯" + - "Aalg" + urls: + - "https://mathworld.wolfram.com/AlgebraicClosure.html" + - "https://en.wikipedia.org/wiki/Algebraic_closure" + - "https://www.encyclopediaofmath.org/index.php/Algebraic_closure" + + - concept: almost-surely + arity: 1 + arguments: [a1] + speech: + en: almost surely of a1 + property: + subject-area: "probability theory" + mathml: + - "Em.s." + urls: + - "https://en.wikipedia.org/wiki/Almost_surely" + + - concept: alternating-factorial + arity: 1 + arguments: [a1] + speech: + en: alternating factorial of a1 + property: function + subject-area: "functions" + mathml: + - "af(x)" + urls: + - "https://en.wikipedia.org/wiki/Alternating_factorial" + + - concept: alternating-group + arity: 1 + arguments: [a1] + speech: + en: alternating group of a1 + property: function + subject-area: "group theory" + mathml: + - "AX" + - "AltX" + urls: + - "https://mathworld.wolfram.com/AlternatingGroup.html" + - "https://en.wikipedia.org/wiki/Alternating_group" + - "https://www.encyclopediaofmath.org/index.php/Alternating_group" + + - concept: alternation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 alternation a2 + property: infix + subject-area: "logic" + mathml: + - "X|Y" + urls: + - "https://en.wikipedia.org/wiki/Alternation_(formal_language_theory)" + - "https://en.wikipedia.org/wiki/%E2%88%A8" + - "https://en.wikipedia.org/wiki/Logical_disjunction" + - "https://www.encyclopediaofmath.org/index.php/Alternation" + alias: + - disjunction + - or + + - concept: alternative-denial + arity: 2 + arguments: [a1, a2] + speech: + en: a1 alternative denial a2 + property: infix, prefix + subject-area: "propositional calculus" + mathml: + - "p|q" + - "p↑q" + - "Dpq" + urls: + - "https://mathworld.wolfram.com/AlternativeDenial.html" + - "https://en.wikipedia.org/wiki/Sheffer_stroke" + alias: + - sheffer-stroke + - nand + + - concept: amalgam + arity: 5 + arguments: [a1, a2, a3, a4, a5] + speech: + en: amalgam of a1 a2 a3 a4 a5 + property: fenced, 5-tuple + subject-area: "model theory" + mathml: + - "(A,f,B,g,C)" + urls: + - "https://en.wikipedia.org/wiki/Amalgamation_property" + - "https://ncatlab.org/nlab/show/amalgamation+property" + + - concept: amalgamated-product + arity: 3 + arguments: [a1, a2, a3] + speech: + en: Free product with amalgamation of a1 and a3 with respect to a2 + property: indexed infix + subject-area: "group theory" + mathml: + - "A⁎CB" + urls: + - "https://math.stackexchange.com/questions/828828/amalgamated-product" + - "https://en.wikipedia.org/wiki/Free_product" + - "https://home.iiserb.ac.in/~kashyap/Group/thesis_abhay.pdf" + alias: + - amalgamated-free-product + - free-product-with-amalgamation + + - concept: analytic-manifold + arity: 0 + arguments: [] + speech: en: analytic manifold - property: symbol - area: "topology" - mathml: - - "Cw" - urls: - - "https://en.wikipedia.org/wiki/Analytic_manifold" - - "https://ncatlab.org/nlab/show/analytic+manifold" - - "https://www.encyclopediaofmath.org/index.php/Analytic_manifold" - - - concept: anger-function - arity: 1 - en: anger function of $1 - property: function - area: "special functions" - mathml: - - "J(x)" - urls: - - "https://mathworld.wolfram.com/AngerFunction.html" - - "https://en.wikipedia.org/wiki/Anger_function" - - "https://dlmf.nist.gov/11.10#E1" - - "https://www.encyclopediaofmath.org/index.php/Anger_function" - - - concept: angle-of-parallelism - arity: 1 - en: angle of parallelism of $1 - property: function - area: "hyperbolic geometry" - mathml: - - "Π(x)" - urls: - - "https://mathworld.wolfram.com/AngleofParallelism.html" - - "https://en.wikipedia.org/wiki/Angle_of_parallelism" - - - concept: angular-momentum - arity: 0 + property: symbol + subject-area: "topology" + mathml: + - "Cw" + urls: + - "https://en.wikipedia.org/wiki/Analytic_manifold" + - "https://ncatlab.org/nlab/show/analytic+manifold" + - "https://www.encyclopediaofmath.org/index.php/Analytic_manifold" + + - concept: anger-function + arity: 1 + arguments: [a1] + speech: + en: anger function of a1 + property: function + subject-area: "special functions" + mathml: + - "J(x)" + urls: + - "https://mathworld.wolfram.com/AngerFunction.html" + - "https://en.wikipedia.org/wiki/Anger_function" + - "https://dlmf.nist.gov/11.10#E1" + - "https://www.encyclopediaofmath.org/index.php/Anger_function" + + - concept: angle-of-parallelism + arity: 1 + arguments: [a1] + speech: + en: angle of parallelism of a1 + property: function + subject-area: "hyperbolic geometry" + mathml: + - "Π(x)" + urls: + - "https://mathworld.wolfram.com/AngleofParallelism.html" + - "https://en.wikipedia.org/wiki/Angle_of_parallelism" + + - concept: angular-momentum + arity: 0 + arguments: [] + speech: en: angular momentum - property: symbol - area: "classical mechanics" - mathml: - - "L" - urls: - - "https://en.wikipedia.org/wiki/Angular_momentum" - - "https://en.wikipedia.org/wiki/Introduction_to_angular_momentum" - - "https://ncatlab.org/nlab/show/angular+momentum" - - - concept: angular-velocity - arity: 0 + property: symbol + subject-area: "classical mechanics" + mathml: + - "L" + urls: + - "https://en.wikipedia.org/wiki/Angular_momentum" + - "https://en.wikipedia.org/wiki/Introduction_to_angular_momentum" + - "https://ncatlab.org/nlab/show/angular+momentum" + + - concept: angular-velocity + arity: 0 + arguments: [] + speech: en: angular velocity - property: symbol - area: "classical mechanics" - mathml: - - "ω" - urls: - - "https://mathworld.wolfram.com/AngularVelocity.html" - - "https://en.wikipedia.org/wiki/Angular_velocity" - - "https://ncatlab.org/nlab/show/angular+velocity" - - - concept: anharmonic-ratio - arity: 4 - en: "anharmonic ratio of $1 , $2 , $3 , $4" - property: fenced - area: "geometry" - mathml: - - "(A,B;C,D)" - urls: - - "https://mathworld.wolfram.com/AnharmonicRatio.html" - - "https://en.wikipedia.org/wiki/Cross-ratio" - - "https://www.encyclopediaofmath.org/index.php/Anharmonic_ratio" - - - concept: annihilator - arity: 1 - en: annihilator of $1 - property: function - area: "ring theory" - mathml: - - "Ann(x)" - urls: - - "https://mathworld.wolfram.com/Annihilator.html" - - "https://en.wikipedia.org/wiki/Annihilator_(ring_theory)" - - "https://www.encyclopediaofmath.org/index.php/Annihilator" - - - concept: annulus - arity: 1 - en: annulus of $1 - property: function - area: "complex analysis" - mathml: - - "ann(x)" - urls: - - "https://en.wikipedia.org/wiki/Annulus_(mathematics)" - - "https://ncatlab.org/nlab/show/annulus" - - "https://mathworld.wolfram.com/Annulus.html" - - - concept: antiparticle - arity: 1 - en: antiparticle of $1 - property: mover - area: "particle physics" - mathml: - - "p¯" - urls: - - "https://en.wikipedia.org/wiki/Antimatter" - - "https://en.wikipedia.org/wiki/Antiparticle" - alias: - - antimatter - - - concept: apartness-relation - arity: 2 - en: $1 apartness relation $2 - property: infix - area: "constructive mathematics" - mathml: - - "X#Y" - urls: - - "https://en.wikipedia.org/wiki/Apartness_relation" - - "https://ncatlab.org/nlab/show/apartness+relation" - - - concept: apery-constant - arity: 0 + property: symbol + subject-area: "classical mechanics" + mathml: + - "ω" + urls: + - "https://mathworld.wolfram.com/AngularVelocity.html" + - "https://en.wikipedia.org/wiki/Angular_velocity" + - "https://ncatlab.org/nlab/show/angular+velocity" + + - concept: anharmonic-ratio + arity: 4 + arguments: [a1, a2, a3, a4] + speech: + en: "anharmonic ratio of a1 , a2 , a3 , a4" + property: fenced + subject-area: "geometry" + mathml: + - "(A,B;C,D)" + urls: + - "https://mathworld.wolfram.com/AnharmonicRatio.html" + - "https://en.wikipedia.org/wiki/Cross-ratio" + - "https://www.encyclopediaofmath.org/index.php/Anharmonic_ratio" + + - concept: annihilator + arity: 1 + arguments: [a1] + speech: + en: annihilator of a1 + property: function + subject-area: "ring theory" + mathml: + - "Ann(x)" + urls: + - "https://mathworld.wolfram.com/Annihilator.html" + - "https://en.wikipedia.org/wiki/Annihilator_(ring_theory)" + - "https://www.encyclopediaofmath.org/index.php/Annihilator" + + - concept: annulus + arity: 1 + arguments: [a1] + speech: + en: annulus of a1 + property: function + subject-area: "complex analysis" + mathml: + - "ann(x)" + urls: + - "https://en.wikipedia.org/wiki/Annulus_(mathematics)" + - "https://ncatlab.org/nlab/show/annulus" + - "https://mathworld.wolfram.com/Annulus.html" + + - concept: antiparticle + arity: 1 + arguments: [a1] + speech: + en: antiparticle of a1 + property: mover + subject-area: "particle physics" + mathml: + - "p¯" + urls: + - "https://en.wikipedia.org/wiki/Antimatter" + - "https://en.wikipedia.org/wiki/Antiparticle" + alias: + - antimatter + + - concept: apartness-relation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 apartness relation a2 + property: infix + subject-area: "constructive mathematics" + mathml: + - "X#Y" + urls: + - "https://en.wikipedia.org/wiki/Apartness_relation" + - "https://ncatlab.org/nlab/show/apartness+relation" + + - concept: apery-constant + arity: 0 + arguments: [] + speech: en: apery constant - property: symbol - area: "special functions" - mathml: - - "ζ(3)" - urls: - - "https://mathworld.wolfram.com/AperysConstant.html" - - "https://en.wikipedia.org/wiki/Zeta(3)" - - "https://en.wikipedia.org/wiki/%CE%96(3)" - - "https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant" - - - concept: arcminute - arity: 1 - en: arcminute of $1 - property: unit - area: "SI-mentioned units" - mathml: - - "arcminX" - - "aminX" - notationa: "mo ′" - urls: - - "https://mathworld.wolfram.com/Arcminute.html" - - "https://en.wikipedia.org/wiki/Minute_of_arc" - - "https://en.wikipedia.org/wiki/Arcsecond" - - "https://en.wikipedia.org/wiki/Second_(angle)" - alias: - - minute-arc - - minute-of-arc - - - concept: arcsecond - arity: 1 - en: arcsecond of $1 - property: unit - area: "SI-mentioned units" - mathml: - - "arcsecX" - - "asecX" - notationa: "mo ′′" - urls: - - "https://mathworld.wolfram.com/Arcminute.html" - - "https://en.wikipedia.org/wiki/Minute_of_arc" - - "https://en.wikipedia.org/wiki/Arcsecond" - - "https://en.wikipedia.org/wiki/Second_(angle)" - - - concept: area - arity: 0 + property: symbol + subject-area: "special functions" + mathml: + - "ζ(3)" + urls: + - "https://mathworld.wolfram.com/AperysConstant.html" + - "https://en.wikipedia.org/wiki/Zeta(3)" + - "https://en.wikipedia.org/wiki/%CE%96(3)" + - "https://en.wikipedia.org/wiki/Ap%C3%A9ry%27s_constant" + + - concept: arcminute + arity: 1 + arguments: [a1] + speech: + en: arcminute of a1 + property: unit + subject-area: "SI-mentioned units" + mathml: + - "arcminX" + - "aminX" + notationa: "mo ′" + urls: + - "https://mathworld.wolfram.com/Arcminute.html" + - "https://en.wikipedia.org/wiki/Minute_of_arc" + - "https://en.wikipedia.org/wiki/Arcsecond" + - "https://en.wikipedia.org/wiki/Second_(angle)" + alias: + - minute-arc + - minute-of-arc + + - concept: arcsecond + arity: 1 + arguments: [a1] + speech: + en: arcsecond of a1 + property: unit + subject-area: "SI-mentioned units" + mathml: + - "arcsecX" + - "asecX" + notationa: "mo ′′" + urls: + - "https://mathworld.wolfram.com/Arcminute.html" + - "https://en.wikipedia.org/wiki/Minute_of_arc" + - "https://en.wikipedia.org/wiki/Arcsecond" + - "https://en.wikipedia.org/wiki/Second_(angle)" + + - concept: area + arity: 0 + arguments: [] + speech: en: area - property: symbol - area: "geometry" - mathml: - - "A" - urls: - - "https://mathworld.wolfram.com/Area.html" - - "https://en.wikipedia.org/wiki/Area" - - "https://www.encyclopediaofmath.org/index.php/Area" - - - concept: arf-invariant - arity: 1 - en: arf invariant of $1 - property: function - area: "geometric topology" - mathml: - - "Arf(x)" - urls: - - "https://mathworld.wolfram.com/ArfInvariant.html" - - "https://en.wikipedia.org/wiki/Arf_invariant" - - "https://en.wikipedia.org/wiki/Arf_invariant_of_a_knot" - - - concept: argument - arity: 1 - en: argument of $1 - property: function - area: "complex analysis" - mathml: - - "Arg(x)" - urls: - - "https://en.wikipedia.org/wiki/Argument_(complex_analysis)" - - - concept: arithmetic-geometric-mean - arity: 1 - en: arithmetic geometric mean of $1 - property: function - area: "special functions" - mathml: - - "agmX" - - "AGMX" - urls: - - "https://mathworld.wolfram.com/Arithmetic-GeometricMean.html" - - "https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean" - - "https://dlmf.nist.gov/19.8#i" - - "https://dlmf.nist.gov/19.8#SS1.p1" - - - concept: associated-legendre-polynomial - arity: 2 - en: associated legendre polynomial of degree $1 and order $2 - property: function - area: "special functions" - mathml: - - "Pℓm(x)" - urls: - - "https://mathworld.wolfram.com/AssociatedLegendrePolynomial.html" - - "https://en.wikipedia.org/wiki/Associated_Legendre_polynomials" - - "https://dlmf.nist.gov/18.30#E6" - - - concept: associator - arity: 3 - en: associator of $1, $2, $3 - property: fenced - area: "algebra" - mathml: - - "[a,b,c]" - urls: - - "https://mathworld.wolfram.com/Associator.html" - - "https://en.wikipedia.org/wiki/Associator" - - "https://ncatlab.org/nlab/show/associator" - - "https://www.encyclopediaofmath.org/index.php/Associator" - - - concept: automorphism-group - arity: 1 - en: automorphism group of $1 - property: function - area: "group theory" - mathml: - - "Aut(x)" - urls: - - "https://mathworld.wolfram.com/AutomorphismGroup.html" - - "https://en.wikipedia.org/wiki/Automorphism" - - - concept: backward-difference - arity: 1 - en: backward difference of $1 - property: operator - area: "special functions" - mathml: - - "∇(x)" - urls: - - "https://mathworld.wolfram.com/BackwardDifference.html" - - "https://en.wikipedia.org/wiki/Finite_difference" - - "https://dlmf.nist.gov/18.1#EGx2" - - - concept: baire-space - arity: 0 + property: symbol + subject-area: "geometry" + mathml: + - "A" + urls: + - "https://mathworld.wolfram.com/Area.html" + - "https://en.wikipedia.org/wiki/Area" + - "https://www.encyclopediaofmath.org/index.php/Area" + + - concept: arf-invariant + arity: 1 + arguments: [a1] + speech: + en: arf invariant of a1 + property: function + subject-area: "geometric topology" + mathml: + - "Arf(x)" + urls: + - "https://mathworld.wolfram.com/ArfInvariant.html" + - "https://en.wikipedia.org/wiki/Arf_invariant" + - "https://en.wikipedia.org/wiki/Arf_invariant_of_a_knot" + + - concept: argument + arity: 1 + arguments: [a1] + speech: + en: argument of a1 + property: function + subject-area: "complex analysis" + mathml: + - "Arg(x)" + urls: + - "https://en.wikipedia.org/wiki/Argument_(complex_analysis)" + + - concept: arithmetic-geometric-mean + arity: 1 + arguments: [a1] + speech: + en: arithmetic geometric mean of a1 + property: function + subject-area: "special functions" + mathml: + - "agmX" + - "AGMX" + urls: + - "https://mathworld.wolfram.com/Arithmetic-GeometricMean.html" + - "https://en.wikipedia.org/wiki/Arithmetic%E2%80%93geometric_mean" + - "https://dlmf.nist.gov/19.8#i" + - "https://dlmf.nist.gov/19.8#SS1.p1" + + - concept: associated-legendre-polynomial + arity: 2 + arguments: [a1, a2] + speech: + en: associated legendre polynomial of degree a1 and order a2 + property: function + subject-area: "special functions" + mathml: + - "Pℓm(x)" + urls: + - "https://mathworld.wolfram.com/AssociatedLegendrePolynomial.html" + - "https://en.wikipedia.org/wiki/Associated_Legendre_polynomials" + - "https://dlmf.nist.gov/18.30#E6" + + - concept: associator + arity: 3 + arguments: [a1, a2, a3] + speech: + en: associator of a1, a2, a3 + property: fenced + subject-area: "algebra" + mathml: + - "[a,b,c]" + urls: + - "https://mathworld.wolfram.com/Associator.html" + - "https://en.wikipedia.org/wiki/Associator" + - "https://ncatlab.org/nlab/show/associator" + - "https://www.encyclopediaofmath.org/index.php/Associator" + + - concept: automorphism-group + arity: 1 + arguments: [a1] + speech: + en: automorphism group of a1 + property: function + subject-area: "group theory" + mathml: + - "Aut(x)" + urls: + - "https://mathworld.wolfram.com/AutomorphismGroup.html" + - "https://en.wikipedia.org/wiki/Automorphism" + + - concept: backward-difference + arity: 1 + arguments: [a1] + speech: + en: backward difference of a1 + property: operator + subject-area: "special functions" + mathml: + - "∇(x)" + urls: + - "https://mathworld.wolfram.com/BackwardDifference.html" + - "https://en.wikipedia.org/wiki/Finite_difference" + - "https://dlmf.nist.gov/18.1#EGx2" + + - concept: baire-space + arity: 0 + arguments: [] + speech: en: baire space - property: symbol - area: "set theory" - mathml: - - "NN" - - "ωω" - urls: - - "https://mathworld.wolfram.com/BaireSpace.html" - - "https://en.wikipedia.org/wiki/Baire_space" - - "https://en.wikipedia.org/wiki/Baire_space_(set_theory)" - - "https://ncatlab.org/nlab/show/Baire+space" - - "https://www.encyclopediaofmath.org/index.php/Baire_space" - - - concept: barrel - arity: 1 - en: $1 barrels - property: unit - area: "imperial units" - mathml: - - "x bbl" - urls: - - "https://mathworld.wolfram.com/Barrel.html" - - "https://en.wikipedia.org/wiki/Barrelled_space" - - "https://en.wikipedia.org/wiki/Barrel_(unit)" - - - concept: bateman-function - arity: 2 + property: symbol + subject-area: "set theory" + mathml: + - "NN" + - "ωω" + urls: + - "https://mathworld.wolfram.com/BaireSpace.html" + - "https://en.wikipedia.org/wiki/Baire_space" + - "https://en.wikipedia.org/wiki/Baire_space_(set_theory)" + - "https://ncatlab.org/nlab/show/Baire+space" + - "https://www.encyclopediaofmath.org/index.php/Baire_space" + + - concept: barrel + arity: 1 + arguments: [a1] + speech: + en: a1 barrels + property: unit + subject-area: "imperial units" + mathml: + - "x bbl" + urls: + - "https://mathworld.wolfram.com/Barrel.html" + - "https://en.wikipedia.org/wiki/Barrelled_space" + - "https://en.wikipedia.org/wiki/Barrel_(unit)" + + - concept: bateman-function + arity: 2 + arguments: [a1, a2] + speech: en: bateman function - property: function - area: "special functions" - mathml: - - "kv(x)" - urls: - - "https://mathworld.wolfram.com/BatemanFunction.html" - - "https://en.wikipedia.org/wiki/Bateman_function" - - "https://www.encyclopediaofmath.org/index.php/Bateman_function" - - - concept: baumslag-solitar-group - arity: 2 + property: function + subject-area: "special functions" + mathml: + - "kv(x)" + urls: + - "https://mathworld.wolfram.com/BatemanFunction.html" + - "https://en.wikipedia.org/wiki/Bateman_function" + - "https://www.encyclopediaofmath.org/index.php/Bateman_function" + + - concept: baumslag-solitar-group + arity: 2 + arguments: [a1, a2] + speech: en: baumslag solitar group - property: function - area: "group theory" - mathml: - - "BS(m,n)" - urls: - - "https://en.wikipedia.org/wiki/Baumslag%E2%80%93Solitar_group" - - "https://www.encyclopediaofmath.org/index.php/Baumslag-Solitar_group" - - - concept: bc - arity: 1 - en: $1 b c - property: postfix - area: "calendar units" - mathml: - - "2024 BC" - urls: - - "https://en.wikipedia.org/wiki/Anno_Domini" - - - concept: beatty-sequence - arity: 1 - en: $1th beatty sequence - property: "indexed symbol" - area: "number theory" - mathml: - - "𝓑r" - urls: - - "https://mathworld.wolfram.com/BeattySequence.html" - - "https://en.wikipedia.org/wiki/Beatty_sequence" - - - concept: bell-number - arity: 1 - en: $1th bell number - property: "indexed symbol" - area: "number theory" - mathml: - - "Bn" - urls: - - "https://mathworld.wolfram.com/BellNumber.html" - - "https://en.wikipedia.org/wiki/Bell_number" - - "https://dlmf.nist.gov/26.7#i" - - "https://www.encyclopediaofmath.org/index.php/Bell_numbers" - - - concept: bell-polynomial - arity: ">=0" - en: $1th bell polynomial of $2, $3, ... - property: "indexed function" - area: "polynomials" - notation: "mrow msub B $1 ($2, ... $n" - urls: - - "https://mathworld.wolfram.com/BellPolynomial.html" - - "https://en.wikipedia.org/wiki/Bell_polynomials" - - "https://www.encyclopediaofmath.org/index.php/Bell_polynomial" - - - concept: berezin-integral - arity: 1 - en: berezin integral of $1 - property: indexed - area: "mathematical physics" - mathml: - - "∫f" - urls: - - "https://en.wikipedia.org/wiki/Berezin_integral" - - "https://en.wikipedia.org/wiki/Grassmann_integral" - - "https://ncatlab.org/nlab/show/Berezin+integral" - - - concept: bergman-space - arity: 2 - en: $1th bergman space of $2 - property: "indexed function" - area: "complex analysis" - mathml: - - "An(X)" - urls: - - "https://mathworld.wolfram.com/BergmanSpace.html" - - "https://en.wikipedia.org/wiki/Bergman_space" - - "https://www.encyclopediaofmath.org/index.php/Bergman_spaces" - - - concept: bernoulli-number - arity: 1 - en: $1th bernoulli number - property: "indexed symbol" - area: "number theory" - mathml: - - "Bx" - urls: - - "https://mathworld.wolfram.com/BernoulliNumber.html" - - "https://en.wikipedia.org/wiki/Bernoulli_number" - - "https://dlmf.nist.gov/24.1#P1" - - "https://dlmf.nist.gov/24.2#i" - - "https://ncatlab.org/nlab/show/Bernoulli+number" - - "https://www.encyclopediaofmath.org/index.php/Bernoulli_numbers" - - - concept: bernoulli-polynomial - arity: 2 - en: bernoulli polynomial $1 $2 - property: "indexed function" - area: "number theory" - mathml: - - "Bn(X)" - urls: - - "https://mathworld.wolfram.com/BernoulliPolynomial.html" - - "https://en.wikipedia.org/wiki/Bernoulli_polynomials" - - "https://dlmf.nist.gov/24.1#P1" - - "https://dlmf.nist.gov/24.2#i" - - "https://www.encyclopediaofmath.org/index.php/Bernoulli_polynomials" - - - concept: bessel-function - arity: 2 - en: $1th bessel function of $2 - property: "indexed function" - area: "special functions" - mathml: - - "Jn(X)" - urls: - - "https://mathworld.wolfram.com/BesselFunction.html" - - "https://en.wikipedia.org/wiki/Bessel_function" - - "https://dlmf.nist.gov/10.1" - - "https://www.encyclopediaofmath.org/index.php/Bessel_functions" - - - concept: bessel-function-of-second-kind - arity: 2 - en: $1th bessel function of second kind of $2 - property: "indexed function" - area: "special functions" - mathml: - - "Yn(X)" - urls: - - "https://mathworld.wolfram.com/BesselFunctionoftheSecondKind.html" - - "https://dlmf.nist.gov/10.2#E3" - - "https://www.encyclopediaofmath.org/index.php/Bessel_function_of_the_second_kind" - - - concept: bessel-polynomial - arity: 2 - en: $1th bessel polynomial of $2 - property: "indexed function" - area: "special functions" - mathml: - - "yn(x)" - urls: - - "https://mathworld.wolfram.com/BesselPolynomial.html" - - "https://en.wikipedia.org/wiki/Bessel_polynomials" - - "https://dlmf.nist.gov/18.34#E1" - - "https://www.encyclopediaofmath.org/index.php/Bessel_polynomials" - - - concept: beta-distribution - arity: 1 - en: beta distribution of $1 - property: function - area: "probability theory" - mathml: - - "BX" - - "BetaX" - - "𝓑𝓮X" - - "βX" - urls: - - "https://mathworld.wolfram.com/BetaDistribution.html" - - "https://en.wikipedia.org/wiki/Beta_distribution" - - - concept: beta-function - arity: 1 - en: beta function of $1 - property: function - area: "special functions" - mathml: - - "BX" - - "βX" - urls: - - "https://mathworld.wolfram.com/BetaFunction.html" - - "https://en.wikipedia.org/wiki/%CE%92(x,_y)" - - "https://en.wikipedia.org/wiki/Beta_function_(physics)" - - "https://en.wikipedia.org/wiki/Beta_function" - - "https://dlmf.nist.gov/5.12" - - "https://dlmf.nist.gov/5.12#E1" - - "https://ncatlab.org/nlab/show/beta+function" - alias: - - euler-integral-of-the-first-kind - - - concept: betti-number - arity: 1 - en: $1th betti number - property: "indexed symbol" - area: "graph theory" - mathml: - - "bx" - urls: - - "https://mathworld.wolfram.com/BettiNumber.html" - - "https://en.wikipedia.org/wiki/Betti_number" - - "https://ncatlab.org/nlab/show/Betti+number" - - "https://www.encyclopediaofmath.org/index.php/Betti_number" - - - concept: biconditional - arity: 2 - en: $1 biconditional $2 - property: infix - area: "logic" - mathml: - - "X⇔Y" - - "X≡Y" - - "XiffY" - urls: - - "https://mathworld.wolfram.com/Biconditional.html" - - "https://ncatlab.org/nlab/show/biconditional" - alias: - - iff - - if-and-only-if - - - concept: big-O - arity: 1 - en: big O of $1 - property: prefix - area: "complexity" - mathml: - - "OX" - urls: - - "https://en.wikipedia.org/wiki/Big_O_notation" - - "https://mathworld.wolfram.com/O.html" - - - concept: bigeometric-integral - arity: 1 - en: bigeometric integral of $1 - property: indexed - area: "calculus" - mathml: - - "∫(f)" - urls: - - "https://en.wikipedia.org/wiki/Product_integral" - - - concept: bijection - arity: 3 - en: bijection, $1, of $2 to $3 - property: mixfix - area: "set theory" - mathml: - - "f:X⤖Y" - urls: - - "https://en.wikipedia.org/wiki/Bijection#Definition" - - - concept: binary-golay-code - arity: 0 + property: function + subject-area: "group theory" + mathml: + - "BS(m,n)" + urls: + - "https://en.wikipedia.org/wiki/Baumslag%E2%80%93Solitar_group" + - "https://www.encyclopediaofmath.org/index.php/Baumslag-Solitar_group" + + - concept: bc + arity: 1 + arguments: [a1] + speech: + en: a1 b c + property: postfix + subject-area: "calendar units" + mathml: + - "2024 BC" + urls: + - "https://en.wikipedia.org/wiki/Anno_Domini" + + - concept: beatty-sequence + arity: 1 + arguments: [a1] + speech: + en: a1th beatty sequence + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "𝓑r" + urls: + - "https://mathworld.wolfram.com/BeattySequence.html" + - "https://en.wikipedia.org/wiki/Beatty_sequence" + + - concept: bell-number + arity: 1 + arguments: [a1] + speech: + en: a1th bell number + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Bn" + urls: + - "https://mathworld.wolfram.com/BellNumber.html" + - "https://en.wikipedia.org/wiki/Bell_number" + - "https://dlmf.nist.gov/26.7#i" + - "https://www.encyclopediaofmath.org/index.php/Bell_numbers" + + - concept: bell-polynomial + arity: ">=0" + speech: + en: a1th bell polynomial of a2, a3, ... + property: "indexed function" + subject-area: "polynomials" + notation: "mrow msub B a1 (a2, ... $n" + urls: + - "https://mathworld.wolfram.com/BellPolynomial.html" + - "https://en.wikipedia.org/wiki/Bell_polynomials" + - "https://www.encyclopediaofmath.org/index.php/Bell_polynomial" + + - concept: berezin-integral + arity: 1 + arguments: [a1] + speech: + en: berezin integral of a1 + property: indexed + subject-area: "mathematical physics" + mathml: + - "∫f" + urls: + - "https://en.wikipedia.org/wiki/Berezin_integral" + - "https://en.wikipedia.org/wiki/Grassmann_integral" + - "https://ncatlab.org/nlab/show/Berezin+integral" + + - concept: bergman-space + arity: 2 + arguments: [a1, a2] + speech: + en: a1th bergman space of a2 + property: "indexed function" + subject-area: "complex analysis" + mathml: + - "An(X)" + urls: + - "https://mathworld.wolfram.com/BergmanSpace.html" + - "https://en.wikipedia.org/wiki/Bergman_space" + - "https://www.encyclopediaofmath.org/index.php/Bergman_spaces" + + - concept: bernoulli-number + arity: 1 + arguments: [a1] + speech: + en: a1th bernoulli number + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Bx" + urls: + - "https://mathworld.wolfram.com/BernoulliNumber.html" + - "https://en.wikipedia.org/wiki/Bernoulli_number" + - "https://dlmf.nist.gov/24.1#P1" + - "https://dlmf.nist.gov/24.2#i" + - "https://ncatlab.org/nlab/show/Bernoulli+number" + - "https://www.encyclopediaofmath.org/index.php/Bernoulli_numbers" + + - concept: bernoulli-polynomial + arity: 2 + arguments: [a1, a2] + speech: + en: bernoulli polynomial a1 a2 + property: "indexed function" + subject-area: "number theory" + mathml: + - "Bn(X)" + urls: + - "https://mathworld.wolfram.com/BernoulliPolynomial.html" + - "https://en.wikipedia.org/wiki/Bernoulli_polynomials" + - "https://dlmf.nist.gov/24.1#P1" + - "https://dlmf.nist.gov/24.2#i" + - "https://www.encyclopediaofmath.org/index.php/Bernoulli_polynomials" + + - concept: bessel-function + arity: 2 + arguments: [a1, a2] + speech: + en: a1th bessel function of a2 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Jn(X)" + urls: + - "https://mathworld.wolfram.com/BesselFunction.html" + - "https://en.wikipedia.org/wiki/Bessel_function" + - "https://dlmf.nist.gov/10.1" + - "https://www.encyclopediaofmath.org/index.php/Bessel_functions" + + - concept: bessel-function-of-second-kind + arity: 2 + arguments: [a1, a2] + speech: + en: a1th bessel function of second kind of a2 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Yn(X)" + urls: + - "https://mathworld.wolfram.com/BesselFunctionoftheSecondKind.html" + - "https://dlmf.nist.gov/10.2#E3" + - "https://www.encyclopediaofmath.org/index.php/Bessel_function_of_the_second_kind" + + - concept: bessel-polynomial + arity: 2 + arguments: [a1, a2] + speech: + en: a1th bessel polynomial of a2 + property: "indexed function" + subject-area: "special functions" + mathml: + - "yn(x)" + urls: + - "https://mathworld.wolfram.com/BesselPolynomial.html" + - "https://en.wikipedia.org/wiki/Bessel_polynomials" + - "https://dlmf.nist.gov/18.34#E1" + - "https://www.encyclopediaofmath.org/index.php/Bessel_polynomials" + + - concept: beta-distribution + arity: 1 + arguments: [a1] + speech: + en: beta distribution of a1 + property: function + subject-area: "probability theory" + mathml: + - "BX" + - "BetaX" + - "𝓑𝓮X" + - "βX" + urls: + - "https://mathworld.wolfram.com/BetaDistribution.html" + - "https://en.wikipedia.org/wiki/Beta_distribution" + + - concept: beta-function + arity: 1 + arguments: [a1] + speech: + en: beta function of a1 + property: function + subject-area: "special functions" + mathml: + - "BX" + - "βX" + urls: + - "https://mathworld.wolfram.com/BetaFunction.html" + - "https://en.wikipedia.org/wiki/%CE%92(x,_y)" + - "https://en.wikipedia.org/wiki/Beta_function_(physics)" + - "https://en.wikipedia.org/wiki/Beta_function" + - "https://dlmf.nist.gov/5.12" + - "https://dlmf.nist.gov/5.12#E1" + - "https://ncatlab.org/nlab/show/beta+function" + alias: + - euler-integral-of-the-first-kind + + - concept: betti-number + arity: 1 + arguments: [a1] + speech: + en: a1th betti number + property: "indexed symbol" + subject-area: "graph theory" + mathml: + - "bx" + urls: + - "https://mathworld.wolfram.com/BettiNumber.html" + - "https://en.wikipedia.org/wiki/Betti_number" + - "https://ncatlab.org/nlab/show/Betti+number" + - "https://www.encyclopediaofmath.org/index.php/Betti_number" + + - concept: biconditional + arity: 2 + arguments: [a1, a2] + speech: + en: a1 biconditional a2 + property: infix + subject-area: "logic" + mathml: + - "X⇔Y" + - "X≡Y" + - "XiffY" + urls: + - "https://mathworld.wolfram.com/Biconditional.html" + - "https://ncatlab.org/nlab/show/biconditional" + alias: + - iff + - if-and-only-if + + - concept: big-O + arity: 1 + arguments: [a1] + speech: + en: big O of a1 + property: prefix + subject-area: "complexity" + mathml: + - "OX" + urls: + - "https://en.wikipedia.org/wiki/Big_O_notation" + - "https://mathworld.wolfram.com/O.html" + + - concept: bigeometric-integral + arity: 1 + arguments: [a1] + speech: + en: bigeometric integral of a1 + property: indexed + subject-area: "calculus" + mathml: + - "∫(f)" + urls: + - "https://en.wikipedia.org/wiki/Product_integral" + + - concept: bijection + arity: 3 + arguments: [a1, a2, a3] + speech: + en: bijection, a1, of a2 to a3 + property: mixfix + subject-area: "set theory" + mathml: + - "f:X⤖Y" + urls: + - "https://en.wikipedia.org/wiki/Bijection#Definition" + + - concept: binary-golay-code + arity: 0 + arguments: [] + speech: en: binary golay code - property: symbol - area: "coding theory" - mathml: - - "G23" - urls: - - "https://mathworld.wolfram.com/BinaryGolayCode.html" - - "https://ncatlab.org/nlab/show/binary+Golay+code" - - - concept: binomial-coefficient - arity: 2 - en: binomial coefficient $1 choose $2 - property: "indexed function" - area: "combinatorics" - mathml: - - "(nk)" - - "Ckn" - urls: - - "https://mathworld.wolfram.com/BinomialCoefficient.html" - - "https://en.wikipedia.org/wiki/Binomial_coefficient" - - "https://dlmf.nist.gov/1.2#E1" - - "https://dlmf.nist.gov/26.3#SS1.p1" - - "https://www.encyclopediaofmath.org/index.php/Binomial_coefficients" - alias: - - combination - - - concept: binomial-distribution - arity: 2 - en: binomial distribution $1 $2 - property: function - area: "probability theory" - mathml: - - "B(n,p)" - urls: - - "https://mathworld.wolfram.com/BinomialDistribution.html" - - "https://en.wikipedia.org/wiki/Binomial_distribution" - - "https://www.encyclopediaofmath.org/index.php/Binomial_distribution" - - - concept: bit - arity: 0 + property: symbol + subject-area: "coding theory" + mathml: + - "G23" + urls: + - "https://mathworld.wolfram.com/BinaryGolayCode.html" + - "https://ncatlab.org/nlab/show/binary+Golay+code" + + - concept: binomial-coefficient + arity: 2 + arguments: [a1, a2] + speech: + en: binomial coefficient a1 choose a2 + property: "indexed function" + subject-area: "combinatorics" + mathml: + - "(nk)" + - "Ckn" + urls: + - "https://mathworld.wolfram.com/BinomialCoefficient.html" + - "https://en.wikipedia.org/wiki/Binomial_coefficient" + - "https://dlmf.nist.gov/1.2#E1" + - "https://dlmf.nist.gov/26.3#SS1.p1" + - "https://www.encyclopediaofmath.org/index.php/Binomial_coefficients" + alias: + - combination + + - concept: binomial-distribution + arity: 2 + arguments: [a1, a2] + speech: + en: binomial distribution a1 a2 + property: function + subject-area: "probability theory" + mathml: + - "B(n,p)" + urls: + - "https://mathworld.wolfram.com/BinomialDistribution.html" + - "https://en.wikipedia.org/wiki/Binomial_distribution" + - "https://www.encyclopediaofmath.org/index.php/Binomial_distribution" + + - concept: bit + arity: 0 + arguments: [] + speech: en: bit - property: symbol - area: "computer science" - mathml: - - "0" - - "1" - urls: - - "https://mathworld.wolfram.com/Bit.html" - - "https://en.wikipedia.org/wiki/Bit" - - "https://www.encyclopediaofmath.org/index.php/Bit" - - - concept: bipolar-set - arity: 1 - en: bipolar set of $1 - property: msup - area: "functional analysis" - mathml: - - "X°°" - urls: - - "https://en.wikipedia.org/wiki/Polar_set" - - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" - - "https://www.encyclopediaofmath.org/index.php/Polar_set" - - - concept: biquaternion - arity: 1 - en: biquaternion of $1 - property: mtable - area: "ring theory" - mathml: - - "(u+hvw+hx−w+hxu−hv)" - urls: - - "https://en.wikipedia.org/wiki/Biquaternion#Linear_representation" - - - concept: blaschke-product - arity: 1 - en: blaschke product of $1 - property: function - area: "complex analysis" - mathml: - - "B(x)" - urls: - - "https://mathworld.wolfram.com/BlaschkeProduct.html" - - "https://en.wikipedia.org/wiki/Blaschke_product" - - "https://www.encyclopediaofmath.org/index.php/Blaschke_product" - - - concept: bloch-constant - arity: 0 + property: symbol + subject-area: "computer science" + mathml: + - "0" + - "1" + urls: + - "https://mathworld.wolfram.com/Bit.html" + - "https://en.wikipedia.org/wiki/Bit" + - "https://www.encyclopediaofmath.org/index.php/Bit" + + - concept: bipolar-set + arity: 1 + arguments: [a1] + speech: + en: bipolar set of a1 + property: msup + subject-area: "functional analysis" + mathml: + - "X°°" + urls: + - "https://en.wikipedia.org/wiki/Polar_set" + - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" + - "https://www.encyclopediaofmath.org/index.php/Polar_set" + + - concept: biquaternion + arity: 1 + arguments: [a1] + speech: + en: biquaternion of a1 + property: mtable + subject-area: "ring theory" + mathml: + - "(u+hvw+hx−w+hxu−hv)" + urls: + - "https://en.wikipedia.org/wiki/Biquaternion#Linear_representation" + + - concept: blaschke-product + arity: 1 + arguments: [a1] + speech: + en: blaschke product of a1 + property: function + subject-area: "complex analysis" + mathml: + - "B(x)" + urls: + - "https://mathworld.wolfram.com/BlaschkeProduct.html" + - "https://en.wikipedia.org/wiki/Blaschke_product" + - "https://www.encyclopediaofmath.org/index.php/Blaschke_product" + + - concept: bloch-constant + arity: 0 + arguments: [] + speech: en: bloch constant - property: symbol - area: "complex analysis" - mathml: - - "B" - urls: - - "https://mathworld.wolfram.com/BlochConstant.html" - - "https://www.encyclopediaofmath.org/index.php/Bloch_constant" - - - concept: boolean-domain - arity: 0 + property: symbol + subject-area: "complex analysis" + mathml: + - "B" + urls: + - "https://mathworld.wolfram.com/BlochConstant.html" + - "https://www.encyclopediaofmath.org/index.php/Bloch_constant" + + - concept: boolean-domain + arity: 0 + arguments: [] + speech: en: boolean domain - property: symbol - area: "abstract algebra" - mathml: - - "𝔹" - urls: - - "https://en.wikipedia.org/wiki/Boolean_domain" - - "https://ncatlab.org/nlab/show/boolean+domain" - - - concept: bottom-type - arity: 0 + property: symbol + subject-area: "abstract algebra" + mathml: + - "𝔹" + urls: + - "https://en.wikipedia.org/wiki/Boolean_domain" + - "https://ncatlab.org/nlab/show/boolean+domain" + + - concept: bottom-type + arity: 0 + arguments: [] + speech: en: bottom type - property: symbol - area: "category theory" - mathml: - - "⊥" - urls: - - "https://ncatlab.org/nlab/show/bottom" - - "https://en.wikipedia.org/wiki/Bottom_type" - alias: - - empty-type - - bottom - - - concept: bottom-element - arity: 0 + property: symbol + subject-area: "category theory" + mathml: + - "⊥" + urls: + - "https://ncatlab.org/nlab/show/bottom" + - "https://en.wikipedia.org/wiki/Bottom_type" + alias: + - empty-type + - bottom + + - concept: bottom-element + arity: 0 + arguments: [] + speech: en: bottom element - property: symbol - area: "order theory" - mathml: - - "⊥" - urls: - - "https://en.wikipedia.org/wiki/Greatest_element_and_least_element" - alias: - - bottom - - least-element - - - concept: boundary - arity: 1 - en: boundary of $1 - property: function - area: "topology" - mathml: - - "bdX" - - "frX" - - "∂X" - urls: - - "https://mathworld.wolfram.com/Boundary.html" - - "https://en.wikipedia.org/wiki/Boundary_(topology)" - - "https://ncatlab.org/nlab/show/boundary" - - "https://www.encyclopediaofmath.org/index.php/Boundary" - alias: - - frontier - - - concept: bounded-variation - arity: 1 - en: bounded variation of $1 - property: function - area: "analysis" - mathml: - - "BV(x)" - urls: - - "https://mathworld.wolfram.com/BoundedVariation.html" - - "https://en.wikipedia.org/wiki/Bounded_variation" - - - concept: box-product - arity: 2 - en: $1 box product $2 - property: infix - area: "graph theory" - mathml: - - "X☐Y" - urls: - - "https://en.wikipedia.org/wiki/Cartesian_product_of_graphs" - alias: - - cartesian-product - - - concept: brauer-group - arity: 1 - en: brauer group of $1 - property: function - area: "group theory" - mathml: - - "Br(x)" - urls: - - "https://mathworld.wolfram.com/BrauerGroup.html" - - "https://en.wikipedia.org/wiki/Brauer_group" - - "https://ncatlab.org/nlab/show/Brauer+group" - - "https://www.encyclopediaofmath.org/index.php/Brauer_group" - - - concept: brun-constant - arity: 0 + property: symbol + subject-area: "order theory" + mathml: + - "⊥" + urls: + - "https://en.wikipedia.org/wiki/Greatest_element_and_least_element" + alias: + - bottom + - least-element + + - concept: boundary + arity: 1 + arguments: [a1] + speech: + en: boundary of a1 + property: function + subject-area: "topology" + mathml: + - "bdX" + - "frX" + - "∂X" + urls: + - "https://mathworld.wolfram.com/Boundary.html" + - "https://en.wikipedia.org/wiki/Boundary_(topology)" + - "https://ncatlab.org/nlab/show/boundary" + - "https://www.encyclopediaofmath.org/index.php/Boundary" + alias: + - frontier + + - concept: bounded-variation + arity: 1 + arguments: [a1] + speech: + en: bounded variation of a1 + property: function + subject-area: "analysis" + mathml: + - "BV(x)" + urls: + - "https://mathworld.wolfram.com/BoundedVariation.html" + - "https://en.wikipedia.org/wiki/Bounded_variation" + + - concept: box-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 box product a2 + property: infix + subject-area: "graph theory" + mathml: + - "X☐Y" + urls: + - "https://en.wikipedia.org/wiki/Cartesian_product_of_graphs" + alias: + - cartesian-product + + - concept: brauer-group + arity: 1 + arguments: [a1] + speech: + en: brauer group of a1 + property: function + subject-area: "group theory" + mathml: + - "Br(x)" + urls: + - "https://mathworld.wolfram.com/BrauerGroup.html" + - "https://en.wikipedia.org/wiki/Brauer_group" + - "https://ncatlab.org/nlab/show/Brauer+group" + - "https://www.encyclopediaofmath.org/index.php/Brauer_group" + + - concept: brun-constant + arity: 0 + arguments: [] + speech: en: brun constant - property: symbol - area: "number theory" - mathml: - - "B4" - urls: - - "https://mathworld.wolfram.com/BrunsConstant.html" - - "https://en.wikipedia.org/wiki/Brun%27s_theorem" - - - concept: burnside-group - arity: 1 - en: burnside group of $1 - property: function - area: "group theory" - mathml: - - "B(x)" - urls: - - "https://www.encyclopediaofmath.org/index.php/Burnside_group" - - - concept: cahen-constant - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "B4" + urls: + - "https://mathworld.wolfram.com/BrunsConstant.html" + - "https://en.wikipedia.org/wiki/Brun%27s_theorem" + + - concept: burnside-group + arity: 1 + arguments: [a1] + speech: + en: burnside group of a1 + property: function + subject-area: "group theory" + mathml: + - "B(x)" + urls: + - "https://www.encyclopediaofmath.org/index.php/Burnside_group" + + - concept: cahen-constant + arity: 0 + arguments: [] + speech: en: cahen constant - property: symbol - area: "number theory" - mathml: - - "C" - urls: - - "https://mathworld.wolfram.com/CahensConstant.html" - - "https://en.wikipedia.org/wiki/Cahen%27s_constant" - - - concept: calderon-toeplitz-operator - arity: 2 - en: calderon toeplitz operator $1 $2 - property: "indexed symbol" - area: "operator theory" - mathml: - - "Tbψ" - urls: - - "https://www.encyclopediaofmath.org/index.php/Calderon-Toeplitz_operator" - - - concept: canonical-commutation-relation - arity: 2 + property: symbol + subject-area: "number theory" + mathml: + - "C" + urls: + - "https://mathworld.wolfram.com/CahensConstant.html" + - "https://en.wikipedia.org/wiki/Cahen%27s_constant" + + - concept: calderon-toeplitz-operator + arity: 2 + arguments: [a1, a2] + speech: + en: calderon toeplitz operator a1 a2 + property: "indexed symbol" + subject-area: "operator theory" + mathml: + - "Tbψ" + urls: + - "https://www.encyclopediaofmath.org/index.php/Calderon-Toeplitz_operator" + + - concept: canonical-commutation-relation + arity: 2 + arguments: [a1, a2] + speech: en: canonical commutation relation - property: fenced - area: "quantum mechanics" - mathml: - - "[x,y]" - urls: - - "https://en.wikipedia.org/wiki/Canonical_commutation_relation" - - - concept: cap-product - arity: 2 - en: $1 cap product $2 - property: infix - area: "algebraic topology" - mathml: - - "X⌢Y" - urls: - - "https://en.wikipedia.org/wiki/Cap_product" - - "https://ncatlab.org/nlab/show/cap+product" - - - concept: cardinality - arity: 1 - en: cardinality of $1 - property: many - area: "set theory" - mathml: - - "#X" - - "card(X)" - urls: - - "https://mathworld.wolfram.com/Cardinality.html" - - "https://en.wikipedia.org/wiki/Cardinality" - - "https://www.encyclopediaofmath.org/index.php/Cardinality" - alias: - - size - - - concept: carmichael-function - arity: 1 - en: carmichael function of $1 - property: function - area: "number theory" - mathml: - - "λ(x)" - urls: - - "https://mathworld.wolfram.com/CarmichaelFunction.html" - - "https://en.wikipedia.org/wiki/Carmichael_function" - - - concept: cartesian-product - arity: 2 - en: $1 cartesian product $2 - property: infix - area: "set theory" - mathml: - - "X×Y" - urls: - - "https://mathworld.wolfram.com/CartesianProduct.html" - - "https://en.wikipedia.org/wiki/Cartesian_product" - - "https://en.wikipedia.org/wiki/Cartesian_product_of_graphs" - - "https://ncatlab.org/nlab/show/cartesian+product" - - "https://www.encyclopediaofmath.org/index.php/Cartesian_product" - - - concept: casimir-element - arity: 0 + property: fenced + subject-area: "quantum mechanics" + mathml: + - "[x,y]" + urls: + - "https://en.wikipedia.org/wiki/Canonical_commutation_relation" + + - concept: cap-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 cap product a2 + property: infix + subject-area: "algebraic topology" + mathml: + - "X⌢Y" + urls: + - "https://en.wikipedia.org/wiki/Cap_product" + - "https://ncatlab.org/nlab/show/cap+product" + + - concept: cardinality + arity: 1 + arguments: [a1] + speech: + en: cardinality of a1 + property: many + subject-area: "set theory" + mathml: + - "#X" + - "card(X)" + urls: + - "https://mathworld.wolfram.com/Cardinality.html" + - "https://en.wikipedia.org/wiki/Cardinality" + - "https://www.encyclopediaofmath.org/index.php/Cardinality" + alias: + - size + + - concept: carmichael-function + arity: 1 + arguments: [a1] + speech: + en: carmichael function of a1 + property: function + subject-area: "number theory" + mathml: + - "λ(x)" + urls: + - "https://mathworld.wolfram.com/CarmichaelFunction.html" + - "https://en.wikipedia.org/wiki/Carmichael_function" + + - concept: cartesian-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 cartesian product a2 + property: infix + subject-area: "set theory" + mathml: + - "X×Y" + urls: + - "https://mathworld.wolfram.com/CartesianProduct.html" + - "https://en.wikipedia.org/wiki/Cartesian_product" + - "https://en.wikipedia.org/wiki/Cartesian_product_of_graphs" + - "https://ncatlab.org/nlab/show/cartesian+product" + - "https://www.encyclopediaofmath.org/index.php/Cartesian_product" + + - concept: casimir-element + arity: 0 + arguments: [] + speech: en: casimir element - property: symbol - area: "lie algebra" - mathml: - - "Ω" - urls: - - "https://en.wikipedia.org/wiki/Casimir_element" - - - concept: catalan-constant - arity: 0 + property: symbol + subject-area: "lie algebra" + mathml: + - "Ω" + urls: + - "https://en.wikipedia.org/wiki/Casimir_element" + + - concept: catalan-constant + arity: 0 + arguments: [] + speech: en: catalan constant - property: symbol - area: "combinatorics" - mathml: - - "G" - urls: - - "https://mathworld.wolfram.com/CatalansConstant.html" - - "https://en.wikipedia.org/wiki/Catalan%27s_constant" - - "https://www.encyclopediaofmath.org/index.php/Catalan_constant" - - - concept: catalan-number - arity: 1 - en: $1th catalan number - property: "indexed symbol" - area: "combinatorics" - mathml: - - "Cx" - urls: - - "https://mathworld.wolfram.com/CatalanNumber.html" - - "https://en.wikipedia.org/wiki/Catalan_number" - - "https://dlmf.nist.gov/26.5#E1" - - - concept: category-of-algebraic-lattices - arity: 0 + property: symbol + subject-area: "combinatorics" + mathml: + - "G" + urls: + - "https://mathworld.wolfram.com/CatalansConstant.html" + - "https://en.wikipedia.org/wiki/Catalan%27s_constant" + - "https://www.encyclopediaofmath.org/index.php/Catalan_constant" + + - concept: catalan-number + arity: 1 + arguments: [a1] + speech: + en: a1th catalan number + property: "indexed symbol" + subject-area: "combinatorics" + mathml: + - "Cx" + urls: + - "https://mathworld.wolfram.com/CatalanNumber.html" + - "https://en.wikipedia.org/wiki/Catalan_number" + - "https://dlmf.nist.gov/26.5#E1" + + - concept: category-of-algebraic-lattices + arity: 0 + arguments: [] + speech: en: category of algebraic lattices - property: symbol - area: "universal algebra" - mathml: - - "AlgCat" - urls: - - "https://ncatlab.org/nlab/show/algebraic+lattice" - - - concept: category-of-sets - arity: 0 + property: symbol + subject-area: "universal algebra" + mathml: + - "AlgCat" + urls: + - "https://ncatlab.org/nlab/show/algebraic+lattice" + + - concept: category-of-sets + arity: 0 + arguments: [] + speech: en: category of sets - property: symbol - area: "category theory" - mathml: - - "Set" - urls: - - "https://en.wikipedia.org/wiki/Category_of_sets" - - "https://www.encyclopediaofmath.org/index.php/Category_of_a_set" - - "https://www.encyclopediaofmath.org/index.php/Category_of_sets" - - - concept: category-of-small-categories - arity: 0 + property: symbol + subject-area: "category theory" + mathml: + - "Set" + urls: + - "https://en.wikipedia.org/wiki/Category_of_sets" + - "https://www.encyclopediaofmath.org/index.php/Category_of_a_set" + - "https://www.encyclopediaofmath.org/index.php/Category_of_sets" + + - concept: category-of-small-categories + arity: 0 + arguments: [] + speech: en: category of small categories - property: symbol - area: "category theory" - mathml: - - "Cat" - urls: - - "https://en.wikipedia.org/wiki/Category_of_small_categories" - - - concept: cauchy-principal-value - arity: 1 - en: cauchy principal value of $1 - property: function - area: "analysis" - mathml: - - "p.v.X" - urls: - - "https://mathworld.wolfram.com/CauchyPrincipalValue.html" - - "https://en.wikipedia.org/wiki/Cauchy_principal_value" - - "https://dlmf.nist.gov/1.4#E24" - - "https://ncatlab.org/nlab/show/Cauchy+principal+value" - - - concept: cauchy-product - arity: 2 - en: $1 cauchy product $2 - property: infix - area: "analysis" - mathml: - - "X⋅Y" - urls: - - "https://mathworld.wolfram.com/CauchyProduct.html" - - "https://en.wikipedia.org/wiki/Cauchy_product" - - - concept: cavitation-number - arity: 0 + property: symbol + subject-area: "category theory" + mathml: + - "Cat" + urls: + - "https://en.wikipedia.org/wiki/Category_of_small_categories" + + - concept: cauchy-principal-value + arity: 1 + arguments: [a1] + speech: + en: cauchy principal value of a1 + property: function + subject-area: "analysis" + mathml: + - "p.v.X" + urls: + - "https://mathworld.wolfram.com/CauchyPrincipalValue.html" + - "https://en.wikipedia.org/wiki/Cauchy_principal_value" + - "https://dlmf.nist.gov/1.4#E24" + - "https://ncatlab.org/nlab/show/Cauchy+principal+value" + + - concept: cauchy-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 cauchy product a2 + property: infix + subject-area: "analysis" + mathml: + - "X⋅Y" + urls: + - "https://mathworld.wolfram.com/CauchyProduct.html" + - "https://en.wikipedia.org/wiki/Cauchy_product" + + - concept: cavitation-number + arity: 0 + arguments: [] + speech: en: cavitation number - property: symbol - area: "physics" - mathml: - - "Ca" - urls: - - "https://en.wikipedia.org/wiki/Euler_number_(physics)#Cavitation_number" - - - concept: cayley-table - arity: 1 - en: cayley table of $1 - property: mtable - area: "group theory" - mathml: - - "×1−111−1−1−11" - urls: - - "https://mathworld.wolfram.com/CayleyTable.html" - - "https://en.wikipedia.org/wiki/Cayley_table" - - "https://www.encyclopediaofmath.org/index.php/Cayley_table" - - - concept: ceiling - arity: 1 - en: ceiling of $1 - property: fenced, function - area: "number theory" - mathml: - - "⌈X⌉" - - "⟧X⟦" - - "]X[" - - "ceil(X)" - urls: - - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions" - - "https://youtu.be/RxNs4SwP6lk" - - - concept: center - arity: 1 - en: center of $1 - property: function - area: "algebra" - mathml: - - "Z(x)" - urls: - - "https://en.wikipedia.org/wiki/Center_(group_theory)" - - "https://en.wikipedia.org/wiki/Center_(algebra)" - - "https://ncatlab.org/nlab/show/center" - alias: - - centre - - - concept: centralizer - arity: 1 - en: centralizer of $1 - property: function - area: "group theory" - mathml: - - "Cx" - urls: - - "https://mathworld.wolfram.com/Centralizer.html" - - "https://en.wikipedia.org/wiki/Centralizer_and_normalizer" - - "https://ncatlab.org/nlab/show/centralizer" - - "https://www.encyclopediaofmath.org/index.php/Centralizer" - - - concept: chain - arity: 1 - en: $1 chains - property: unit - area: "imperial units" - mathml: - - "x chain" - urls: - - "https://en.wikipedia.org/wiki/Chain_(unit)" - - - concept: champernowne-constant - arity: 0 + property: symbol + subject-area: "physics" + mathml: + - "Ca" + urls: + - "https://en.wikipedia.org/wiki/Euler_number_(physics)#Cavitation_number" + + - concept: cayley-table + arity: 1 + arguments: [a1] + speech: + en: cayley table of a1 + property: mtable + subject-area: "group theory" + mathml: + - "×1−111−1−1−11" + urls: + - "https://mathworld.wolfram.com/CayleyTable.html" + - "https://en.wikipedia.org/wiki/Cayley_table" + - "https://www.encyclopediaofmath.org/index.php/Cayley_table" + + - concept: ceiling + arity: 1 + arguments: [a1] + speech: + en: ceiling of a1 + property: fenced, function + subject-area: "number theory" + mathml: + - "⌈X⌉" + - "⟧X⟦" + - "]X[" + - "ceil(X)" + urls: + - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions" + - "https://youtu.be/RxNs4SwP6lk" + + - concept: center + arity: 1 + arguments: [a1] + speech: + en: center of a1 + property: function + subject-area: "algebra" + mathml: + - "Z(x)" + urls: + - "https://en.wikipedia.org/wiki/Center_(group_theory)" + - "https://en.wikipedia.org/wiki/Center_(algebra)" + - "https://ncatlab.org/nlab/show/center" + alias: + - centre + + - concept: centralizer + arity: 1 + arguments: [a1] + speech: + en: centralizer of a1 + property: function + subject-area: "group theory" + mathml: + - "Cx" + urls: + - "https://mathworld.wolfram.com/Centralizer.html" + - "https://en.wikipedia.org/wiki/Centralizer_and_normalizer" + - "https://ncatlab.org/nlab/show/centralizer" + - "https://www.encyclopediaofmath.org/index.php/Centralizer" + + - concept: chain + arity: 1 + arguments: [a1] + speech: + en: a1 chains + property: unit + subject-area: "imperial units" + mathml: + - "x chain" + urls: + - "https://en.wikipedia.org/wiki/Chain_(unit)" + + - concept: champernowne-constant + arity: 0 + arguments: [] + speech: en: champernowne constant - property: constant - area: "number theory" - mathml: - - "C" - - "C10" - urls: - - "https://mathworld.wolfram.com/ChampernowneConstant.html" - - "https://en.wikipedia.org/wiki/Champernowne_constant" - - - concept: character - arity: 1 - en: character of $1 - property: "indexed function" - area: "group theory" - mathml: - - "χ(x)" - urls: - - "https://mathworld.wolfram.com/Character.html" - - "https://en.wikipedia.org/wiki/Character_(mathematics)" - - "https://en.wikipedia.org/wiki/Event-driven_finite-state_machine" - - "https://en.wikipedia.org/wiki/Character_theory" - - "https://en.wikipedia.org/wiki/Multiplicative_character" - - "https://ncatlab.org/nlab/show/character" - - - concept: characteristic - arity: 1 - en: characteristic of $1 - property: function - area: "ring theory" - mathml: - - "char(x)" - urls: - - "https://mathworld.wolfram.com/Characteristic.html" - - "https://en.wikipedia.org/wiki/Characteristic_(algebra)" - - "https://ncatlab.org/nlab/show/characteristic" - - "https://www.encyclopediaofmath.org/index.php/Characteristic" - - - concept: characteristic-function - arity: 1 - en: characteristic function of $1 - property: "indexed function, function" - area: "probability theory" - mathml: - - "𝟏X" - - "1{X}" - urls: - - "https://mathworld.wolfram.com/CharacteristicFunction.html" - - "https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)" - - "https://en.wikipedia.org/wiki/Indicator_function" - - "https://en.wikipedia.org/wiki/Characteristic_function_(convex_analysis)" - - "https://ncatlab.org/nlab/show/characteristic+function" - - "https://www.encyclopediaofmath.org/index.php/Characteristic_function" - - "https://en.wikipedia.org/wiki/Expected_value#Interchanging_limits_and_expectation" - alias: - - indicator-function - - - concept: characteristic-subgroup - arity: 2 - en: $1 characteristic subgroup $2 - property: infix - area: "group theory" - mathml: - - "XcharY" - urls: - - "https://en.wikipedia.org/wiki/Characteristic_subgroup" - - "https://www.encyclopediaofmath.org/index.php/Characteristic_subgroup" - - - concept: charlier-polynomial - arity: 1 - en: charlier polynomial of $1 - property: function - area: "special functions" - mathml: - - "Cx" - urls: - - "https://mathworld.wolfram.com/CharlierPolynomial.html" - - "https://en.wikipedia.org/wiki/Charlier_polynomials" - - "https://dlmf.nist.gov/18.19#T1.t1.r11" - - "https://www.encyclopediaofmath.org/index.php/Charlier_polynomials" - - - concept: chebyshev-polynomial-of-first-kind - arity: 1 - en: chebyshev polynomial of first kind of $1 - property: function - area: "number theory" - mathml: - - "θX" - - "ϑX" - - "TX" - urls: - - "https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html" - - "https://en.wikipedia.org/wiki/Chebyshev_polynomials" - - "https://dlmf.nist.gov/18.3#T1.t1.r8" - alias: - - first-chebyshev-function - - - concept: chebyshev-polynomial-of-second-kind - arity: 1 - en: chebyshev polynomial of second kind of $1 - property: function - area: "number theory" - mathml: - - "ψX" - - "UX" - urls: - - "https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html" - - "https://en.wikipedia.org/wiki/Chebyshev_polynomials" - - "https://dlmf.nist.gov/18.3#T1.t1.r11" - alias: - - second-chebyshev-function - - - concept: cheeger-constant - arity: 1 - en: cheeger constant of $1 - property: function - area: "Riemannian geometry" - mathml: - - "h(x)" - urls: - - "https://en.wikipedia.org/wiki/Cheeger_constant" - - - concept: cheeger-number - arity: 1 - en: cheeger number of $1 - property: function - area: "graph theory" - mathml: - - "h(x)" - urls: - - "https://en.wikipedia.org/wiki/Cheeger_constant_(graph_theory)" - alias: - - cheeger-constant - - isoperimetric-number - - - concept: chemical-equilibrium - arity: 2 - en: $1 chemical equilibrium $2 - property: infix - area: "chemistry" - mathml: - - "X⇌Y" - urls: - - "https://en.wikipedia.org/wiki/Chemical_equilibrium" - alias: - - equilibrium - - - concept: chi-squared-distribution - arity: 0 + property: constant + subject-area: "number theory" + mathml: + - "C" + - "C10" + urls: + - "https://mathworld.wolfram.com/ChampernowneConstant.html" + - "https://en.wikipedia.org/wiki/Champernowne_constant" + + - concept: character + arity: 1 + arguments: [a1] + speech: + en: character of a1 + property: "indexed function" + subject-area: "group theory" + mathml: + - "χ(x)" + urls: + - "https://mathworld.wolfram.com/Character.html" + - "https://en.wikipedia.org/wiki/Character_(mathematics)" + - "https://en.wikipedia.org/wiki/Event-driven_finite-state_machine" + - "https://en.wikipedia.org/wiki/Character_theory" + - "https://en.wikipedia.org/wiki/Multiplicative_character" + - "https://ncatlab.org/nlab/show/character" + + - concept: characteristic + arity: 1 + arguments: [a1] + speech: + en: characteristic of a1 + property: function + subject-area: "ring theory" + mathml: + - "char(x)" + urls: + - "https://mathworld.wolfram.com/Characteristic.html" + - "https://en.wikipedia.org/wiki/Characteristic_(algebra)" + - "https://ncatlab.org/nlab/show/characteristic" + - "https://www.encyclopediaofmath.org/index.php/Characteristic" + + - concept: characteristic-function + arity: 1 + arguments: [a1] + speech: + en: characteristic function of a1 + property: "indexed function, function" + subject-area: "probability theory" + mathml: + - "𝟏X" + - "1{X}" + urls: + - "https://mathworld.wolfram.com/CharacteristicFunction.html" + - "https://en.wikipedia.org/wiki/Characteristic_function_(probability_theory)" + - "https://en.wikipedia.org/wiki/Indicator_function" + - "https://en.wikipedia.org/wiki/Characteristic_function_(convex_analysis)" + - "https://ncatlab.org/nlab/show/characteristic+function" + - "https://www.encyclopediaofmath.org/index.php/Characteristic_function" + - "https://en.wikipedia.org/wiki/Expected_value#Interchanging_limits_and_expectation" + alias: + - indicator-function + + - concept: characteristic-subgroup + arity: 2 + arguments: [a1, a2] + speech: + en: a1 characteristic subgroup a2 + property: infix + subject-area: "group theory" + mathml: + - "XcharY" + urls: + - "https://en.wikipedia.org/wiki/Characteristic_subgroup" + - "https://www.encyclopediaofmath.org/index.php/Characteristic_subgroup" + + - concept: charlier-polynomial + arity: 1 + arguments: [a1] + speech: + en: charlier polynomial of a1 + property: function + subject-area: "special functions" + mathml: + - "Cx" + urls: + - "https://mathworld.wolfram.com/CharlierPolynomial.html" + - "https://en.wikipedia.org/wiki/Charlier_polynomials" + - "https://dlmf.nist.gov/18.19#T1.t1.r11" + - "https://www.encyclopediaofmath.org/index.php/Charlier_polynomials" + + - concept: chebyshev-polynomial-of-first-kind + arity: 1 + arguments: [a1] + speech: + en: chebyshev polynomial of first kind of a1 + property: function + subject-area: "number theory" + mathml: + - "θX" + - "ϑX" + - "TX" + urls: + - "https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html" + - "https://en.wikipedia.org/wiki/Chebyshev_polynomials" + - "https://dlmf.nist.gov/18.3#T1.t1.r8" + alias: + - first-chebyshev-function + + - concept: chebyshev-polynomial-of-second-kind + arity: 1 + arguments: [a1] + speech: + en: chebyshev polynomial of second kind of a1 + property: function + subject-area: "number theory" + mathml: + - "ψX" + - "UX" + urls: + - "https://mathworld.wolfram.com/ChebyshevPolynomialoftheSecondKind.html" + - "https://en.wikipedia.org/wiki/Chebyshev_polynomials" + - "https://dlmf.nist.gov/18.3#T1.t1.r11" + alias: + - second-chebyshev-function + + - concept: cheeger-constant + arity: 1 + arguments: [a1] + speech: + en: cheeger constant of a1 + property: function + subject-area: "Riemannian geometry" + mathml: + - "h(x)" + urls: + - "https://en.wikipedia.org/wiki/Cheeger_constant" + + - concept: cheeger-number + arity: 1 + arguments: [a1] + speech: + en: cheeger number of a1 + property: function + subject-area: "graph theory" + mathml: + - "h(x)" + urls: + - "https://en.wikipedia.org/wiki/Cheeger_constant_(graph_theory)" + alias: + - cheeger-constant + - isoperimetric-number + + - concept: chemical-equilibrium + arity: 2 + arguments: [a1, a2] + speech: + en: a1 chemical equilibrium a2 + property: infix + subject-area: "chemistry" + mathml: + - "X⇌Y" + urls: + - "https://en.wikipedia.org/wiki/Chemical_equilibrium" + alias: + - equilibrium + + - concept: chi-squared-distribution + arity: 0 + arguments: [] + speech: en: chi squared distribution - property: symbol - area: "probability theory" - mathml: - - "χ2" - urls: - - "https://mathworld.wolfram.com/Chi-SquaredDistribution.html" - - "https://en.wikipedia.org/wiki/Chi-squared_distribution" - - "https://www.encyclopediaofmath.org/index.php/Chi-squared_distribution" - - - concept: chord - arity: 1 - en: chord of $1 - property: function - area: "geometry" - mathml: - - "crd(x)" - urls: - - "https://en.wikipedia.org/wiki/Chord_(geometry)" - - - concept: christoffel-symbol-of-first-kind - arity: 3 - en: christoffel symbol of first kind of $1, $2, $3 - property: "indexed symbol" - area: "Riemannian geometry" - mathml: - - "Γkij" - urls: - - "https://mathworld.wolfram.com/ChristoffelSymbol.html" - - "https://en.wikipedia.org/wiki/Christoffel_symbols" - - "https://ncatlab.org/nlab/show/Christoffel+symbols" - - "https://www.encyclopediaofmath.org/index.php/Christoffel_symbol" - - - concept: christoffel-symbol-of-second-kind - arity: 3 - en: christoffel symbol of second kind of $1 $2 $3 - property: "indexed symbol" - area: "Riemannian geometry" - mathml: - - "Γkij" - urls: - - "https://mathworld.wolfram.com/ChristoffelSymbol.html" - - "https://en.wikipedia.org/wiki/Christoffel_symbols" - - "https://ncatlab.org/nlab/show/Christoffel+symbols" - - "https://www.encyclopediaofmath.org/index.php/Christoffel_symbol" - - - concept: chromatic-polynomial - arity: 1 - en: chromatic polynomial of $1 - property: function - area: "graph theory" - mathml: - - "Px" - - "πx" - - "χx" - urls: - - "https://mathworld.wolfram.com/ChromaticPolynomial.html" - - "https://en.wikipedia.org/wiki/Chromatic_polynomial" - - - concept: classifying-space - arity: 1 - en: classifying space of $1 - property: function - area: "group theory" - mathml: - - "BX" - - "ℬX" - urls: - - "https://en.wikipedia.org/wiki/Classifying_space" - - "https://ncatlab.org/nlab/show/classifying+space" - - "https://www.encyclopediaofmath.org/index.php/Classifying_space" - - - concept: clausen-function - arity: 1 - en: clausen function of $1 - property: function - area: "special functions" - mathml: - - "Cl2(φ)" - urls: - - "https://en.wikipedia.org/wiki/Clausen_function" - - - concept: clebsch-gordan-coefficient - arity: 8 - en: clebsch gordan coefficient $1 $2 $3 $4 $5 $6 $7 $8 - property: fenced - area: "special functions" - mathml: - - "(j1j2m1m2|j1j2jm)" - - "⟨j1j2m1m2|j1j2jm⟩" - urls: - - "https://mathworld.wolfram.com/Clebsch-GordanCoefficient.html" - - "https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients" - - "https://dlmf.nist.gov/34.1#p4" - - "https://ncatlab.org/nlab/show/Clebsch-Gordan+coefficient" - - - concept: clifford-algebra - arity: 1 - en: clifford algebra of $1 - property: function - area: "universal algebra" - mathml: - - "Cl(x)" - urls: - - "https://en.wikipedia.org/wiki/Clifford_algebra" - - - concept: clique - arity: 0 + property: symbol + subject-area: "probability theory" + mathml: + - "χ2" + urls: + - "https://mathworld.wolfram.com/Chi-SquaredDistribution.html" + - "https://en.wikipedia.org/wiki/Chi-squared_distribution" + - "https://www.encyclopediaofmath.org/index.php/Chi-squared_distribution" + + - concept: chord + arity: 1 + arguments: [a1] + speech: + en: chord of a1 + property: function + subject-area: "geometry" + mathml: + - "crd(x)" + urls: + - "https://en.wikipedia.org/wiki/Chord_(geometry)" + + - concept: christoffel-symbol-of-first-kind + arity: 3 + arguments: [a1, a2, a3] + speech: + en: christoffel symbol of first kind of a1, a2, a3 + property: "indexed symbol" + subject-area: "Riemannian geometry" + mathml: + - "Γkij" + urls: + - "https://mathworld.wolfram.com/ChristoffelSymbol.html" + - "https://en.wikipedia.org/wiki/Christoffel_symbols" + - "https://ncatlab.org/nlab/show/Christoffel+symbols" + - "https://www.encyclopediaofmath.org/index.php/Christoffel_symbol" + + - concept: christoffel-symbol-of-second-kind + arity: 3 + arguments: [a1, a2, a3] + speech: + en: christoffel symbol of second kind of a1 a2 a3 + property: "indexed symbol" + subject-area: "Riemannian geometry" + mathml: + - "Γkij" + urls: + - "https://mathworld.wolfram.com/ChristoffelSymbol.html" + - "https://en.wikipedia.org/wiki/Christoffel_symbols" + - "https://ncatlab.org/nlab/show/Christoffel+symbols" + - "https://www.encyclopediaofmath.org/index.php/Christoffel_symbol" + + - concept: chromatic-polynomial + arity: 1 + arguments: [a1] + speech: + en: chromatic polynomial of a1 + property: function + subject-area: "graph theory" + mathml: + - "Px" + - "πx" + - "χx" + urls: + - "https://mathworld.wolfram.com/ChromaticPolynomial.html" + - "https://en.wikipedia.org/wiki/Chromatic_polynomial" + + - concept: classifying-space + arity: 1 + arguments: [a1] + speech: + en: classifying space of a1 + property: function + subject-area: "group theory" + mathml: + - "BX" + - "ℬX" + urls: + - "https://en.wikipedia.org/wiki/Classifying_space" + - "https://ncatlab.org/nlab/show/classifying+space" + - "https://www.encyclopediaofmath.org/index.php/Classifying_space" + + - concept: clausen-function + arity: 1 + arguments: [a1] + speech: + en: clausen function of a1 + property: function + subject-area: "special functions" + mathml: + - "Cl2(φ)" + urls: + - "https://en.wikipedia.org/wiki/Clausen_function" + + - concept: clebsch-gordan-coefficient + arity: 8 + arguments: [a1, a2, a3, a4, a6, a7, a8] + speech: + en: clebsch gordan coefficient a1 a2 a3 a4 a5 a6 a7 a8 + property: fenced + subject-area: "special functions" + mathml: + - "(j1j2m1m2|j1j2jm)" + - "⟨j1j2m1m2|j1j2jm⟩" + urls: + - "https://mathworld.wolfram.com/Clebsch-GordanCoefficient.html" + - "https://en.wikipedia.org/wiki/Clebsch%E2%80%93Gordan_coefficients" + - "https://dlmf.nist.gov/34.1#p4" + - "https://ncatlab.org/nlab/show/Clebsch-Gordan+coefficient" + + - concept: clifford-algebra + arity: 1 + arguments: [a1] + speech: + en: clifford algebra of a1 + property: function + subject-area: "universal algebra" + mathml: + - "Cl(x)" + urls: + - "https://en.wikipedia.org/wiki/Clifford_algebra" + + - concept: clique + arity: 0 + arguments: [] + speech: en: clique - property: symbol - area: "graph theory" - mathml: - - "C" - urls: - - "https://mathworld.wolfram.com/Clique.html" - - "https://en.wikipedia.org/wiki/Clique_(graph_theory)" - - "https://ncatlab.org/nlab/show/clique" - - - concept: clique-number - arity: 1 - en: clique number of $1 - property: function - area: "graph theory" - mathml: - - "ω(x)" - urls: - - "https://en.wikipedia.org/wiki/Clique_number" - - - concept: closed-ball - arity: 2 - en: closed ball $1 $2 - property: mixfix - area: "topology" - mathml: - - "Br[p]" - urls: - - "https://mathworld.wolfram.com/OpenBall.html" - - "https://en.wikipedia.org/wiki/Ball_(mathematics)" - alias: - - closed-metric-ball - - - concept: closed-interval - arity: 2 + property: symbol + subject-area: "graph theory" + mathml: + - "C" + urls: + - "https://mathworld.wolfram.com/Clique.html" + - "https://en.wikipedia.org/wiki/Clique_(graph_theory)" + - "https://ncatlab.org/nlab/show/clique" + + - concept: clique-number + arity: 1 + arguments: [a1] + speech: + en: clique number of a1 + property: function + subject-area: "graph theory" + mathml: + - "ω(x)" + urls: + - "https://en.wikipedia.org/wiki/Clique_number" + + - concept: closed-ball + arity: 2 + arguments: [a1, a2] + speech: + en: closed ball a1 a2 + property: mixfix + subject-area: "topology" + mathml: + - "Br[p]" + urls: + - "https://mathworld.wolfram.com/OpenBall.html" + - "https://en.wikipedia.org/wiki/Ball_(mathematics)" + alias: + - closed-metric-ball + + - concept: closed-interval + arity: 2 + arguments: [a1, a2] + speech: en: closed interval - property: fenced - area: "calculus" - mathml: - - "[x,y]" - urls: - - "https://mathworld.wolfram.com/ClosedInterval.html" - - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r29" - - - concept: closed-neighbourhood - arity: 2 - en: closed neighbourhood of $2 in $1 - property: "indexed function, function" - area: "graph theory" - mathml: - - "Nv[G]" - urls: - - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)" - - - concept: closure - arity: 1 - en: closure of $1 - property: "function, msup" - area: "abstract algebra,, topology" - mathml: - - "clX" - - "ClX" - - "X−" - urls: - - "https://mathworld.wolfram.com/Closure.html" - - "https://en.wikipedia.org/wiki/Congruence_closure" - - "https://en.wikipedia.org/wiki/Closure_(mathematics)" - - "https://en.wikipedia.org/wiki/Closure_(topology)" - - "https://en.wikipedia.org/wiki/Closure_problem" - - - concept: codimension - arity: 1 - en: codimension of $1 - property: function - area: "linear algebra" - mathml: - - "codim(x)" - urls: - - "https://mathworld.wolfram.com/Codimension.html" - - "https://en.wikipedia.org/wiki/Codimension" - - "https://ncatlab.org/nlab/show/codimension" - - "https://www.encyclopediaofmath.org/index.php/Codimension" - - - concept: cofinality - arity: 1 - en: cofinality of $1 - property: function - area: "order theory" - mathml: - - "cf(x)" - urls: - - "https://en.wikipedia.org/wiki/Cofinality" - - "https://ncatlab.org/nlab/show/cofinality" - - - concept: cofinite-filter - arity: 0 + property: fenced + subject-area: "calculus" + mathml: + - "[x,y]" + urls: + - "https://mathworld.wolfram.com/ClosedInterval.html" + - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r29" + + - concept: closed-neighbourhood + arity: 2 + arguments: [a1, a2] + speech: + en: closed neighbourhood of a2 in a1 + property: "indexed function, function" + subject-area: "graph theory" + mathml: + - "Nv[G]" + urls: + - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)" + + - concept: closure + arity: 1 + arguments: [a1] + speech: + en: closure of a1 + property: "function, msup" + subject-area: "abstract algebra,, topology" + mathml: + - "clX" + - "ClX" + - "X−" + urls: + - "https://mathworld.wolfram.com/Closure.html" + - "https://en.wikipedia.org/wiki/Congruence_closure" + - "https://en.wikipedia.org/wiki/Closure_(mathematics)" + - "https://en.wikipedia.org/wiki/Closure_(topology)" + - "https://en.wikipedia.org/wiki/Closure_problem" + + - concept: codimension + arity: 1 + arguments: [a1] + speech: + en: codimension of a1 + property: function + subject-area: "linear algebra" + mathml: + - "codim(x)" + urls: + - "https://mathworld.wolfram.com/Codimension.html" + - "https://en.wikipedia.org/wiki/Codimension" + - "https://ncatlab.org/nlab/show/codimension" + - "https://www.encyclopediaofmath.org/index.php/Codimension" + + - concept: cofinality + arity: 1 + arguments: [a1] + speech: + en: cofinality of a1 + property: function + subject-area: "order theory" + mathml: + - "cf(x)" + urls: + - "https://en.wikipedia.org/wiki/Cofinality" + - "https://ncatlab.org/nlab/show/cofinality" + + - concept: cofinite-filter + arity: 0 + arguments: [] + speech: en: cofinite filter - property: symbol - area: "order theory" - mathml: - - "F" - urls: - - "https://mathworld.wolfram.com/CofiniteFilter.html" - - "https://en.wikipedia.org/wiki/Fr%C3%A9chet_filter" - alias: - - frechet-filter - - - concept: coherence - arity: 1 - en: coherence of $1 - property: "indexed function" - area: "signal processing, quantum physics" - mathml: - - "CX" - - "γX" - urls: - - "https://en.wikipedia.org/wiki/Coherence_(signal_processing)" - - "https://en.wikipedia.org/wiki/Coherence_(physics)" - - - concept: coimage - arity: 1 - en: coimage of $1 - property: function - area: "abstract algebra" - mathml: - - "coim(x)" - urls: - - "https://en.wikipedia.org/wiki/Coimage" - - "https://ncatlab.org/nlab/show/coimage" - - - concept: cokernel - arity: 1 - en: cokernel of $1 - property: function - area: "category theory" - mathml: - - "coker(x)" - urls: - - "https://mathworld.wolfram.com/Cokernel.html" - - "https://en.wikipedia.org/wiki/Cokernel" - - "https://ncatlab.org/nlab/show/cokernel" - - "https://www.encyclopediaofmath.org/index.php/Cokernel" - - - concept: column-vector - arity: ">=0" - en: column vector of $1 $2 ... - property: mtable - area: "linear algebra" - mathml: - - "(xyz)" - urls: - - "https://mathworld.wolfram.com/ColumnVector.html" - - "https://en.wikipedia.org/wiki/Column_vector" - - - concept: comma-category - arity: 2 - en: comma category $1 $2 - property: mixfix - area: "category theory" - mathml: - - "(x↓y)" - urls: - - "https://en.wikipedia.org/wiki/Comma_category" - - - concept: commutator - arity: 2 + property: symbol + subject-area: "order theory" + mathml: + - "F" + urls: + - "https://mathworld.wolfram.com/CofiniteFilter.html" + - "https://en.wikipedia.org/wiki/Fr%C3%A9chet_filter" + alias: + - frechet-filter + + - concept: coherence + arity: 1 + arguments: [a1] + speech: + en: coherence of a1 + property: "indexed function" + subject-area: "signal processing, quantum physics" + mathml: + - "CX" + - "γX" + urls: + - "https://en.wikipedia.org/wiki/Coherence_(signal_processing)" + - "https://en.wikipedia.org/wiki/Coherence_(physics)" + + - concept: coimage + arity: 1 + arguments: [a1] + speech: + en: coimage of a1 + property: function + subject-area: "abstract algebra" + mathml: + - "coim(x)" + urls: + - "https://en.wikipedia.org/wiki/Coimage" + - "https://ncatlab.org/nlab/show/coimage" + + - concept: cokernel + arity: 1 + arguments: [a1] + speech: + en: cokernel of a1 + property: function + subject-area: "category theory" + mathml: + - "coker(x)" + urls: + - "https://mathworld.wolfram.com/Cokernel.html" + - "https://en.wikipedia.org/wiki/Cokernel" + - "https://ncatlab.org/nlab/show/cokernel" + - "https://www.encyclopediaofmath.org/index.php/Cokernel" + + - concept: column-vector + arity: ">=0" + speech: + en: column vector of a1 a2 ... + property: mtable + subject-area: "linear algebra" + mathml: + - "(xyz)" + urls: + - "https://mathworld.wolfram.com/ColumnVector.html" + - "https://en.wikipedia.org/wiki/Column_vector" + + - concept: comma-category + arity: 2 + arguments: [a1, a2] + speech: + en: comma category a1 a2 + property: mixfix + subject-area: "category theory" + mathml: + - "(x↓y)" + urls: + - "https://en.wikipedia.org/wiki/Comma_category" + + - concept: commutator + arity: 2 + arguments: [a1, a2] + speech: en: commutator - property: fenced - area: "abstract algebra" - mathml: - - "[a,b]" - urls: - - "https://mathworld.wolfram.com/Commutator.html" - - "https://en.wikipedia.org/wiki/Commutator" - - "https://ncatlab.org/nlab/show/commutator" - - "https://www.encyclopediaofmath.org/index.php/Commutator" - - - concept: commutator-subgroup - arity: 1 - en: commutator subgroup of $1 - property: msup, fenced - area: "abstract algebra" - mathml: - - "X'" - - "X(1)" - - "[X,X]" - notationb: "msup $1 (1)" - notationa: "mrow [ $1, $1 ]" - urls: - - "https://mathworld.wolfram.com/CommutatorSubgroup.html" - - "https://en.wikipedia.org/wiki/Commutator_subgroup" - - "https://en.wikipedia.org/wiki/Derived_series" - - "https://ncatlab.org/nlab/show/commutator+subgroup" - - "https://www.encyclopediaofmath.org/index.php/Commutator_subgroup" - alias: - - derived-subgroup - - - concept: companion-lehmer-number - arity: 1 - en: companion lehmer number of $1 - property: "indexed function" - area: "number theory" - mathml: - - "Vx" - urls: - - "https://mathworld.wolfram.com/LehmerNumber.html" - - "https://mathworld.wolfram.com/LehmersNumber.html" - - "https://en.wikipedia.org/wiki/Lehmer_number" - - - concept: comparability - arity: 2 - en: $1 comparability $2 - property: infix - area: "order theory" - mathml: - - "X⪋Y" - urls: - - "https://en.wikipedia.org/wiki/Comparability" - alias: - - comparable - - - concept: complement-of-interval - arity: 2 + property: fenced + subject-area: "abstract algebra" + mathml: + - "[a,b]" + urls: + - "https://mathworld.wolfram.com/Commutator.html" + - "https://en.wikipedia.org/wiki/Commutator" + - "https://ncatlab.org/nlab/show/commutator" + - "https://www.encyclopediaofmath.org/index.php/Commutator" + + - concept: commutator-subgroup + arity: 1 + arguments: [a1] + speech: + en: commutator subgroup of a1 + property: msup, fenced + subject-area: "abstract algebra" + mathml: + - "X'" + - "X(1)" + - "[X,X]" + notationb: "msup a1 (1)" + notationa: "mrow [ a1, a1 ]" + urls: + - "https://mathworld.wolfram.com/CommutatorSubgroup.html" + - "https://en.wikipedia.org/wiki/Commutator_subgroup" + - "https://en.wikipedia.org/wiki/Derived_series" + - "https://ncatlab.org/nlab/show/commutator+subgroup" + - "https://www.encyclopediaofmath.org/index.php/Commutator_subgroup" + alias: + - derived-subgroup + + - concept: companion-lehmer-number + arity: 1 + arguments: [a1] + speech: + en: companion lehmer number of a1 + property: "indexed function" + subject-area: "number theory" + mathml: + - "Vx" + urls: + - "https://mathworld.wolfram.com/LehmerNumber.html" + - "https://mathworld.wolfram.com/LehmersNumber.html" + - "https://en.wikipedia.org/wiki/Lehmer_number" + + - concept: comparability + arity: 2 + arguments: [a1, a2] + speech: + en: a1 comparability a2 + property: infix + subject-area: "order theory" + mathml: + - "X⪋Y" + urls: + - "https://en.wikipedia.org/wiki/Comparability" + alias: + - comparable + + - concept: complement-of-interval + arity: 2 + arguments: [a1, a2] + speech: en: complement of interval - property: fenced - area: "order theory" - mathml: - - "]a,b[" - urls: - - "https://en.wikipedia.org/wiki/Interval_(mathematics)" - - - concept: complementary-nome - arity: 1 - en: complementary nome of $1 - property: function - area: "special functions" - mathml: - - "q1(k)" - urls: - - "https://mathworld.wolfram.com/Nome.html" - - "https://en.wikipedia.org/wiki/Nome_(mathematics)" - - - concept: complete-graph - arity: 1 + property: fenced + subject-area: "order theory" + mathml: + - "]a,b[" + urls: + - "https://en.wikipedia.org/wiki/Interval_(mathematics)" + + - concept: complementary-nome + arity: 1 + arguments: [a1] + speech: + en: complementary nome of a1 + property: function + subject-area: "special functions" + mathml: + - "q1(k)" + urls: + - "https://mathworld.wolfram.com/Nome.html" + - "https://en.wikipedia.org/wiki/Nome_(mathematics)" + + - concept: complete-graph + arity: 1 + arguments: [a1] + speech: en: complete graph - property: symbol - area: "graph theory" - mathml: - - "Kx" - urls: - - "https://mathworld.wolfram.com/CompleteGraph.html" - - "https://en.wikipedia.org/wiki/Complete_graph" - alias: - - "Also complete bipartite graph: `K_{n,m}`" - - - concept: complex-conjugate - arity: 1 - en: complex conjugate of $1 - property: msup - area: "complex analysis" - mathml: - - "X*" - notationa: "mover $1 ¯" - urls: - - "https://mathworld.wolfram.com/ComplexConjugate.html" - - "https://en.wikipedia.org/wiki/Complex_conjugate" - - "https://dlmf.nist.gov/1.9#E11" - - - concept: complex-projective-space - arity: 0 + property: symbol + subject-area: "graph theory" + mathml: + - "Kx" + urls: + - "https://mathworld.wolfram.com/CompleteGraph.html" + - "https://en.wikipedia.org/wiki/Complete_graph" + alias: + - "Also complete bipartite graph: `K_{n,m}`" + + - concept: complex-conjugate + arity: 1 + arguments: [a1] + speech: + en: complex conjugate of a1 + property: msup + subject-area: "complex analysis" + mathml: + - "X*" + notationa: "mover a1 ¯" + urls: + - "https://mathworld.wolfram.com/ComplexConjugate.html" + - "https://en.wikipedia.org/wiki/Complex_conjugate" + - "https://dlmf.nist.gov/1.9#E11" + + - concept: complex-projective-space + arity: 0 + arguments: [] + speech: en: complex projective space - property: symbol - area: "projective geometry" - mathml: - - "ℂ⁢ℙ" - urls: - - "https://mathworld.wolfram.com/ProjectiveSpace.html" - - "https://en.wikipedia.org/wiki/Algebraic_geometry_of_projective_spaces" - - "https://en.wikipedia.org/wiki/Projective_space" - - "https://ncatlab.org/nlab/show/projective+space" - - "https://www.encyclopediaofmath.org/index.php/Projective_space" - - - concept: complexification - arity: 1 - en: complexification of $1 - property: msup - area: "complex manifolds" - mathml: - - "Xℂ" - - "XC" - urls: - - "https://en.wikipedia.org/wiki/Complexification" - - "https://ncatlab.org/nlab/show/complexification" - - "https://www.encyclopediaofmath.org/index.php/Complexification_of_a_vector_space" - alias: - - complexification-of-vector-space - - - concept: composition - arity: 2 - en: $1 composition $2 - property: infix - area: "algebra" - mathml: - - "X∘Y" - urls: - - "https://mathworld.wolfram.com/Composition.html" - - "https://ncatlab.org/nlab/show/composition" - - "https://www.encyclopediaofmath.org/index.php/Composition" - alias: - - compose - - - - - concept: compound-interest-nominal-rate - arity: 1 + property: symbol + subject-area: "projective geometry" + mathml: + - "ℂ⁢ℙ" + urls: + - "https://mathworld.wolfram.com/ProjectiveSpace.html" + - "https://en.wikipedia.org/wiki/Algebraic_geometry_of_projective_spaces" + - "https://en.wikipedia.org/wiki/Projective_space" + - "https://ncatlab.org/nlab/show/projective+space" + - "https://www.encyclopediaofmath.org/index.php/Projective_space" + + - concept: complexification + arity: 1 + arguments: [a1] + speech: + en: complexification of a1 + property: msup + subject-area: "complex manifolds" + mathml: + - "Xℂ" + - "XC" + urls: + - "https://en.wikipedia.org/wiki/Complexification" + - "https://ncatlab.org/nlab/show/complexification" + - "https://www.encyclopediaofmath.org/index.php/Complexification_of_a_vector_space" + alias: + - complexification-of-vector-space + + - concept: composition + arity: 2 + arguments: [a1, a2] + speech: + en: a1 composition a2 + property: infix + subject-area: "algebra" + mathml: + - "X∘Y" + urls: + - "https://mathworld.wolfram.com/Composition.html" + - "https://ncatlab.org/nlab/show/composition" + - "https://www.encyclopediaofmath.org/index.php/Composition" + alias: + - compose + + + + - concept: compound-interest-nominal-rate + arity: 1 + arguments: [a1] + speech: en: nominal rate - property: msup - area: "finance" - mathml: - - "i(n)" - urls: - - "https://mathworld.wolfram.com/CompoundInterest.html" - - "https://en.wikipedia.org/wiki/Compound_interest" - - - concept: concentration - arity: 1 - en: concentration of $1 - property: fenced - area: "chemistry" - mathml: - - "[x]" - urls: - - "https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/04._Reactions_in_Aqueous_Solution/4.5%3A_Concentration_of_Solutions" - - - concept: condition-number - arity: 1 - en: condition number of $1 - property: function - area: "numerical analysis" - mathml: - - "κ(x)" - urls: - - "https://en.wikipedia.org/wiki/Condition_number" - - "https://dlmf.nist.gov/3.2#SS5.p1" - - "https://www.encyclopediaofmath.org/index.php/Condition_number" - - - concept: conditional-expectation - arity: 2 - en: conditional expectation $1 $2 - property: mixfix - area: "probability theory" - mathml: - - "E(x|y)" - urls: - - "https://en.wikipedia.org/wiki/Conditional_expectation" - - "https://ncatlab.org/nlab/show/conditional+expectation" - - - concept: conditional-probability - arity: 2 - en: conditional probability $1 $2 - property: mixfix - area: "probability theory" - mathml: - - "P(x|y)" - urls: - - "https://mathworld.wolfram.com/ConditionalProbability.html" - - "https://en.wikipedia.org/wiki/Conditional_probability" - - "https://www.encyclopediaofmath.org/index.php/Conditional_probability" - - - concept: conductor - arity: 1 - en: conductor of $1 - property: function - area: "algebraic number theory" - mathml: - - "𝔣⁢(x)" - urls: - - "https://en.wikipedia.org/wiki/Conductor_(class_field_theory)" - - - concept: contraction-operator - arity: 2 - en: $1 contraction operator $2 - property: infix - area: "algebraic geometry" - mathml: - - "X⌟Y" - urls: - - "https://arxiv.org/abs/1104.1240" - - - concept: contrast-function - arity: 2 - en: contrast function $1 $2 - property: mixfix - area: "statistics" - mathml: - - "D(x|y)" - urls: - - "https://en.wikipedia.org/wiki/Divergence_(statistics)" - alias: - - divergence - - - concept: configuration - arity: 4 - en: "configuration $1 sub $2, $3 sub $4" - property: mixfix - area: "geometry" - mathml: - - "(ab,cd)" - urls: - - "https://mathworld.wolfram.com/Configuration.html" - - "https://en.wikipedia.org/wiki/Configuration_(geometry)" - - "https://www.encyclopediaofmath.org/index.php/Configuration" - - - concept: congruence-relation - arity: 2 - en: $1 congruence relation $2 - property: infix - area: "algebra, geometry" - mathml: - - "x≡y" - - "x≅y" - urls: - - "https://en.wikipedia.org/wiki/Congruence_relation" - - "https://mathworld.wolfram.com/Congruence.html" - - "https://en.wikipedia.org/wiki/Congruence_(general_relativity)" - - "https://en.wikipedia.org/wiki/Congruence_(manifolds)" - - "https://en.wikipedia.org/wiki/Congruence_(geometry)" - - "https://ncatlab.org/nlab/show/congruence" - - "https://www.encyclopediaofmath.org/index.php/Congruence" - alias: - - congruence - - congruent - - - concept: conjugacy-class - arity: 1 - en: conjugacy class of $1 - property: function - area: "group theory" - mathml: - - "Cl(x)" - urls: - - "https://mathworld.wolfram.com/ConjugacyClass.html" - - "https://en.wikipedia.org/wiki/Conjugacy_class" - - "https://ncatlab.org/nlab/show/conjugacy+class" - - - concept: conjugate-transpose - arity: 1 - en: conjugate transpose of $1 - property: msup - area: "linear algebra" - mathml: - - "XH" - - "X*" - urls: - - "https://mathworld.wolfram.com/ConjugateTranspose.html" - - "https://en.wikipedia.org/wiki/Conjugate_transpose" - - - concept: connected-sum - arity: 2 - en: $1 connected sum $2 - property: infix - area: "topology" - mathml: - - "X#Y" - urls: - - "https://mathworld.wolfram.com/ConnectedSum.html" - - "https://en.wikipedia.org/wiki/Connected_sum" - - "https://www.encyclopediaofmath.org/index.php/Connected_sum" - - - concept: connectivity - arity: 1 - en: connectivity of $1 - property: function - area: "graph theory" - mathml: - - "κ(x)" - urls: - - "https://mathworld.wolfram.com/Connectivity.html" - - "https://en.wikipedia.org/wiki/Connectivity_(graph_theory)" - - "https://www.encyclopediaofmath.org/index.php/Connectivity" - - - concept: constant-of-integration - arity: 0 + property: msup + subject-area: "finance" + mathml: + - "i(n)" + urls: + - "https://mathworld.wolfram.com/CompoundInterest.html" + - "https://en.wikipedia.org/wiki/Compound_interest" + + - concept: concentration + arity: 1 + arguments: [a1] + speech: + en: concentration of a1 + property: fenced + subject-area: "chemistry" + mathml: + - "[x]" + urls: + - "https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/04._Reactions_in_Aqueous_Solution/4.5%3A_Concentration_of_Solutions" + + - concept: condition-number + arity: 1 + arguments: [a1] + speech: + en: condition number of a1 + property: function + subject-area: "numerical analysis" + mathml: + - "κ(x)" + urls: + - "https://en.wikipedia.org/wiki/Condition_number" + - "https://dlmf.nist.gov/3.2#SS5.p1" + - "https://www.encyclopediaofmath.org/index.php/Condition_number" + + - concept: conditional-expectation + arity: 2 + arguments: [a1, a2] + speech: + en: conditional expectation a1 a2 + property: mixfix + subject-area: "probability theory" + mathml: + - "E(x|y)" + urls: + - "https://en.wikipedia.org/wiki/Conditional_expectation" + - "https://ncatlab.org/nlab/show/conditional+expectation" + + - concept: conditional-probability + arity: 2 + arguments: [a1, a2] + speech: + en: conditional probability a1 a2 + property: mixfix + subject-area: "probability theory" + mathml: + - "P(x|y)" + urls: + - "https://mathworld.wolfram.com/ConditionalProbability.html" + - "https://en.wikipedia.org/wiki/Conditional_probability" + - "https://www.encyclopediaofmath.org/index.php/Conditional_probability" + + - concept: conductor + arity: 1 + arguments: [a1] + speech: + en: conductor of a1 + property: function + subject-area: "algebraic number theory" + mathml: + - "𝔣⁢(x)" + urls: + - "https://en.wikipedia.org/wiki/Conductor_(class_field_theory)" + + - concept: contraction-operator + arity: 2 + arguments: [a1, a2] + speech: + en: a1 contraction operator a2 + property: infix + subject-area: "algebraic geometry" + mathml: + - "X⌟Y" + urls: + - "https://arxiv.org/abs/1104.1240" + + - concept: contrast-function + arity: 2 + arguments: [a1, a2] + speech: + en: contrast function a1 a2 + property: mixfix + subject-area: "statistics" + mathml: + - "D(x|y)" + urls: + - "https://en.wikipedia.org/wiki/Divergence_(statistics)" + alias: + - divergence + + - concept: configuration + arity: 4 + arguments: [a1, a2, a3, a4] + speech: + en: "configuration a1 sub a2, a3 sub a4" + property: mixfix + subject-area: "geometry" + mathml: + - "(ab,cd)" + urls: + - "https://mathworld.wolfram.com/Configuration.html" + - "https://en.wikipedia.org/wiki/Configuration_(geometry)" + - "https://www.encyclopediaofmath.org/index.php/Configuration" + + - concept: congruence-relation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 congruence relation a2 + property: infix + subject-area: "algebra, geometry" + mathml: + - "x≡y" + - "x≅y" + urls: + - "https://en.wikipedia.org/wiki/Congruence_relation" + - "https://mathworld.wolfram.com/Congruence.html" + - "https://en.wikipedia.org/wiki/Congruence_(general_relativity)" + - "https://en.wikipedia.org/wiki/Congruence_(manifolds)" + - "https://en.wikipedia.org/wiki/Congruence_(geometry)" + - "https://ncatlab.org/nlab/show/congruence" + - "https://www.encyclopediaofmath.org/index.php/Congruence" + alias: + - congruence + - congruent + + - concept: conjugacy-class + arity: 1 + arguments: [a1] + speech: + en: conjugacy class of a1 + property: function + subject-area: "group theory" + mathml: + - "Cl(x)" + urls: + - "https://mathworld.wolfram.com/ConjugacyClass.html" + - "https://en.wikipedia.org/wiki/Conjugacy_class" + - "https://ncatlab.org/nlab/show/conjugacy+class" + + - concept: conjugate-transpose + arity: 1 + arguments: [a1] + speech: + en: conjugate transpose of a1 + property: msup + subject-area: "linear algebra" + mathml: + - "XH" + - "X*" + urls: + - "https://mathworld.wolfram.com/ConjugateTranspose.html" + - "https://en.wikipedia.org/wiki/Conjugate_transpose" + + - concept: connected-sum + arity: 2 + arguments: [a1, a2] + speech: + en: a1 connected sum a2 + property: infix + subject-area: "topology" + mathml: + - "X#Y" + urls: + - "https://mathworld.wolfram.com/ConnectedSum.html" + - "https://en.wikipedia.org/wiki/Connected_sum" + - "https://www.encyclopediaofmath.org/index.php/Connected_sum" + + - concept: connectivity + arity: 1 + arguments: [a1] + speech: + en: connectivity of a1 + property: function + subject-area: "graph theory" + mathml: + - "κ(x)" + urls: + - "https://mathworld.wolfram.com/Connectivity.html" + - "https://en.wikipedia.org/wiki/Connectivity_(graph_theory)" + - "https://www.encyclopediaofmath.org/index.php/Connectivity" + + - concept: constant-of-integration + arity: 0 + arguments: [] + speech: en: constant of integration - property: constant - area: "calculus" - mathml: - - "C" - urls: - - "https://mathworld.wolfram.com/ConstantofIntegration.html" - - "https://en.wikipedia.org/wiki/Constant_of_integration" - - - concept: containment - arity: 2 - en: $1 containment $2 - property: infix - area: "computer science" - mathml: - - "X≤Y" - urls: - - "https://en.wikipedia.org/wiki/Encompassment_ordering" - - "https://en.wikipedia.org/wiki/Subset" - - "https://en.wikipedia.org/wiki/%E2%8A%83" - alias: - - encompassment - - - concept: contingency-table - arity: 1 - en: contingency table of $1 - property: mtable - area: "statistics" - mathml: - - "......" - urls: - - "https://mathworld.wolfram.com/ContingencyTable.html" - - "https://en.wikipedia.org/wiki/Contingency_table" - alias: - - two-way-frequency-table - - - concept: continued-fraction - arity: 1 - en: continued fraction $1 - property: mixfix - area: "number theory" - mathml: - - "a0+1a1+⋱" - urls: - - "https://mathworld.wolfram.com/ContinuedFraction.html" - - "https://en.wikipedia.org/wiki/Continued_fraction" - - "https://dlmf.nist.gov/1.12#i" - - "https://ncatlab.org/nlab/show/continued+fraction" - - "https://www.encyclopediaofmath.org/index.php/Continued_fraction" - alias: - - anthyphairetic-ratio - - chain-fraction - - - concept: continuum - arity: 0 + property: constant + subject-area: "calculus" + mathml: + - "C" + urls: + - "https://mathworld.wolfram.com/ConstantofIntegration.html" + - "https://en.wikipedia.org/wiki/Constant_of_integration" + + - concept: containment + arity: 2 + arguments: [a1, a2] + speech: + en: a1 containment a2 + property: infix + subject-area: "computer science" + mathml: + - "X≤Y" + urls: + - "https://en.wikipedia.org/wiki/Encompassment_ordering" + - "https://en.wikipedia.org/wiki/Subset" + - "https://en.wikipedia.org/wiki/%E2%8A%83" + alias: + - encompassment + + - concept: contingency-table + arity: 1 + arguments: [a1] + speech: + en: contingency table of a1 + property: mtable + subject-area: "statistics" + mathml: + - "......" + urls: + - "https://mathworld.wolfram.com/ContingencyTable.html" + - "https://en.wikipedia.org/wiki/Contingency_table" + alias: + - two-way-frequency-table + + - concept: continued-fraction + arity: 1 + arguments: [a1] + speech: + en: continued fraction a1 + property: mixfix + subject-area: "number theory" + mathml: + - "a0+1a1+⋱" + urls: + - "https://mathworld.wolfram.com/ContinuedFraction.html" + - "https://en.wikipedia.org/wiki/Continued_fraction" + - "https://dlmf.nist.gov/1.12#i" + - "https://ncatlab.org/nlab/show/continued+fraction" + - "https://www.encyclopediaofmath.org/index.php/Continued_fraction" + alias: + - anthyphairetic-ratio + - chain-fraction + + - concept: continuum + arity: 0 + arguments: [] + speech: en: continuum - property: constant - area: "set theory" - mathml: - - "𝔠" - urls: - - "https://mathworld.wolfram.com/Continuum.html" - - "https://en.wikipedia.org/wiki/List_of_continuity-related_topics" - - "https://en.wikipedia.org/wiki/Linear_continuum" - - "https://en.wikipedia.org/wiki/Continuum_(set_theory)" - - "https://en.wikipedia.org/wiki/Continuum_(topology)" - - "https://ncatlab.org/nlab/show/continuum" - - "https://www.encyclopediaofmath.org/index.php/Continuum" - - - concept: contradiction - arity: 0 + property: constant + subject-area: "set theory" + mathml: + - "𝔠" + urls: + - "https://mathworld.wolfram.com/Continuum.html" + - "https://en.wikipedia.org/wiki/List_of_continuity-related_topics" + - "https://en.wikipedia.org/wiki/Linear_continuum" + - "https://en.wikipedia.org/wiki/Continuum_(set_theory)" + - "https://en.wikipedia.org/wiki/Continuum_(topology)" + - "https://ncatlab.org/nlab/show/continuum" + - "https://www.encyclopediaofmath.org/index.php/Continuum" + + - concept: contradiction + arity: 0 + arguments: [] + speech: en: contradiction - property: constant - area: "logic" - mathml: - - "⊥" - urls: - - "https://mathworld.wolfram.com/Contradiction.html" - - "https://en.wikipedia.org/wiki/Contradiction" - - "https://ncatlab.org/nlab/show/contradiction" - - - concept: converge - arity: 1 - en: $1 converges - property: postfix - area: "computer science" - mathml: - - "x↓" - urls: - - "https://en.wikipedia.org/wiki/Divergence_(computer_science)" - alias: - - convergence - - - concept: converse - arity: 1 - en: converse of $1 - property: msup - area: "relational algebra" - mathml: - - "X˘" - urls: - - "https://en.wikipedia.org/wiki/Relation_algebra" - alias: - - reciprocal - - - concept: converse-graph - arity: 1 - en: converse graph of $1 - property: msup - area: "graph theory" - mathml: - - "X'" - - "XT" - - "XR" - urls: - - "https://en.wikipedia.org/wiki/Transpose_graph" - alias: - - transpose-graph - - reverse-graph - - - concept: convolution - arity: 2 - en: $1 convolution $2 - property: infix - area: "functional analysis" - mathml: - - "X∗Y" - urls: - - "https://mathworld.wolfram.com/Convolution.html" - - "https://en.wikipedia.org/wiki/List_of_convolutions_of_probability_distributions" - - "https://en.wikipedia.org/wiki/Convolution_(computer_science)" - - "https://en.wikipedia.org/wiki/Convolution" - alias: - - convolve - - - concept: conway-group - arity: 0 + property: constant + subject-area: "logic" + mathml: + - "⊥" + urls: + - "https://mathworld.wolfram.com/Contradiction.html" + - "https://en.wikipedia.org/wiki/Contradiction" + - "https://ncatlab.org/nlab/show/contradiction" + + - concept: converge + arity: 1 + arguments: [a1] + speech: + en: a1 converges + property: postfix + subject-area: "computer science" + mathml: + - "x↓" + urls: + - "https://en.wikipedia.org/wiki/Divergence_(computer_science)" + alias: + - convergence + + - concept: converse + arity: 1 + arguments: [a1] + speech: + en: converse of a1 + property: msup + subject-area: "relational algebra" + mathml: + - "X˘" + urls: + - "https://en.wikipedia.org/wiki/Relation_algebra" + alias: + - reciprocal + + - concept: converse-graph + arity: 1 + arguments: [a1] + speech: + en: converse graph of a1 + property: msup + subject-area: "graph theory" + mathml: + - "X'" + - "XT" + - "XR" + urls: + - "https://en.wikipedia.org/wiki/Transpose_graph" + alias: + - transpose-graph + - reverse-graph + + - concept: convolution + arity: 2 + arguments: [a1, a2] + speech: + en: a1 convolution a2 + property: infix + subject-area: "functional analysis" + mathml: + - "X∗Y" + urls: + - "https://mathworld.wolfram.com/Convolution.html" + - "https://en.wikipedia.org/wiki/List_of_convolutions_of_probability_distributions" + - "https://en.wikipedia.org/wiki/Convolution_(computer_science)" + - "https://en.wikipedia.org/wiki/Convolution" + alias: + - convolve + + - concept: conway-group + arity: 0 + arguments: [] + speech: en: conway group - property: symbol - area: "group theory" - mathml: - - "Co0" - - "Co1" - - "Co2" - - "Co3" - urls: - - "https://mathworld.wolfram.com/ConwayGroups.html" - - "https://en.wikipedia.org/wiki/Conway_group" - - "https://en.wikipedia.org/wiki/Conway_group_Co1" - - "https://en.wikipedia.org/wiki/Conway_group_Co2" - - "https://en.wikipedia.org/wiki/Conway_group_Co3" - - - concept: coprime - arity: 2 - en: $1 coprime $2 - property: infix - area: "number theory" - mathml: - - "X⊥Y" - urls: - - "https://mathworld.wolfram.com/Coprime.html" - - "https://en.wikipedia.org/wiki/Coprime_integers" - alias: - - relatively-prime - - mutually-prime - - - concept: coproduct - arity: 2 - en: coproduct of $1 and $2 - property: indexed - area: "topology, category theory" - mathml: - - "X⊔Y" - urls: - - "https://mathworld.wolfram.com/Coproduct.html" - - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)" - - "https://en.wikipedia.org/wiki/Coproduct" - - "https://ncatlab.org/nlab/show/coproduct" - - "https://www.encyclopediaofmath.org/index.php/Coproduct" - - - concept: correlation - arity: 1 - en: correlation of $1 - property: function - area: "statistics" - mathml: - - "corr(x)" - urls: - - "https://en.wikipedia.org/wiki/Correlation_and_dependence" - - - concept: correlation-ratio - arity: 0 + property: symbol + subject-area: "group theory" + mathml: + - "Co0" + - "Co1" + - "Co2" + - "Co3" + urls: + - "https://mathworld.wolfram.com/ConwayGroups.html" + - "https://en.wikipedia.org/wiki/Conway_group" + - "https://en.wikipedia.org/wiki/Conway_group_Co1" + - "https://en.wikipedia.org/wiki/Conway_group_Co2" + - "https://en.wikipedia.org/wiki/Conway_group_Co3" + + - concept: coprime + arity: 2 + arguments: [a1, a2] + speech: + en: a1 coprime a2 + property: infix + subject-area: "number theory" + mathml: + - "X⊥Y" + urls: + - "https://mathworld.wolfram.com/Coprime.html" + - "https://en.wikipedia.org/wiki/Coprime_integers" + alias: + - relatively-prime + - mutually-prime + + - concept: coproduct + arity: 2 + arguments: [a1, a2] + speech: + en: coproduct of a1 and a2 + property: indexed + subject-area: "topology, category theory" + mathml: + - "X⊔Y" + urls: + - "https://mathworld.wolfram.com/Coproduct.html" + - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)" + - "https://en.wikipedia.org/wiki/Coproduct" + - "https://ncatlab.org/nlab/show/coproduct" + - "https://www.encyclopediaofmath.org/index.php/Coproduct" + + - concept: correlation + arity: 1 + arguments: [a1] + speech: + en: correlation of a1 + property: function + subject-area: "statistics" + mathml: + - "corr(x)" + urls: + - "https://en.wikipedia.org/wiki/Correlation_and_dependence" + + - concept: correlation-ratio + arity: 0 + arguments: [] + speech: en: correlation ratio - property: symbol - area: "statistics" - mathml: - - "η" - urls: - - "https://mathworld.wolfram.com/CorrelationRatio.html" - - "https://en.wikipedia.org/wiki/Correlation_ratio" - - "https://www.encyclopediaofmath.org/index.php/Correlation_ratio" - - - concept: cosine-integral - arity: 1 - en: cosine integral of $1 - property: operator - area: "special-functions" - mathml: - - "Ci(x)" - urls: - - "https://mathworld.wolfram.com/CosineIntegral.html" - - "https://dlmf.nist.gov/6.2#ii" - - "https://dlmf.nist.gov/6.2#E11" - - "https://dlmf.nist.gov/6.2#E12" - - - concept: coupling-constant - arity: 0 + property: symbol + subject-area: "statistics" + mathml: + - "η" + urls: + - "https://mathworld.wolfram.com/CorrelationRatio.html" + - "https://en.wikipedia.org/wiki/Correlation_ratio" + - "https://www.encyclopediaofmath.org/index.php/Correlation_ratio" + + - concept: cosine-integral + arity: 1 + arguments: [a1] + speech: + en: cosine integral of a1 + property: operator + subject-area: "special-functions" + mathml: + - "Ci(x)" + urls: + - "https://mathworld.wolfram.com/CosineIntegral.html" + - "https://dlmf.nist.gov/6.2#ii" + - "https://dlmf.nist.gov/6.2#E11" + - "https://dlmf.nist.gov/6.2#E12" + + - concept: coupling-constant + arity: 0 + arguments: [] + speech: en: coupling constant - property: symbol - area: "gauge theory" - mathml: - - "g" - urls: - - "https://en.wikipedia.org/wiki/Coupling_constant" - alias: - - gauge-coupling-parameter - - coupling - - - concept: covariance - arity: 1 - en: covariance of $1 - property: function - area: "statistics" - mathml: - - "cov(x)" - urls: - - "https://mathworld.wolfram.com/Covariance.html" - - "https://en.wikipedia.org/wiki/Covariance_operator" - - "https://en.wikipedia.org/wiki/Covariance" - - "https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors" - - "https://www.encyclopediaofmath.org/index.php/Covariance" - - - concept: covariant-derivative - arity: 1 - en: covariant derivative of $1 - property: "indexed operator" - area: "differential geometry" - mathml: - - "∇x" - urls: - - "https://mathworld.wolfram.com/CovariantDerivative.html" - - "https://en.wikipedia.org/wiki/Covariant_derivative" - - "https://ncatlab.org/nlab/show/covariant+derivative" - - "https://www.encyclopediaofmath.org/index.php/Covariant_derivative" - - - concept: covariation - arity: 3 - en: covariation of $1 and $2 over $3 - property: indexed fenced - area: "stochastic processes" - mathml: - - "[X,Y]t" - urls: - - "https://en.wikipedia.org/wiki/Quadratic_variation" - alias: - - cross-variance - - - concept: covering-relation - arity: 2 - en: $1 covering relation $2 - property: infix - area: "order theory" - mathml: - - "X⋖Y" - - "X<:Y" - urls: - - "https://en.wikipedia.org/wiki/Partially_ordered_set" - - "https://en.wikipedia.org/wiki/Covering_relation" - - - concept: cross-product - arity: 2 - en: $1 cross product $2 - property: infix - area: "linear algebra" - mathml: - - "X×Y" - urls: - - "https://mathworld.wolfram.com/CrossProduct.html" - - "https://en.wikipedia.org/wiki/Cross_product" - - "https://ncatlab.org/nlab/show/cross+product" - - "https://www.encyclopediaofmath.org/index.php/Cross_product" - alias: - - vector-product - - - concept: cross-ratio - arity: 4 - en: "cross ratio of $1, $2, $3, $4" - property: fenced - area: "geometry" - mathml: - - "(A,B;C,D)" - urls: - - "https://mathworld.wolfram.com/Cross-Ratio.html" - - "https://en.wikipedia.org/wiki/Cross-ratio" - alias: - - double-ratio - - - concept: crossing-number - arity: 1 - en: crossing number of $1 - property: function - area: "graph theory" - mathml: - - "Cr(x)" - urls: - - "https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)" - - "https://en.wikipedia.org/wiki/Crossing_number_(knot_theory)" - - "https://ncatlab.org/nlab/show/crossing+number" - - - concept: cullen-number - arity: 1 - en: $1th cullen number - property: "indexed symbol" - area: "number theory" - mathml: - - "Cx" - urls: - - "https://mathworld.wolfram.com/CullenNumber.html" - - "https://en.wikipedia.org/wiki/Cullen_number" - - - concept: cumulant - arity: 1 - en: cumulant of $1 - property: "indexed symbol" - area: "probability theory" - mathml: - - "κx" - urls: - - "https://mathworld.wolfram.com/Cumulant.html" - - "https://en.wikipedia.org/wiki/Cumulant" - - "https://en.wikipedia.org/wiki/Cumulant-generating_function" - - "https://ncatlab.org/nlab/show/cumulant" - - "https://www.encyclopediaofmath.org/index.php/Cumulant" - - - concept: cumulative-distribution-function - arity: 1 - en: cumulative distribution function of $1 - property: "indexed symbol" - area: "probability theory" - mathml: - - "Fx" - urls: - - "https://mathworld.wolfram.com/CumulativeDistributionFunction.html" - - "https://en.wikipedia.org/wiki/Cumulative_distribution_function" - alias: - - cdf - - distribution-function - - - concept: cup-product - arity: 2 - en: $1 cup product $2 - property: infix - area: "algebraic topology" - mathml: - - "X⌣Y" - urls: - - "https://en.wikipedia.org/wiki/Cup_product" - - "https://ncatlab.org/nlab/show/cup+product" - - - concept: curl - arity: 1 - en: curl of $1 - property: function - area: "vector calculus" - mathml: - - "curlX" - - "rotX" - notationa: "mrow ∇ × $1" - urls: - - "https://mathworld.wolfram.com/Curl.html" - - "https://en.wikipedia.org/wiki/Curl_(mathematics)" - - "https://ncatlab.org/nlab/show/curl" - - "https://www.encyclopediaofmath.org/index.php/Curl" - - - concept: current - arity: 1 - en: current of $1 - property: fenced - area: "differential topology" - mathml: - - "[M]" - - "⟦M⟧" - urls: - - "https://mathworld.wolfram.com/Current.html" - - "https://en.wikipedia.org/wiki/Current_(mathematics)" - - "https://www.encyclopediaofmath.org/index.php/Current" - - - concept: curvature - arity: 1 - en: curvature of $1 - property: function - area: "differential geometry" - mathml: - - "κ(x)" - urls: - - "https://mathworld.wolfram.com/Curvature.html" - - "https://en.wikipedia.org/wiki/Geodesic_curvature" - - "https://en.wikipedia.org/wiki/Curvature" - - "https://ncatlab.org/nlab/show/curvature" - - "https://www.encyclopediaofmath.org/index.php/Curvature" - - - concept: cycle - arity: 1 - en: cycle $1 - property: fenced - area: "combinatorics" - mathml: - - "(126)(35)" - urls: - - "https://en.wikipedia.org/wiki/Permutation#Cycle_notation" - - "https://en.wikipedia.org/wiki/Transposition_(mathematics)" - - "https://en.wikipedia.org/wiki/Cycles_and_fixed_points" - - - concept: cycle-gene - arity: 0 + property: symbol + subject-area: "gauge theory" + mathml: + - "g" + urls: + - "https://en.wikipedia.org/wiki/Coupling_constant" + alias: + - gauge-coupling-parameter + - coupling + + - concept: covariance + arity: 1 + arguments: [a1] + speech: + en: covariance of a1 + property: function + subject-area: "statistics" + mathml: + - "cov(x)" + urls: + - "https://mathworld.wolfram.com/Covariance.html" + - "https://en.wikipedia.org/wiki/Covariance_operator" + - "https://en.wikipedia.org/wiki/Covariance" + - "https://en.wikipedia.org/wiki/Covariance_and_contravariance_of_vectors" + - "https://www.encyclopediaofmath.org/index.php/Covariance" + + - concept: covariant-derivative + arity: 1 + arguments: [a1] + speech: + en: covariant derivative of a1 + property: "indexed operator" + subject-area: "differential geometry" + mathml: + - "∇x" + urls: + - "https://mathworld.wolfram.com/CovariantDerivative.html" + - "https://en.wikipedia.org/wiki/Covariant_derivative" + - "https://ncatlab.org/nlab/show/covariant+derivative" + - "https://www.encyclopediaofmath.org/index.php/Covariant_derivative" + + - concept: covariation + arity: 3 + arguments: [a1, a2, a3] + speech: + en: covariation of a1 and a2 over a3 + property: indexed fenced + subject-area: "stochastic processes" + mathml: + - "[X,Y]t" + urls: + - "https://en.wikipedia.org/wiki/Quadratic_variation" + alias: + - cross-variance + + - concept: covering-relation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 covering relation a2 + property: infix + subject-area: "order theory" + mathml: + - "X⋖Y" + - "X<:Y" + urls: + - "https://en.wikipedia.org/wiki/Partially_ordered_set" + - "https://en.wikipedia.org/wiki/Covering_relation" + + - concept: cross-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 cross product a2 + property: infix + subject-area: "linear algebra" + mathml: + - "X×Y" + urls: + - "https://mathworld.wolfram.com/CrossProduct.html" + - "https://en.wikipedia.org/wiki/Cross_product" + - "https://ncatlab.org/nlab/show/cross+product" + - "https://www.encyclopediaofmath.org/index.php/Cross_product" + alias: + - vector-product + + - concept: cross-ratio + arity: 4 + arguments: [a1, a2, a3, a4] + speech: + en: "cross ratio of a1, a2, a3, a4" + property: fenced + subject-area: "geometry" + mathml: + - "(A,B;C,D)" + urls: + - "https://mathworld.wolfram.com/Cross-Ratio.html" + - "https://en.wikipedia.org/wiki/Cross-ratio" + alias: + - double-ratio + + - concept: crossing-number + arity: 1 + arguments: [a1] + speech: + en: crossing number of a1 + property: function + subject-area: "graph theory" + mathml: + - "Cr(x)" + urls: + - "https://en.wikipedia.org/wiki/Crossing_number_(graph_theory)" + - "https://en.wikipedia.org/wiki/Crossing_number_(knot_theory)" + - "https://ncatlab.org/nlab/show/crossing+number" + + - concept: cullen-number + arity: 1 + arguments: [a1] + speech: + en: a1th cullen number + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Cx" + urls: + - "https://mathworld.wolfram.com/CullenNumber.html" + - "https://en.wikipedia.org/wiki/Cullen_number" + + - concept: cumulant + arity: 1 + arguments: [a1] + speech: + en: cumulant of a1 + property: "indexed symbol" + subject-area: "probability theory" + mathml: + - "κx" + urls: + - "https://mathworld.wolfram.com/Cumulant.html" + - "https://en.wikipedia.org/wiki/Cumulant" + - "https://en.wikipedia.org/wiki/Cumulant-generating_function" + - "https://ncatlab.org/nlab/show/cumulant" + - "https://www.encyclopediaofmath.org/index.php/Cumulant" + + - concept: cumulative-distribution-function + arity: 1 + arguments: [a1] + speech: + en: cumulative distribution function of a1 + property: "indexed symbol" + subject-area: "probability theory" + mathml: + - "Fx" + urls: + - "https://mathworld.wolfram.com/CumulativeDistributionFunction.html" + - "https://en.wikipedia.org/wiki/Cumulative_distribution_function" + alias: + - cdf + - distribution-function + + - concept: cup-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 cup product a2 + property: infix + subject-area: "algebraic topology" + mathml: + - "X⌣Y" + urls: + - "https://en.wikipedia.org/wiki/Cup_product" + - "https://ncatlab.org/nlab/show/cup+product" + + - concept: curl + arity: 1 + arguments: [a1] + speech: + en: curl of a1 + property: function + subject-area: "vector calculus" + mathml: + - "curlX" + - "rotX" + notationa: "mrow ∇ × a1" + urls: + - "https://mathworld.wolfram.com/Curl.html" + - "https://en.wikipedia.org/wiki/Curl_(mathematics)" + - "https://ncatlab.org/nlab/show/curl" + - "https://www.encyclopediaofmath.org/index.php/Curl" + + - concept: current + arity: 1 + arguments: [a1] + speech: + en: current of a1 + property: fenced + subject-area: "differential topology" + mathml: + - "[M]" + - "⟦M⟧" + urls: + - "https://mathworld.wolfram.com/Current.html" + - "https://en.wikipedia.org/wiki/Current_(mathematics)" + - "https://www.encyclopediaofmath.org/index.php/Current" + + - concept: curvature + arity: 1 + arguments: [a1] + speech: + en: curvature of a1 + property: function + subject-area: "differential geometry" + mathml: + - "κ(x)" + urls: + - "https://mathworld.wolfram.com/Curvature.html" + - "https://en.wikipedia.org/wiki/Geodesic_curvature" + - "https://en.wikipedia.org/wiki/Curvature" + - "https://ncatlab.org/nlab/show/curvature" + - "https://www.encyclopediaofmath.org/index.php/Curvature" + + - concept: cycle + arity: 1 + arguments: [a1] + speech: + en: cycle a1 + property: fenced + subject-area: "combinatorics" + mathml: + - "(126)(35)" + urls: + - "https://en.wikipedia.org/wiki/Permutation#Cycle_notation" + - "https://en.wikipedia.org/wiki/Transposition_(mathematics)" + - "https://en.wikipedia.org/wiki/Cycles_and_fixed_points" + + - concept: cycle-gene + arity: 0 + arguments: [] + speech: en: cycle gene - property: symbol - area: "genetics" - mathml: - - "cyc" - urls: - - "https://en.wikipedia.org/wiki/Cycle_(gene)" - - - concept: cyclotomic-field - arity: 1 - en: cyclotomic field of $1 - property: embellished symbol - area: "number theory" - mathml: - - "𝐐(ζn)" - urls: - - "https://mathworld.wolfram.com/CyclotomicField.html" - - "https://en.wikipedia.org/wiki/Cyclotomic_field" - - "https://ncatlab.org/nlab/show/cyclotomic+field" - - "https://www.encyclopediaofmath.org/index.php/Cyclotomic_field" - - - concept: cyclotomic-polynomial - arity: 1 - en: $1th cyclotomic polynomial - property: "indexed symbol" - area: "number theory" - mathml: - - "Φx" - urls: - - "https://mathworld.wolfram.com/CyclotomicPolynomial.html" - - "https://en.wikipedia.org/wiki/Cyclotomic_polynomial" - - "https://www.encyclopediaofmath.org/index.php/Cyclotomic_polynomials" - - - concept: dalembert-operator - arity: 1 - en: dalembert operator of $1 - property: prefix - area: "partial differential equations" - mathml: - - "☐x" - urls: - - "https://en.wikipedia.org/wiki/D%27Alembert_operator" - - "https://www.encyclopediaofmath.org/index.php/D'Alembert_operator" - alias: - - dalembertian - - wave-operator - - box-operator - - - concept: davenport-constant - arity: 1 - en: davenport constant of $1 - property: function - area: "group theory" - mathml: - - "D(x)" - urls: - - "https://mathworld.wolfram.com/DavenportConstant.html" - - "https://en.wikipedia.org/wiki/Davenport_constant" - - "https://www.encyclopediaofmath.org/index.php/Davenport_constant" - - - concept: dawson-function - arity: 1 - en: dawson function of $1 - property: function - area: "special-functions" - mathml: - - "FX" - - "DX" - notationb: "mi sub D -" - notationa: "mi sub D +" - urls: - - "https://mathworld.wolfram.com/DawsonsIntegral.html" - - "https://en.wikipedia.org/wiki/Dawson_function" - - "https://dlmf.nist.gov/7.2#ii" - - "https://dlmf.nist.gov/7.2#E5" - alias: - - dawson-integral - - - concept: decrease - arity: 1 - en: decrease of $1 - property: postfix - area: "physics" - mathml: - - "x↓" - urls: - - "https://youtu.be/HZ7a9YkF204?t=4705" - - - concept: decrease-tends-to - arity: 2 - en: $1 decrease tends to $2 - property: infix - area: "calculus" - mathml: - - "X↘Y" - urls: - - "https://math.stackexchange.com/questions/1886232/what-does-this-notation-mean-limes-from-left-right" - - "http://pi.math.cornell.edu/~web6720/MATH%206710%20notes.pdf" - - - concept: dedekind-eta-function - arity: 1 - en: dedekind eta function of $1 - property: function - area: "special functions" - mathml: - - "η(x)" - urls: - - "https://mathworld.wolfram.com/DedekindEtaFunction.html" - - "https://en.wikipedia.org/wiki/Dedekind_eta_function" - - "https://ncatlab.org/nlab/show/Dedekind+eta+function" - - - concept: dedekind-zeta-function - arity: 1 - en: dedekind zeta function of $1 - property: function - area: "special functions" - mathml: - - "ζ(x)" - urls: - - "https://en.wikipedia.org/wiki/Dedekind_zeta_function" - - - concept: deductive-closure - arity: 1 - en: deductive closure of $1 - property: function - area: "logic" - mathml: - - "DedX" - - "ThX" - urls: - - "https://en.wikipedia.org/wiki/Deductive_closure" - - - concept: defined-as - arity: 2 - en: $1 defined as $2 - property: infix - area: "general" - mathml: - - "X≜Y" - - "X≝Y" - - "X:=Y" - - "X=defY" - - "X:Y" - urls: - - "https://math.stackexchange.com/questions/522864/what-is-the-symbol-triangleq" - - "https://drive.google.com/file/d/1z_dcQ6lsOA_0CsH55fwcg4hQF_w22olM/view" - alias: - - defined-to-be-equal-to - - equal-to-by-definition - - - concept: degree - arity: 1 - en: degree of $1 - property: prefix, postfix - area: "physics, geometry" - mathml: - - "x°" - urls: - - "https://mathworld.wolfram.com/Degree.html" - - "https://en.wikipedia.org/wiki/Degree_(angle)" - - "https://en.wikipedia.org/wiki/Degree_(temperature)" - - "https://ncatlab.org/nlab/show/degree" - - "https://www.encyclopediaofmath.org/index.php/Degree" - - - concept: degree-of-graph - arity: 1 - en: degree of graph of $1 - property: function - area: "graph theory" - mathml: - - "deg(x)" - urls: - - "https://en.wikipedia.org/wiki/Degree_(graph_theory)" - alias: - - valency - - degree - - - concept: degree-of-freedom - arity: 0 + property: symbol + subject-area: "genetics" + mathml: + - "cyc" + urls: + - "https://en.wikipedia.org/wiki/Cycle_(gene)" + + - concept: cyclotomic-field + arity: 1 + arguments: [a1] + speech: + en: cyclotomic field of a1 + property: embellished symbol + subject-area: "number theory" + mathml: + - "𝐐(ζn)" + urls: + - "https://mathworld.wolfram.com/CyclotomicField.html" + - "https://en.wikipedia.org/wiki/Cyclotomic_field" + - "https://ncatlab.org/nlab/show/cyclotomic+field" + - "https://www.encyclopediaofmath.org/index.php/Cyclotomic_field" + + - concept: cyclotomic-polynomial + arity: 1 + arguments: [a1] + speech: + en: a1th cyclotomic polynomial + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Φx" + urls: + - "https://mathworld.wolfram.com/CyclotomicPolynomial.html" + - "https://en.wikipedia.org/wiki/Cyclotomic_polynomial" + - "https://www.encyclopediaofmath.org/index.php/Cyclotomic_polynomials" + + - concept: dalembert-operator + arity: 1 + arguments: [a1] + speech: + en: dalembert operator of a1 + property: prefix + subject-area: "partial differential equations" + mathml: + - "☐x" + urls: + - "https://en.wikipedia.org/wiki/D%27Alembert_operator" + - "https://www.encyclopediaofmath.org/index.php/D'Alembert_operator" + alias: + - dalembertian + - wave-operator + - box-operator + + - concept: davenport-constant + arity: 1 + arguments: [a1] + speech: + en: davenport constant of a1 + property: function + subject-area: "group theory" + mathml: + - "D(x)" + urls: + - "https://mathworld.wolfram.com/DavenportConstant.html" + - "https://en.wikipedia.org/wiki/Davenport_constant" + - "https://www.encyclopediaofmath.org/index.php/Davenport_constant" + + - concept: dawson-function + arity: 1 + arguments: [a1] + speech: + en: dawson function of a1 + property: function + subject-area: "special-functions" + mathml: + - "FX" + - "DX" + notationb: "mi sub D -" + notationa: "mi sub D +" + urls: + - "https://mathworld.wolfram.com/DawsonsIntegral.html" + - "https://en.wikipedia.org/wiki/Dawson_function" + - "https://dlmf.nist.gov/7.2#ii" + - "https://dlmf.nist.gov/7.2#E5" + alias: + - dawson-integral + + - concept: decrease + arity: 1 + arguments: [a1] + speech: + en: decrease of a1 + property: postfix + subject-area: "physics" + mathml: + - "x↓" + urls: + - "https://youtu.be/HZ7a9YkF204?t=4705" + + - concept: decrease-tends-to + arity: 2 + arguments: [a1, a2] + speech: + en: a1 decrease tends to a2 + property: infix + subject-area: "calculus" + mathml: + - "X↘Y" + urls: + - "https://math.stackexchange.com/questions/1886232/what-does-this-notation-mean-limes-from-left-right" + - "http://pi.math.cornell.edu/~web6720/MATH%206710%20notes.pdf" + + - concept: dedekind-eta-function + arity: 1 + arguments: [a1] + speech: + en: dedekind eta function of a1 + property: function + subject-area: "special functions" + mathml: + - "η(x)" + urls: + - "https://mathworld.wolfram.com/DedekindEtaFunction.html" + - "https://en.wikipedia.org/wiki/Dedekind_eta_function" + - "https://ncatlab.org/nlab/show/Dedekind+eta+function" + + - concept: dedekind-zeta-function + arity: 1 + arguments: [a1] + speech: + en: dedekind zeta function of a1 + property: function + subject-area: "special functions" + mathml: + - "ζ(x)" + urls: + - "https://en.wikipedia.org/wiki/Dedekind_zeta_function" + + - concept: deductive-closure + arity: 1 + arguments: [a1] + speech: + en: deductive closure of a1 + property: function + subject-area: "logic" + mathml: + - "DedX" + - "ThX" + urls: + - "https://en.wikipedia.org/wiki/Deductive_closure" + + - concept: defined-as + arity: 2 + arguments: [a1, a2] + speech: + en: a1 defined as a2 + property: infix + subject-area: "general" + mathml: + - "X≜Y" + - "X≝Y" + - "X:=Y" + - "X=defY" + - "X:Y" + urls: + - "https://math.stackexchange.com/questions/522864/what-is-the-symbol-triangleq" + - "https://drive.google.com/file/d/1z_dcQ6lsOA_0CsH55fwcg4hQF_w22olM/view" + alias: + - defined-to-be-equal-to + - equal-to-by-definition + + - concept: degree + arity: 1 + arguments: [a1] + speech: + en: degree of a1 + property: prefix, postfix + subject-area: "physics, geometry" + mathml: + - "x°" + urls: + - "https://mathworld.wolfram.com/Degree.html" + - "https://en.wikipedia.org/wiki/Degree_(angle)" + - "https://en.wikipedia.org/wiki/Degree_(temperature)" + - "https://ncatlab.org/nlab/show/degree" + - "https://www.encyclopediaofmath.org/index.php/Degree" + + - concept: degree-of-graph + arity: 1 + arguments: [a1] + speech: + en: degree of graph of a1 + property: function + subject-area: "graph theory" + mathml: + - "deg(x)" + urls: + - "https://en.wikipedia.org/wiki/Degree_(graph_theory)" + alias: + - valency + - degree + + - concept: degree-of-freedom + arity: 0 + arguments: [] + speech: en: degree of freedom - property: symbol - area: "statistics" - mathml: - - "ν" - urls: - - "https://mathworld.wolfram.com/DegreeofFreedom.html" - - "https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)#Notation" - - - concept: degree-of-mapping - arity: 1 - en: degree of mapping of $1 - property: function - area: "topology" - mathml: - - "deg(x)" - urls: - - "https://en.wikipedia.org/wiki/Degree_of_a_continuous_mapping" - alias: - - degree - - - concept: degree-of-polynomial - arity: 1 - en: degree of polynomial of $1 - property: function - area: "polynomials" - mathml: - - "deg(x)" - urls: - - "https://en.wikipedia.org/wiki/Degree_of_a_polynomial" - alias: - - degree - - - concept: dependence-relation - arity: 2 - en: $1 dependence relation $2 - property: infix - area: "linear algebra" - mathml: - - "X◃Y" - urls: - - "https://en.wikipedia.org/wiki/Dependence_relation" - - - concept: dereference - arity: 1 - en: dereference of $1 - property: prefix - area: "programming languages" - mathml: - - "!x" - urls: - - "https://arxiv.org/pdf/1208.5915.pdf" - - - concept: derivation-tree - arity: 2 - en: derivation $1, $2 - property: mfrac - area: "logic" - mathml: - - "PQR" - urls: - - "https://www.encyclopediaofmath.org/index.php/Derivation_tree" - - - concept: derived-category - arity: 1 - en: derived category of $1 - property: function - area: "category theory" - mathml: - - "D(x)" - urls: - - "https://en.wikipedia.org/wiki/Derived_category" - - "https://ncatlab.org/nlab/show/derived+category" - - "https://www.encyclopediaofmath.org/index.php/Derived_category" - - - concept: diagonal-functor - arity: 0 + property: symbol + subject-area: "statistics" + mathml: + - "ν" + urls: + - "https://mathworld.wolfram.com/DegreeofFreedom.html" + - "https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)#Notation" + + - concept: degree-of-mapping + arity: 1 + arguments: [a1] + speech: + en: degree of mapping of a1 + property: function + subject-area: "topology" + mathml: + - "deg(x)" + urls: + - "https://en.wikipedia.org/wiki/Degree_of_a_continuous_mapping" + alias: + - degree + + - concept: degree-of-polynomial + arity: 1 + arguments: [a1] + speech: + en: degree of polynomial of a1 + property: function + subject-area: "polynomials" + mathml: + - "deg(x)" + urls: + - "https://en.wikipedia.org/wiki/Degree_of_a_polynomial" + alias: + - degree + + - concept: dependence-relation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 dependence relation a2 + property: infix + subject-area: "linear algebra" + mathml: + - "X◃Y" + urls: + - "https://en.wikipedia.org/wiki/Dependence_relation" + + - concept: dereference + arity: 1 + arguments: [a1] + speech: + en: dereference of a1 + property: prefix + subject-area: "programming languages" + mathml: + - "!x" + urls: + - "https://arxiv.org/pdf/1208.5915.pdf" + + - concept: derivation-tree + arity: 2 + arguments: [a1, a2] + speech: + en: derivation a1, a2 + property: mfrac + subject-area: "logic" + mathml: + - "PQR" + urls: + - "https://www.encyclopediaofmath.org/index.php/Derivation_tree" + + - concept: derived-category + arity: 1 + arguments: [a1] + speech: + en: derived category of a1 + property: function + subject-area: "category theory" + mathml: + - "D(x)" + urls: + - "https://en.wikipedia.org/wiki/Derived_category" + - "https://ncatlab.org/nlab/show/derived+category" + - "https://www.encyclopediaofmath.org/index.php/Derived_category" + + - concept: diagonal-functor + arity: 0 + arguments: [] + speech: en: diagonal functor - property: symbol - area: "category theory" - mathml: - - "Δ" - urls: - - "https://en.wikipedia.org/wiki/Diagonal_functor" - - "https://ncatlab.org/nlab/show/diagonal+functor" - - - concept: diagonal-intersection - arity: 1 - en: diagonal intersection of $1 - property: function - area: "set theory" - mathml: - - "Δ(x)" - urls: - - "https://en.wikipedia.org/wiki/Diagonal_intersection" - - - concept: diagonal-matrix - arity: 1 - en: diagonal matrix of $1 - property: function - area: "linear algebra" - mathml: - - "diag(x)" - urls: - - "https://en.wikipedia.org/wiki/Diagonal_matrix" - - - concept: diameter - arity: 1 - en: diameter of $1 - property: symbol, prefix unit - area: "geometry" - mathml: - - "dX" - - "⌀x" - notationb: "mi DIA" - notationa: "mi dia" - urls: - - "https://en.wikipedia.org/wiki/Diameter#Symbol" - - - concept: dickman-function - arity: 1 - en: dickman function of $1 - property: function - area: "special functions" - mathml: - - "ρ(x)" - urls: - - "https://mathworld.wolfram.com/DickmanFunction.html" - - "https://en.wikipedia.org/wiki/Dickman_function" - - "https://www.encyclopediaofmath.org/index.php/Dickman_function" - alias: - - dickman-de-bruijn-function - - - concept: different-ideal - arity: 1 - en: different ideal of $1 - property: function - area: "algebraic number theory" - mathml: - - "δx" - urls: - - "https://en.wikipedia.org/wiki/Different_ideal" - alias: - - different - - - concept: differential-entropy - arity: 1 - en: differential entropy of $1 - property: function - area: "information theory" - mathml: - - "h(x)" - urls: - - "https://mathworld.wolfram.com/DifferentialEntropy.html" - - "https://en.wikipedia.org/wiki/Differential_entropy" - - "https://www.encyclopediaofmath.org/index.php/Differential_entropy" - alias: - - continuous-entropy - - - concept: differential-operator - arity: 1 - en: differential operator with respect to $1 - property: prefix - area: "calculus" - mathml: - - "Dx" - - "∂x" - - "ddx" - notationa: "mfrac d mrow d $1" - urls: - - "https://mathworld.wolfram.com/DifferentialOperator.html" - - "https://en.wikipedia.org/wiki/Differential_operator" - - "https://ncatlab.org/nlab/show/differential+operator" - - "https://www.encyclopediaofmath.org/index.php/Differential_operator" - alias: - - newton-leibniz-operator - - differential - - diff - - - concept: digamma-function - arity: 0 + property: symbol + subject-area: "category theory" + mathml: + - "Δ" + urls: + - "https://en.wikipedia.org/wiki/Diagonal_functor" + - "https://ncatlab.org/nlab/show/diagonal+functor" + + - concept: diagonal-intersection + arity: 1 + arguments: [a1] + speech: + en: diagonal intersection of a1 + property: function + subject-area: "set theory" + mathml: + - "Δ(x)" + urls: + - "https://en.wikipedia.org/wiki/Diagonal_intersection" + + - concept: diagonal-matrix + arity: 1 + arguments: [a1] + speech: + en: diagonal matrix of a1 + property: function + subject-area: "linear algebra" + mathml: + - "diag(x)" + urls: + - "https://en.wikipedia.org/wiki/Diagonal_matrix" + + - concept: diameter + arity: 1 + arguments: [a1] + speech: + en: diameter of a1 + property: symbol, prefix unit + subject-area: "geometry" + mathml: + - "dX" + - "⌀x" + notationb: "mi DIA" + notationa: "mi dia" + urls: + - "https://en.wikipedia.org/wiki/Diameter#Symbol" + + - concept: dickman-function + arity: 1 + arguments: [a1] + speech: + en: dickman function of a1 + property: function + subject-area: "special functions" + mathml: + - "ρ(x)" + urls: + - "https://mathworld.wolfram.com/DickmanFunction.html" + - "https://en.wikipedia.org/wiki/Dickman_function" + - "https://www.encyclopediaofmath.org/index.php/Dickman_function" + alias: + - dickman-de-bruijn-function + + - concept: different-ideal + arity: 1 + arguments: [a1] + speech: + en: different ideal of a1 + property: function + subject-area: "algebraic number theory" + mathml: + - "δx" + urls: + - "https://en.wikipedia.org/wiki/Different_ideal" + alias: + - different + + - concept: differential-entropy + arity: 1 + arguments: [a1] + speech: + en: differential entropy of a1 + property: function + subject-area: "information theory" + mathml: + - "h(x)" + urls: + - "https://mathworld.wolfram.com/DifferentialEntropy.html" + - "https://en.wikipedia.org/wiki/Differential_entropy" + - "https://www.encyclopediaofmath.org/index.php/Differential_entropy" + alias: + - continuous-entropy + + - concept: differential-operator + arity: 1 + arguments: [a1] + speech: + en: differential operator with respect to a1 + property: prefix + subject-area: "calculus" + mathml: + - "Dx" + - "∂x" + - "ddx" + notationa: "mfrac d mrow d a1" + urls: + - "https://mathworld.wolfram.com/DifferentialOperator.html" + - "https://en.wikipedia.org/wiki/Differential_operator" + - "https://ncatlab.org/nlab/show/differential+operator" + - "https://www.encyclopediaofmath.org/index.php/Differential_operator" + alias: + - newton-leibniz-operator + - differential + - diff + + - concept: digamma-function + arity: 0 + arguments: [] + speech: en: digamma function - property: symbol - area: "special functions" - mathml: - - "ψ0" - - "ψ(0)" - - "F" - urls: - - "https://mathworld.wolfram.com/DigammaFunction.html" - - "https://en.wikipedia.org/wiki/Digamma_function" - - - concept: dihedral-group - arity: 1 - en: $1th dihedral group - property: symbol - area: "group theory" - mathml: - - "Dn" - - "Dihn" - - "D2n" - urls: - - "https://mathworld.wolfram.com/DihedralGroup.html" - - "https://en.wikipedia.org/wiki/Dihedral_group" - - - concept: dilation - arity: 2 - en: $1 dilation $2 - property: infix - area: "mathematical morphology" - mathml: - - "X⊕Y" - urls: - - "https://en.wikipedia.org/wiki/Dilation_(morphology)" - - - concept: dilogarithm - arity: 1 - en: dilogarithm of $1 - property: function - area: "special functions" - mathml: - - "L2z" - urls: - - "https://mathworld.wolfram.com/Dilogarithm.html" - - "https://en.wikipedia.org/wiki/Spence%27s_function" - - "https://dlmf.nist.gov/25.12#E1" - - "https://ncatlab.org/nlab/show/dilogarithm" - - "https://ncatlab.org/nlab/show/dilogarithm" - alias: - - spence-function - - - concept: dimension - arity: 1 - en: dimension of $1 - property: "function, fenced" - area: "linear algebra, graph theory" - mathml: - - "dimX" - - "[x]" - urls: - - "https://mathworld.wolfram.com/Dimension.html" - - "https://en.wikipedia.org/wiki/Dimension_(mathematics_and_physics)" - - "https://en.wikipedia.org/wiki/Dimension_(graph_theory)" - - "https://en.wikipedia.org/wiki/Order_dimension" - - "https://en.wikipedia.org/wiki/Dimensions_(animation)" - - "https://en.wikipedia.org/wiki/Dimension_(vector_space)" - - "https://en.wikipedia.org/wiki/Dimension_of_an_algebraic_variety" - - "https://en.wikipedia.org/wiki/Slowly_changing_dimension" - - "https://en.wikipedia.org/wiki/Scaling_dimension" - - "https://ncatlab.org/nlab/show/dimension" - - "https://www.encyclopediaofmath.org/index.php/Dimension" - - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions" - - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions" - - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values" - - - concept: dirac-delta-function - arity: 1 - en: dirac delta function of $1 - property: function - area: "analysis" - mathml: - - "δ(x)" - urls: - - "https://mathworld.wolfram.com/DiracDeltaFunction.html" - - "https://en.wikipedia.org/wiki/Dirac_delta_function" - alias: - - delta-function - - - concept: dirac-matrix - arity: 0 + property: symbol + subject-area: "special functions" + mathml: + - "ψ0" + - "ψ(0)" + - "F" + urls: + - "https://mathworld.wolfram.com/DigammaFunction.html" + - "https://en.wikipedia.org/wiki/Digamma_function" + + - concept: dihedral-group + arity: 1 + arguments: [a1] + speech: + en: a1th dihedral group + property: symbol + subject-area: "group theory" + mathml: + - "Dn" + - "Dihn" + - "D2n" + urls: + - "https://mathworld.wolfram.com/DihedralGroup.html" + - "https://en.wikipedia.org/wiki/Dihedral_group" + + - concept: dilation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 dilation a2 + property: infix + subject-area: "mathematical morphology" + mathml: + - "X⊕Y" + urls: + - "https://en.wikipedia.org/wiki/Dilation_(morphology)" + + - concept: dilogarithm + arity: 1 + arguments: [a1] + speech: + en: dilogarithm of a1 + property: function + subject-area: "special functions" + mathml: + - "L2z" + urls: + - "https://mathworld.wolfram.com/Dilogarithm.html" + - "https://en.wikipedia.org/wiki/Spence%27s_function" + - "https://dlmf.nist.gov/25.12#E1" + - "https://ncatlab.org/nlab/show/dilogarithm" + - "https://ncatlab.org/nlab/show/dilogarithm" + alias: + - spence-function + + - concept: dimension + arity: 1 + arguments: [a1] + speech: + en: dimension of a1 + property: "function, fenced" + subject-area: "linear algebra, graph theory" + mathml: + - "dimX" + - "[x]" + urls: + - "https://mathworld.wolfram.com/Dimension.html" + - "https://en.wikipedia.org/wiki/Dimension_(mathematics_and_physics)" + - "https://en.wikipedia.org/wiki/Dimension_(graph_theory)" + - "https://en.wikipedia.org/wiki/Order_dimension" + - "https://en.wikipedia.org/wiki/Dimensions_(animation)" + - "https://en.wikipedia.org/wiki/Dimension_(vector_space)" + - "https://en.wikipedia.org/wiki/Dimension_of_an_algebraic_variety" + - "https://en.wikipedia.org/wiki/Slowly_changing_dimension" + - "https://en.wikipedia.org/wiki/Scaling_dimension" + - "https://ncatlab.org/nlab/show/dimension" + - "https://www.encyclopediaofmath.org/index.php/Dimension" + - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions" + - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions" + - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values" + + - concept: dirac-delta-function + arity: 1 + arguments: [a1] + speech: + en: dirac delta function of a1 + property: function + subject-area: "analysis" + mathml: + - "δ(x)" + urls: + - "https://mathworld.wolfram.com/DiracDeltaFunction.html" + - "https://en.wikipedia.org/wiki/Dirac_delta_function" + alias: + - delta-function + + - concept: dirac-matrix + arity: 0 + arguments: [] + speech: en: dirac matrix - property: constant - area: "mathematical physics" - mathml: - - "γ0" - - "γ1" - - "γ2" - - "γ3" - urls: - - "https://mathworld.wolfram.com/DiracMatrices.html" - - "https://en.wikipedia.org/wiki/Gamma_matrices" - - "https://www.encyclopediaofmath.org/index.php/Dirac_matrices" - alias: - - gamma-matrix - - - concept: dirac-measure - arity: 1 - en: dirac measure of $1 - property: function - area: "measure theory" - mathml: - - "δ(x)" - urls: - - "https://en.wikipedia.org/wiki/Dirac_measure" - - - concept: dirac-operator - arity: 1 - en: dirac operator of $1 - property: function - area: "differential operators" - mathml: - - "D(x)" - urls: - - "https://mathworld.wolfram.com/DiracOperator.html" - - "https://en.wikipedia.org/wiki/Dirac_operator" - - "https://ncatlab.org/nlab/show/Dirac+operator" - - - concept: direct-limit - arity: 1 - en: direct limit of $1 - property: prefix - area: "category theory" - mathml: - - "lim→A" - urls: - - "https://mathworld.wolfram.com/DirectLimit.html" - - "https://en.wikipedia.org/wiki/Direct_limit" - - "https://ncatlab.org/nlab/show/direct+limit" - - - concept: direct-product - arity: 2 - en: $1 direct product $2 - property: infix - area: "abstract algebra" - mathml: - - "X×Y" - urls: - - "https://mathworld.wolfram.com/DirectProduct.html" - - "https://en.wikipedia.org/wiki/Direct_product" - - "https://en.wikipedia.org/wiki/Direct_product_of_groups" - - "https://ncatlab.org/nlab/show/direct+product" - - "https://www.encyclopediaofmath.org/index.php/Direct_product" - - - concept: direct-sum - arity: 2 - en: $1 direct sum $2 - property: infix - area: "abstract algebra" - mathml: - - "X⊕Y" - urls: - - "https://mathworld.wolfram.com/DirectSum.html" - - "https://en.wikipedia.org/wiki/Direct_sum" - - "https://en.wikipedia.org/wiki/Direct_sum_of_modules" - - "https://en.wikipedia.org/wiki/Skew_and_direct_sums_of_permutations" - - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)" - - "https://en.wikipedia.org/wiki/Direct_sum_of_groups" - - "https://ncatlab.org/nlab/show/direct+sum" - - "https://www.encyclopediaofmath.org/index.php/Direct_sum" - - - concept: directional-derivative - arity: 1 - en: directional derivative of $1 - property: "function, mixfix" - area: "differential calculus" - mathml: - - "∇vf" - - "Dvf" - - "v⋅∇f" - urls: - - "https://mathworld.wolfram.com/DirectionalDerivative.html" - - "https://en.wikipedia.org/wiki/Directional_derivative" - - "https://ncatlab.org/nlab/show/directional+derivative" - - - concept: dirichlet-character - arity: 1 - en: dirichlet character of $1 - property: function - area: "special-functions" - mathml: - - "χ(x)" - urls: - - "https://mathworld.wolfram.com/DirichletCharacter.html" - - "https://en.wikipedia.org/wiki/Dirichlet_character" - - "https://dlmf.nist.gov/27.8" - - "https://www.encyclopediaofmath.org/index.php/Dirichlet_character" - - - concept: dirichlet-convolution - arity: 2 - en: $1 dirichlet convolution $2 - property: infix - area: "number theory" - mathml: - - "X∗Y" - urls: - - "https://en.wikipedia.org/wiki/Dirichlet_convolution" - - "https://www.encyclopediaofmath.org/index.php/Dirichlet_convolution" - - - concept: dirichlet-distribution - arity: 0 + property: constant + subject-area: "mathematical physics" + mathml: + - "γ0" + - "γ1" + - "γ2" + - "γ3" + urls: + - "https://mathworld.wolfram.com/DiracMatrices.html" + - "https://en.wikipedia.org/wiki/Gamma_matrices" + - "https://www.encyclopediaofmath.org/index.php/Dirac_matrices" + alias: + - gamma-matrix + + - concept: dirac-measure + arity: 1 + arguments: [a1] + speech: + en: dirac measure of a1 + property: function + subject-area: "measure theory" + mathml: + - "δ(x)" + urls: + - "https://en.wikipedia.org/wiki/Dirac_measure" + + - concept: dirac-operator + arity: 1 + arguments: [a1] + speech: + en: dirac operator of a1 + property: function + subject-area: "differential operators" + mathml: + - "D(x)" + urls: + - "https://mathworld.wolfram.com/DiracOperator.html" + - "https://en.wikipedia.org/wiki/Dirac_operator" + - "https://ncatlab.org/nlab/show/Dirac+operator" + + - concept: direct-limit + arity: 1 + arguments: [a1] + speech: + en: direct limit of a1 + property: prefix + subject-area: "category theory" + mathml: + - "lim→A" + urls: + - "https://mathworld.wolfram.com/DirectLimit.html" + - "https://en.wikipedia.org/wiki/Direct_limit" + - "https://ncatlab.org/nlab/show/direct+limit" + + - concept: direct-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 direct product a2 + property: infix + subject-area: "abstract algebra" + mathml: + - "X×Y" + urls: + - "https://mathworld.wolfram.com/DirectProduct.html" + - "https://en.wikipedia.org/wiki/Direct_product" + - "https://en.wikipedia.org/wiki/Direct_product_of_groups" + - "https://ncatlab.org/nlab/show/direct+product" + - "https://www.encyclopediaofmath.org/index.php/Direct_product" + + - concept: direct-sum + arity: 2 + arguments: [a1, a2] + speech: + en: a1 direct sum a2 + property: infix + subject-area: "abstract algebra" + mathml: + - "X⊕Y" + urls: + - "https://mathworld.wolfram.com/DirectSum.html" + - "https://en.wikipedia.org/wiki/Direct_sum" + - "https://en.wikipedia.org/wiki/Direct_sum_of_modules" + - "https://en.wikipedia.org/wiki/Skew_and_direct_sums_of_permutations" + - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)" + - "https://en.wikipedia.org/wiki/Direct_sum_of_groups" + - "https://ncatlab.org/nlab/show/direct+sum" + - "https://www.encyclopediaofmath.org/index.php/Direct_sum" + + - concept: directional-derivative + arity: 1 + arguments: [a1] + speech: + en: directional derivative of a1 + property: "function, mixfix" + subject-area: "differential calculus" + mathml: + - "∇vf" + - "Dvf" + - "v⋅∇f" + urls: + - "https://mathworld.wolfram.com/DirectionalDerivative.html" + - "https://en.wikipedia.org/wiki/Directional_derivative" + - "https://ncatlab.org/nlab/show/directional+derivative" + + - concept: dirichlet-character + arity: 1 + arguments: [a1] + speech: + en: dirichlet character of a1 + property: function + subject-area: "special-functions" + mathml: + - "χ(x)" + urls: + - "https://mathworld.wolfram.com/DirichletCharacter.html" + - "https://en.wikipedia.org/wiki/Dirichlet_character" + - "https://dlmf.nist.gov/27.8" + - "https://www.encyclopediaofmath.org/index.php/Dirichlet_character" + + - concept: dirichlet-convolution + arity: 2 + arguments: [a1, a2] + speech: + en: a1 dirichlet convolution a2 + property: infix + subject-area: "number theory" + mathml: + - "X∗Y" + urls: + - "https://en.wikipedia.org/wiki/Dirichlet_convolution" + - "https://www.encyclopediaofmath.org/index.php/Dirichlet_convolution" + + - concept: dirichlet-distribution + arity: 0 + arguments: [] + speech: en: dirichlet distribution - property: symbol - area: "statistics" - mathml: - - "Dir" - urls: - - "https://mathworld.wolfram.com/DirichletDistribution.html" - - "https://en.wikipedia.org/wiki/Dirichlet_distribution" - - "https://www.encyclopediaofmath.org/index.php/Dirichlet_distribution" - - - concept: dirichlet-eta-function - arity: 1 - en: dirichlet eta function of $1 - property: function - area: "analytic number theory" - mathml: - - "η(x)" - urls: - - "https://mathworld.wolfram.com/DirichletEtaFunction.html" - - "https://en.wikipedia.org/wiki/%CE%97(x)" - - "https://en.wikipedia.org/wiki/Dirichlet_eta_function" - - - concept: dirichlet-kernel - arity: 1 - en: dirichlet kernel of $1 - property: function - area: "mathematical analysis" - mathml: - - "Dnf" - urls: - - "https://mathworld.wolfram.com/DirichletKernel.html" - - "https://en.wikipedia.org/wiki/Dirichlet_kernel" - - "https://www.encyclopediaofmath.org/index.php/Dirichlet_kernel" - - - concept: dirichlet-l-function - arity: 1 - en: dirichlet l function of $1 - property: function - area: "special-functions" - mathml: - - "L(x)" - urls: - - "https://mathworld.wolfram.com/DirichletL-Function.html" - - "https://en.wikipedia.org/wiki/Dirichlet_L-function" - alias: - - dirichlet-l-series - - - concept: discrete-valuation - arity: 1 - en: discrete valuation of $1 - property: function - area: "commutative algebra" - mathml: - - "ν(x)" - urls: - - "https://en.wikipedia.org/wiki/Discrete_valuation" - - "https://ncatlab.org/nlab/show/discrete+valuation" - - - concept: discriminant - arity: 1 - en: discriminant of $1 - property: function - area: "polynomials" - mathml: - - "DiscX" - - "DX" - - "ΔX" - urls: - - "https://mathworld.wolfram.com/Discriminant.html" - - "https://en.wikipedia.org/wiki/Discriminant" - - "https://ncatlab.org/nlab/show/discriminant" - - "https://www.encyclopediaofmath.org/index.php/Discriminant" - - - concept: disjoint-union - arity: 1 - en: disjoint union of $1 - property: indexed - area: "set theory" - mathml: - - "⨆i∈AAi" - urls: - - "https://mathworld.wolfram.com/DisjointUnion.html" - - "https://en.wikipedia.org/wiki/Disjoint_union" - - "https://en.wikipedia.org/wiki/Tagged_union" - - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)" - - "https://ncatlab.org/nlab/show/disjoint+union" + property: symbol + subject-area: "statistics" + mathml: + - "Dir" + urls: + - "https://mathworld.wolfram.com/DirichletDistribution.html" + - "https://en.wikipedia.org/wiki/Dirichlet_distribution" + - "https://www.encyclopediaofmath.org/index.php/Dirichlet_distribution" + + - concept: dirichlet-eta-function + arity: 1 + arguments: [a1] + speech: + en: dirichlet eta function of a1 + property: function + subject-area: "analytic number theory" + mathml: + - "η(x)" + urls: + - "https://mathworld.wolfram.com/DirichletEtaFunction.html" + - "https://en.wikipedia.org/wiki/%CE%97(x)" + - "https://en.wikipedia.org/wiki/Dirichlet_eta_function" + + - concept: dirichlet-kernel + arity: 1 + arguments: [a1] + speech: + en: dirichlet kernel of a1 + property: function + subject-area: "mathematical analysis" + mathml: + - "Dnf" + urls: + - "https://mathworld.wolfram.com/DirichletKernel.html" + - "https://en.wikipedia.org/wiki/Dirichlet_kernel" + - "https://www.encyclopediaofmath.org/index.php/Dirichlet_kernel" + + - concept: dirichlet-l-function + arity: 1 + arguments: [a1] + speech: + en: dirichlet l function of a1 + property: function + subject-area: "special-functions" + mathml: + - "L(x)" + urls: + - "https://mathworld.wolfram.com/DirichletL-Function.html" + - "https://en.wikipedia.org/wiki/Dirichlet_L-function" + alias: + - dirichlet-l-series + + - concept: discrete-valuation + arity: 1 + arguments: [a1] + speech: + en: discrete valuation of a1 + property: function + subject-area: "commutative algebra" + mathml: + - "ν(x)" + urls: + - "https://en.wikipedia.org/wiki/Discrete_valuation" + - "https://ncatlab.org/nlab/show/discrete+valuation" + + - concept: discriminant + arity: 1 + arguments: [a1] + speech: + en: discriminant of a1 + property: function + subject-area: "polynomials" + mathml: + - "DiscX" + - "DX" + - "ΔX" + urls: + - "https://mathworld.wolfram.com/Discriminant.html" + - "https://en.wikipedia.org/wiki/Discriminant" + - "https://ncatlab.org/nlab/show/discriminant" + - "https://www.encyclopediaofmath.org/index.php/Discriminant" + + - concept: disjoint-union + arity: 1 + arguments: [a1] + speech: + en: disjoint union of a1 + property: indexed + subject-area: "set theory" + mathml: + - "⨆i∈AAi" + urls: + - "https://mathworld.wolfram.com/DisjointUnion.html" + - "https://en.wikipedia.org/wiki/Disjoint_union" + - "https://en.wikipedia.org/wiki/Tagged_union" + - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)" + - "https://ncatlab.org/nlab/show/disjoint+union" - - concept: disjoint-union - arity: 2 - en: disjoint union of $1 and $2 - property: infix - area: "set theory" - mathml: - - "A*B" - urls: - - "https://mathworld.wolfram.com/DisjointUnion.html" - - "https://en.wikipedia.org/wiki/Disjoint_union" - - "https://en.wikipedia.org/wiki/Tagged_union" - - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)" - - "https://ncatlab.org/nlab/show/disjoint+union" - - - concept: distance - arity: 2 + - concept: disjoint-union + arity: 2 + arguments: [a1, a2] + speech: + en: disjoint union of a1 and a2 + property: infix + subject-area: "set theory" + mathml: + - "A*B" + urls: + - "https://mathworld.wolfram.com/DisjointUnion.html" + - "https://en.wikipedia.org/wiki/Disjoint_union" + - "https://en.wikipedia.org/wiki/Tagged_union" + - "https://en.wikipedia.org/wiki/Disjoint_union_(topology)" + - "https://ncatlab.org/nlab/show/disjoint+union" + + - concept: distance + arity: 2 + arguments: [a1, a2] + speech: en: distance - property: fenced - area: "geometry" - mathml: - - "|X Y|" - urls: - - "https://en.wikipedia.org/wiki/Distance" - - - concept: diverge - arity: 1 - en: $1 diverges - property: postfix - area: "computer science" - mathml: - - "x↑" - urls: - - "https://en.wikipedia.org/wiki/Divergence_(computer_science)" - alias: - - divergence - - - concept: divergence - arity: 1 - en: divergence of $1 - property: "function, mixfix" - area: "vector calculus" - mathml: - - "divf" - - "∇⋅f" - urls: - - "https://mathworld.wolfram.com/Divergence.html" - - "https://en.wikipedia.org/wiki/Divergence_(computer_science)" - - "https://en.wikipedia.org/wiki/Divergence" - - "https://en.wikipedia.org/wiki/Divergence_(statistics)" - - "https://ncatlab.org/nlab/show/divergence" - - "https://www.encyclopediaofmath.org/index.php/Divergence" - - - concept: divided-difference - arity: ">=0" - en: divided difference of $1 .. - property: "fenced, mixfix" - area: "special functions" - mathml: - - "[x,y,z]" - - "[x,y,z]" - - "f[x,y,z]" - - "D[x,y,z]f" - urls: - - "https://mathworld.wolfram.com/DividedDifference.html" - - "https://en.wikipedia.org/wiki/Divided_differences" - - "https://dlmf.nist.gov/3.3#SS3.p1" - - - concept: divisible-by - arity: 2 - en: $1 divisible by $2 - property: infix - area: "number theory" - mathml: - - "X|Y" - - "Y⋮X" - - "Y/X" - urls: - - "https://youtu.be/9dyK_op-Ocw?t=251" - - "https://en.wikipedia.org/wiki/Divisor" - - "https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D0%BB%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C" - - "https://youtu.be/a3wyG2mkmxc?t=32" - alias: - - divides - - - - concept: divisor-function - arity: 1 - en: divisor function of $1 - property: indexed - area: "number theory" - mathml: - - "σ(x)" - urls: - - "https://mathworld.wolfram.com/DivisorFunction.html" - - "https://en.wikipedia.org/wiki/D(n)" - - "https://en.wikipedia.org/wiki/%CE%A3(n)" - - "https://en.wikipedia.org/wiki/Divisor_function" - - "https://dlmf.nist.gov/27.2#E9" - - "https://dlmf.nist.gov/27.2#SS1.p4" - - - concept: domain - arity: 1 - en: domain of $1 - property: function - area: "set theory" - mathml: - - "dom(x)" - urls: - - "https://en.wikipedia.org/wiki/Domain_of_a_function" - - - concept: domain-of-discourse - arity: 0 + property: fenced + subject-area: "geometry" + mathml: + - "|X Y|" + urls: + - "https://en.wikipedia.org/wiki/Distance" + + - concept: diverge + arity: 1 + arguments: [a1] + speech: + en: a1 diverges + property: postfix + subject-area: "computer science" + mathml: + - "x↑" + urls: + - "https://en.wikipedia.org/wiki/Divergence_(computer_science)" + alias: + - divergence + + - concept: divergence + arity: 1 + arguments: [a1] + speech: + en: divergence of a1 + property: "function, mixfix" + subject-area: "vector calculus" + mathml: + - "divf" + - "∇⋅f" + urls: + - "https://mathworld.wolfram.com/Divergence.html" + - "https://en.wikipedia.org/wiki/Divergence_(computer_science)" + - "https://en.wikipedia.org/wiki/Divergence" + - "https://en.wikipedia.org/wiki/Divergence_(statistics)" + - "https://ncatlab.org/nlab/show/divergence" + - "https://www.encyclopediaofmath.org/index.php/Divergence" + + - concept: divided-difference + arity: ">=0" + speech: + en: divided difference of a1 .. + property: "fenced, mixfix" + subject-area: "special functions" + mathml: + - "[x,y,z]" + - "[x,y,z]" + - "f[x,y,z]" + - "D[x,y,z]f" + urls: + - "https://mathworld.wolfram.com/DividedDifference.html" + - "https://en.wikipedia.org/wiki/Divided_differences" + - "https://dlmf.nist.gov/3.3#SS3.p1" + + - concept: divisible-by + arity: 2 + arguments: [a1, a2] + speech: + en: a1 divisible by a2 + property: infix + subject-area: "number theory" + mathml: + - "X|Y" + - "Y⋮X" + - "Y/X" + urls: + - "https://youtu.be/9dyK_op-Ocw?t=251" + - "https://en.wikipedia.org/wiki/Divisor" + - "https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D0%BB%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C" + - "https://youtu.be/a3wyG2mkmxc?t=32" + alias: + - divides + + + - concept: divisor-function + arity: 1 + arguments: [a1] + speech: + en: divisor function of a1 + property: indexed + subject-area: "number theory" + mathml: + - "σ(x)" + urls: + - "https://mathworld.wolfram.com/DivisorFunction.html" + - "https://en.wikipedia.org/wiki/D(n)" + - "https://en.wikipedia.org/wiki/%CE%A3(n)" + - "https://en.wikipedia.org/wiki/Divisor_function" + - "https://dlmf.nist.gov/27.2#E9" + - "https://dlmf.nist.gov/27.2#SS1.p4" + + - concept: domain + arity: 1 + arguments: [a1] + speech: + en: domain of a1 + property: function + subject-area: "set theory" + mathml: + - "dom(x)" + urls: + - "https://en.wikipedia.org/wiki/Domain_of_a_function" + + - concept: domain-of-discourse + arity: 0 + arguments: [] + speech: en: domain of discourse - property: symbol - area: "formal semantics" - mathml: - - "𝔻" - urls: - - "https://en.wikipedia.org/wiki/Domain_of_discourse" - alias: - - universe-of-discourse - - - concept: domination-number - arity: 1 - en: domination number of $1 - property: function - area: "graph theory" - mathml: - - "γ(x)" - urls: - - "https://mathworld.wolfram.com/DominationNumber.html" - - "https://en.wikipedia.org/wiki/Dominating_set" - - "https://en.wikipedia.org/wiki/Domination_number" - - "https://en.wikipedia.org/wiki/Independent_domination_number" - - "https://en.wikipedia.org/wiki/Domination_analysis" - - "https://en.wikipedia.org/wiki/Domination_perfect_graph" - - - concept: dot-product - arity: 2 - en: $1 dot product $2 - property: infix - area: "linear algebra" - mathml: - - "X⋅Y" - urls: - - "https://mathworld.wolfram.com/DotProduct.html" - - "https://en.wikipedia.org/wiki/Dot_product" - alias: - - scalar-product - - - concept: double-bond - arity: 2 - en: $1 double bond $2 - property: infix - area: "chemistry" - mathml: - - "X=Y" - urls: - - "https://en.wikipedia.org/wiki/Double_bond" - - - concept: double-category - arity: 2 - en: $1 double category $2 - property: infix - area: "category theory" - mathml: - - "X⇉Y" - urls: - - "https://ncatlab.org/nlab/show/double+category" - - - concept: double-factorial - arity: 1 - en: double factorial of $1 - property: postfix - area: "combinatorics" - mathml: - - "10‼" - urls: - - "https://mathworld.wolfram.com/DoubleFactorial.html" - - "https://en.wikipedia.org/wiki/Double_factorial" - - "https://arxiv.org/pdf/0806.2334.pdf" - alias: - - semifactorial - - - concept: double-mersenne-number - arity: 0 + property: symbol + subject-area: "formal semantics" + mathml: + - "𝔻" + urls: + - "https://en.wikipedia.org/wiki/Domain_of_discourse" + alias: + - universe-of-discourse + + - concept: domination-number + arity: 1 + arguments: [a1] + speech: + en: domination number of a1 + property: function + subject-area: "graph theory" + mathml: + - "γ(x)" + urls: + - "https://mathworld.wolfram.com/DominationNumber.html" + - "https://en.wikipedia.org/wiki/Dominating_set" + - "https://en.wikipedia.org/wiki/Domination_number" + - "https://en.wikipedia.org/wiki/Independent_domination_number" + - "https://en.wikipedia.org/wiki/Domination_analysis" + - "https://en.wikipedia.org/wiki/Domination_perfect_graph" + + - concept: dot-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 dot product a2 + property: infix + subject-area: "linear algebra" + mathml: + - "X⋅Y" + urls: + - "https://mathworld.wolfram.com/DotProduct.html" + - "https://en.wikipedia.org/wiki/Dot_product" + alias: + - scalar-product + + - concept: double-bond + arity: 2 + arguments: [a1, a2] + speech: + en: a1 double bond a2 + property: infix + subject-area: "chemistry" + mathml: + - "X=Y" + urls: + - "https://en.wikipedia.org/wiki/Double_bond" + + - concept: double-category + arity: 2 + arguments: [a1, a2] + speech: + en: a1 double category a2 + property: infix + subject-area: "category theory" + mathml: + - "X⇉Y" + urls: + - "https://ncatlab.org/nlab/show/double+category" + + - concept: double-factorial + arity: 1 + arguments: [a1] + speech: + en: double factorial of a1 + property: postfix + subject-area: "combinatorics" + mathml: + - "10‼" + urls: + - "https://mathworld.wolfram.com/DoubleFactorial.html" + - "https://en.wikipedia.org/wiki/Double_factorial" + - "https://arxiv.org/pdf/0806.2334.pdf" + alias: + - semifactorial + + - concept: double-mersenne-number + arity: 0 + arguments: [] + speech: en: double mersenne number - property: symbol - area: "number theory" - mathml: - - "MMp" - urls: - - "https://mathworld.wolfram.com/DoubleMersenneNumber.html" - - "https://en.wikipedia.org/wiki/Double_Mersenne_number" - - "https://en.wikipedia.org/wiki/Double_Mersenne_prime" - - "https://en.wikipedia.org/wiki/Catalan%27s_Mersenne_conjecture" - - - concept: drinfeld-center - arity: 1 - en: drinfeld center of $1 - property: prefix - area: "category theory" - mathml: - - "𝒵(x)" - urls: - - "https://en.wikipedia.org/wiki/Center_(category_theory)" - alias: - - center - - - concept: dual-basis - arity: 1 - en: dual basis of $1 - property: msup - area: "linear algebra" - mathml: - - "X*" - urls: - - "https://mathworld.wolfram.com/DualBasis.html" - - "https://en.wikipedia.org/wiki/Dual_basis" - - "https://ncatlab.org/nlab/show/dual+basis" - - "https://www.encyclopediaofmath.org/index.php/Dual_basis" - alias: - - dual-set - - reciprocal-basis - - - concept: dual-bundle - arity: 1 - en: dual bundle of $1 - property: msup - area: "vector bundles" - mathml: - - "X*" - urls: - - "https://mathworld.wolfram.com/DualBundle.html" - - "https://en.wikipedia.org/wiki/Dual_bundle" - - "https://www.encyclopediaofmath.org/index.php/Dual_bundle" - alias: - - dual - - - concept: dual-space - arity: 1 - en: dual space of $1 - property: msup - area: "linear algebra" - mathml: - - "V*" - - "V′" - urls: - - "https://mathworld.wolfram.com/DualSpace.html" - - "https://en.wikipedia.org/wiki/Dual_space" - - "https://ncatlab.org/nlab/show/dual+space" - alias: - - dual - - - concept: duodecimal - arity: 1 - en: duodecimal of $1 - property: unit - area: "arithmetic" - mathml: - - "nz" - - "n12" - - "ndoz" - urls: - - "https://mathworld.wolfram.com/Duodecimal.html" - - "https://en.wikipedia.org/wiki/Duodecimal#Base_notation" - alias: - - base-twelve - - dozenal - - - concept: e-function - arity: 1 - en: e function of $1 - property: function - area: "special functions" - mathml: - - "E(x)" - urls: - - "https://mathworld.wolfram.com/E-Function.html" - - "https://en.wikipedia.org/wiki/E-function" - - "https://en.wikipedia.org/wiki/MacRobert_E_function" - - "https://www.encyclopediaofmath.org/index.php/E-function" - - - concept: eccentricity - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "MMp" + urls: + - "https://mathworld.wolfram.com/DoubleMersenneNumber.html" + - "https://en.wikipedia.org/wiki/Double_Mersenne_number" + - "https://en.wikipedia.org/wiki/Double_Mersenne_prime" + - "https://en.wikipedia.org/wiki/Catalan%27s_Mersenne_conjecture" + + - concept: drinfeld-center + arity: 1 + arguments: [a1] + speech: + en: drinfeld center of a1 + property: prefix + subject-area: "category theory" + mathml: + - "𝒵(x)" + urls: + - "https://en.wikipedia.org/wiki/Center_(category_theory)" + alias: + - center + + - concept: dual-basis + arity: 1 + arguments: [a1] + speech: + en: dual basis of a1 + property: msup + subject-area: "linear algebra" + mathml: + - "X*" + urls: + - "https://mathworld.wolfram.com/DualBasis.html" + - "https://en.wikipedia.org/wiki/Dual_basis" + - "https://ncatlab.org/nlab/show/dual+basis" + - "https://www.encyclopediaofmath.org/index.php/Dual_basis" + alias: + - dual-set + - reciprocal-basis + + - concept: dual-bundle + arity: 1 + arguments: [a1] + speech: + en: dual bundle of a1 + property: msup + subject-area: "vector bundles" + mathml: + - "X*" + urls: + - "https://mathworld.wolfram.com/DualBundle.html" + - "https://en.wikipedia.org/wiki/Dual_bundle" + - "https://www.encyclopediaofmath.org/index.php/Dual_bundle" + alias: + - dual + + - concept: dual-space + arity: 1 + arguments: [a1] + speech: + en: dual space of a1 + property: msup + subject-area: "linear algebra" + mathml: + - "V*" + - "V′" + urls: + - "https://mathworld.wolfram.com/DualSpace.html" + - "https://en.wikipedia.org/wiki/Dual_space" + - "https://ncatlab.org/nlab/show/dual+space" + alias: + - dual + + - concept: duodecimal + arity: 1 + arguments: [a1] + speech: + en: duodecimal of a1 + property: unit + subject-area: "arithmetic" + mathml: + - "nz" + - "n12" + - "ndoz" + urls: + - "https://mathworld.wolfram.com/Duodecimal.html" + - "https://en.wikipedia.org/wiki/Duodecimal#Base_notation" + alias: + - base-twelve + - dozenal + + - concept: e-function + arity: 1 + arguments: [a1] + speech: + en: e function of a1 + property: function + subject-area: "special functions" + mathml: + - "E(x)" + urls: + - "https://mathworld.wolfram.com/E-Function.html" + - "https://en.wikipedia.org/wiki/E-function" + - "https://en.wikipedia.org/wiki/MacRobert_E_function" + - "https://www.encyclopediaofmath.org/index.php/E-function" + + - concept: eccentricity + arity: 0 + arguments: [] + speech: en: eccentricity - property: symbol - area: "analytic geometry, graph theory" - mathml: - - "e" - - "ϵ" - urls: - - "https://mathworld.wolfram.com/Eccentricity.html" - - "https://en.wikipedia.org/wiki/Eccentricity_(mathematics)" - - "https://www.encyclopediaofmath.org/index.php/Eccentricity" - - - concept: edge-cover-number - arity: 1 - en: edge cover number of $1 - property: function - area: "graph theory" - mathml: - - "ρ(x)" - urls: - - "https://mathworld.wolfram.com/EdgeCoverNumber.html" - - "https://en.wikipedia.org/wiki/Edge_covering_number" - - - concept: effective-domain - arity: 1 - en: effective domain of $1 - property: function - area: "convex analysis" - mathml: - - "dom(x)" - urls: - - "https://en.wikipedia.org/wiki/Effective_domain" - - - concept: efficiency - arity: 1 - en: efficiency of $1 - property: function - area: "statistics" - mathml: - - "e(x)" - urls: - - "https://en.wikipedia.org/wiki/Antenna_efficiency" - - "https://en.wikipedia.org/wiki/Efficiency_(statistics)" - - "https://en.wikipedia.org/wiki/Efficiency" - - - concept: einstein-tensor - arity: 0 + property: symbol + subject-area: "analytic geometry, graph theory" + mathml: + - "e" + - "ϵ" + urls: + - "https://mathworld.wolfram.com/Eccentricity.html" + - "https://en.wikipedia.org/wiki/Eccentricity_(mathematics)" + - "https://www.encyclopediaofmath.org/index.php/Eccentricity" + + - concept: edge-cover-number + arity: 1 + arguments: [a1] + speech: + en: edge cover number of a1 + property: function + subject-area: "graph theory" + mathml: + - "ρ(x)" + urls: + - "https://mathworld.wolfram.com/EdgeCoverNumber.html" + - "https://en.wikipedia.org/wiki/Edge_covering_number" + + - concept: effective-domain + arity: 1 + arguments: [a1] + speech: + en: effective domain of a1 + property: function + subject-area: "convex analysis" + mathml: + - "dom(x)" + urls: + - "https://en.wikipedia.org/wiki/Effective_domain" + + - concept: efficiency + arity: 1 + arguments: [a1] + speech: + en: efficiency of a1 + property: function + subject-area: "statistics" + mathml: + - "e(x)" + urls: + - "https://en.wikipedia.org/wiki/Antenna_efficiency" + - "https://en.wikipedia.org/wiki/Efficiency_(statistics)" + - "https://en.wikipedia.org/wiki/Efficiency" + + - concept: einstein-tensor + arity: 0 + arguments: [] + speech: en: einstein tensor - property: symbol - area: "general relativity" - mathml: - - "G" - urls: - - "https://mathworld.wolfram.com/EinsteinTensor.html" - - "https://en.wikipedia.org/wiki/Einstein_tensor" - - "https://ncatlab.org/nlab/show/Einstein+tensor" - - - concept: elliptic-function - arity: 1 - en: elliptic function of $1 - property: function - area: "special functions" - mathml: - - "cnX" - - "snX" - - "dnX" - urls: - - "https://mathworld.wolfram.com/EllipticFunction.html" - - "https://en.wikipedia.org/wiki/Elliptic_function" - - "https://ncatlab.org/nlab/show/elliptic+function" - - "https://www.encyclopediaofmath.org/index.php/Elliptic_function" - - "https://mathworld.wolfram.com/JacobiEllipticFunctions.html" - - - concept: end - arity: 0 + property: symbol + subject-area: "general relativity" + mathml: + - "G" + urls: + - "https://mathworld.wolfram.com/EinsteinTensor.html" + - "https://en.wikipedia.org/wiki/Einstein_tensor" + - "https://ncatlab.org/nlab/show/Einstein+tensor" + + - concept: elliptic-function + arity: 1 + arguments: [a1] + speech: + en: elliptic function of a1 + property: function + subject-area: "special functions" + mathml: + - "cnX" + - "snX" + - "dnX" + urls: + - "https://mathworld.wolfram.com/EllipticFunction.html" + - "https://en.wikipedia.org/wiki/Elliptic_function" + - "https://ncatlab.org/nlab/show/elliptic+function" + - "https://www.encyclopediaofmath.org/index.php/Elliptic_function" + - "https://mathworld.wolfram.com/JacobiEllipticFunctions.html" + + - concept: end + arity: 0 + arguments: [] + speech: en: end - property: symbol - area: "category theory" - mathml: - - "e" - urls: - - "https://en.wikipedia.org/wiki/End_(category_theory)" - - "https://ncatlab.org/nlab/show/end" - - - concept: endomorphism-monoid - arity: 1 - en: endomorphism monoid of $1 - property: function - area: "category theory" - mathml: - - "End(x)" - urls: - - "https://mathworld.wolfram.com/Endomorphism.html" - - "https://en.wikipedia.org/wiki/Endomorphism" - - "https://ncatlab.org/nlab/show/endomorphism" - - "https://www.encyclopediaofmath.org/index.php/Endomorphism" - - - concept: energy - arity: 0 + property: symbol + subject-area: "category theory" + mathml: + - "e" + urls: + - "https://en.wikipedia.org/wiki/End_(category_theory)" + - "https://ncatlab.org/nlab/show/end" + + - concept: endomorphism-monoid + arity: 1 + arguments: [a1] + speech: + en: endomorphism monoid of a1 + property: function + subject-area: "category theory" + mathml: + - "End(x)" + urls: + - "https://mathworld.wolfram.com/Endomorphism.html" + - "https://en.wikipedia.org/wiki/Endomorphism" + - "https://ncatlab.org/nlab/show/endomorphism" + - "https://www.encyclopediaofmath.org/index.php/Endomorphism" + + - concept: energy + arity: 0 + arguments: [] + speech: en: energy - property: symbol - area: "physics" - mathml: - - "E" - urls: - - "https://ncatlab.org/nlab/show/energy" - - - concept: energy-of-signal - arity: 0 + property: symbol + subject-area: "physics" + mathml: + - "E" + urls: + - "https://ncatlab.org/nlab/show/energy" + + - concept: energy-of-signal + arity: 0 + arguments: [] + speech: en: energy of signal - property: symbol - area: "signal processing" - mathml: - - "Es" - urls: - - "https://en.wikipedia.org/wiki/Energy_(signal_processing)" - - "https://en.wikipedia.org/wiki/Energy_(signal_processing)" - - - concept: entropy - arity: 1 - en: entropy of $1 - property: unit - area: "physics" - mathml: - - "S(x)" - urls: - - "https://en.wikipedia.org/wiki/Entropy" - - "https://en.wikipedia.org/wiki/Entropy_(arrow_of_time)" - - "https://en.wikipedia.org/wiki/Entropy_(classical_thermodynamics)" - - "https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)" - - "https://en.wikipedia.org/wiki/History_of_entropy" - - - concept: epigraph - arity: 1 - en: epigraph of $1 - property: function - area: "analysis" - mathml: - - "epi(x)" - urls: - - "https://en.wikipedia.org/wiki/Epigraph_(mathematics)" - - - concept: epsilon-number - arity: 0 + property: symbol + subject-area: "signal processing" + mathml: + - "Es" + urls: + - "https://en.wikipedia.org/wiki/Energy_(signal_processing)" + - "https://en.wikipedia.org/wiki/Energy_(signal_processing)" + + - concept: entropy + arity: 1 + arguments: [a1] + speech: + en: entropy of a1 + property: unit + subject-area: "physics" + mathml: + - "S(x)" + urls: + - "https://en.wikipedia.org/wiki/Entropy" + - "https://en.wikipedia.org/wiki/Entropy_(arrow_of_time)" + - "https://en.wikipedia.org/wiki/Entropy_(classical_thermodynamics)" + - "https://en.wikipedia.org/wiki/Entropy_(statistical_thermodynamics)" + - "https://en.wikipedia.org/wiki/History_of_entropy" + + - concept: epigraph + arity: 1 + arguments: [a1] + speech: + en: epigraph of a1 + property: function + subject-area: "analysis" + mathml: + - "epi(x)" + urls: + - "https://en.wikipedia.org/wiki/Epigraph_(mathematics)" + + - concept: epsilon-number + arity: 0 + arguments: [] + speech: en: epsilon number - property: symbol - area: "ordinal numbers" - mathml: - - "ε" - urls: - - "https://en.wikipedia.org/wiki/Epsilon_numbers_(mathematics)" - - - concept: equalizer - arity: 1 - en: equalizer of $1 - property: function - area: "set theory" - mathml: - - "Eq(x)" - urls: - - "https://mathworld.wolfram.com/Equalizer.html" - - "https://en.wikipedia.org/wiki/Equaliser_(mathematics)" - - "https://ncatlab.org/nlab/show/equalizer" - alias: - - difference-kernel - - equaliser - - - concept: equivalence-class - arity: 1 - en: equivalence class of $1 - property: fenced - area: "set theory" - mathml: - - "[X]" - urls: - - "https://mathworld.wolfram.com/EquivalenceClass.html" - - "https://en.wikipedia.org/wiki/Equivalence_class" - - "https://en.wikipedia.org/wiki/Equivalence_class_(music)" - - "https://ncatlab.org/nlab/show/equivalence+class" - - "https://www.encyclopediaofmath.org/index.php/Equivalence_class" - - - concept: equivalence-relation - arity: 2 - en: $1 equivalence relation $2 - property: infix - area: "set theory" - mathml: - - "X~Y" - urls: - - "https://mathworld.wolfram.com/EquivalenceRelation.html" - - "https://en.wikipedia.org/wiki/Equivalence_relation" - - "https://ncatlab.org/nlab/show/equivalence+relation" - - "https://www.encyclopediaofmath.org/index.php/Equivalence_relation" - alias: - - equivalence - - - concept: equivariant-cohomology - arity: 2 - en: equivariant cohomology $1 $2 - property: function - area: "algebraic topology" - mathml: - - "HG*(X;Λ)" - urls: - - "https://en.wikipedia.org/wiki/Equivariant_cohomology" - - "https://ncatlab.org/nlab/show/equivariant+cohomology" - - "https://www.encyclopediaofmath.org/index.php/Equivariant_cohomology" - - - concept: erdos-borwein-constant - arity: 0 + property: symbol + subject-area: "ordinal numbers" + mathml: + - "ε" + urls: + - "https://en.wikipedia.org/wiki/Epsilon_numbers_(mathematics)" + + - concept: equalizer + arity: 1 + arguments: [a1] + speech: + en: equalizer of a1 + property: function + subject-area: "set theory" + mathml: + - "Eq(x)" + urls: + - "https://mathworld.wolfram.com/Equalizer.html" + - "https://en.wikipedia.org/wiki/Equaliser_(mathematics)" + - "https://ncatlab.org/nlab/show/equalizer" + alias: + - difference-kernel + - equaliser + + - concept: equivalence-class + arity: 1 + arguments: [a1] + speech: + en: equivalence class of a1 + property: fenced + subject-area: "set theory" + mathml: + - "[X]" + urls: + - "https://mathworld.wolfram.com/EquivalenceClass.html" + - "https://en.wikipedia.org/wiki/Equivalence_class" + - "https://en.wikipedia.org/wiki/Equivalence_class_(music)" + - "https://ncatlab.org/nlab/show/equivalence+class" + - "https://www.encyclopediaofmath.org/index.php/Equivalence_class" + + - concept: equivalence-relation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 equivalence relation a2 + property: infix + subject-area: "set theory" + mathml: + - "X~Y" + urls: + - "https://mathworld.wolfram.com/EquivalenceRelation.html" + - "https://en.wikipedia.org/wiki/Equivalence_relation" + - "https://ncatlab.org/nlab/show/equivalence+relation" + - "https://www.encyclopediaofmath.org/index.php/Equivalence_relation" + alias: + - equivalence + + - concept: equivariant-cohomology + arity: 2 + arguments: [a1, a2] + speech: + en: equivariant cohomology a1 a2 + property: function + subject-area: "algebraic topology" + mathml: + - "HG*(X;Λ)" + urls: + - "https://en.wikipedia.org/wiki/Equivariant_cohomology" + - "https://ncatlab.org/nlab/show/equivariant+cohomology" + - "https://www.encyclopediaofmath.org/index.php/Equivariant_cohomology" + + - concept: erdos-borwein-constant + arity: 0 + arguments: [] + speech: en: erdos borwein constant - property: symbol - area: "number theory" - mathml: - - "E" - urls: - - "https://mathworld.wolfram.com/Erdos-BorweinConstant.html" - - "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Borwein_constant" - - - concept: error-function - arity: 1 - en: error function of $1 - property: function - area: "special functions" - mathml: - - "erfX" - - "erfcX" - - "wX" - urls: - - "https://mathworld.wolfram.com/ErrorFunction.html" - - "https://en.wikipedia.org/wiki/Error_function" - - "https://dlmf.nist.gov/7.2#i" - - "https://dlmf.nist.gov/7.2#E1" - - - concept: essential-extension - arity: 2 - en: $1 essential extension $2 - property: infix - area: "abstract algebra" - mathml: - - "X⊆eY" - - "X⊴Y" - - "X⊂Y" - urls: - - "https://en.wikipedia.org/wiki/Essential_extension" - alias: - - essential-submodule - - large-submodule - - - concept: essential-infimum - arity: 1 - en: essential infimum of $1 - property: function - area: "measure theory" - mathml: - - "ess infx" - urls: - - "https://mathworld.wolfram.com/essentialsupremum.html" - - "https://en.wikipedia.org/wiki/essential_supremum_and_essential_infimum" - - "https://ncatlab.org/nlab/show/essential+supremum" - - - concept: essential-supremum - arity: 1 - en: essential supremum of $1 - property: function - area: "measure theory" - mathml: - - "ess supx" - urls: - - "https://mathworld.wolfram.com/EssentialSupremum.html" - - "https://en.wikipedia.org/wiki/Essential_supremum_and_essential_infimum" - - "https://ncatlab.org/nlab/show/essential+supremum" - - - concept: estimated - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "E" + urls: + - "https://mathworld.wolfram.com/Erdos-BorweinConstant.html" + - "https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Borwein_constant" + + - concept: error-function + arity: 1 + arguments: [a1] + speech: + en: error function of a1 + property: function + subject-area: "special functions" + mathml: + - "erfX" + - "erfcX" + - "wX" + urls: + - "https://mathworld.wolfram.com/ErrorFunction.html" + - "https://en.wikipedia.org/wiki/Error_function" + - "https://dlmf.nist.gov/7.2#i" + - "https://dlmf.nist.gov/7.2#E1" + + - concept: essential-extension + arity: 2 + arguments: [a1, a2] + speech: + en: a1 essential extension a2 + property: infix + subject-area: "abstract algebra" + mathml: + - "X⊆eY" + - "X⊴Y" + - "X⊂Y" + urls: + - "https://en.wikipedia.org/wiki/Essential_extension" + alias: + - essential-submodule + - large-submodule + + - concept: essential-infimum + arity: 1 + arguments: [a1] + speech: + en: essential infimum of a1 + property: function + subject-area: "measure theory" + mathml: + - "ess infx" + urls: + - "https://mathworld.wolfram.com/essentialsupremum.html" + - "https://en.wikipedia.org/wiki/essential_supremum_and_essential_infimum" + - "https://ncatlab.org/nlab/show/essential+supremum" + + - concept: essential-supremum + arity: 1 + arguments: [a1] + speech: + en: essential supremum of a1 + property: function + subject-area: "measure theory" + mathml: + - "ess supx" + urls: + - "https://mathworld.wolfram.com/EssentialSupremum.html" + - "https://en.wikipedia.org/wiki/Essential_supremum_and_essential_infimum" + - "https://ncatlab.org/nlab/show/essential+supremum" + + - concept: estimated + arity: 0 + arguments: [] + speech: en: estimated - property: symbol - area: "symbols" - mathml: - - "℮" - urls: - - "https://en.wikipedia.org/wiki/Estimation" - alias: - - estimated-sign - - e-mark - - - concept: etale-cohomology - arity: 1 - en: etale cohomology of $1 - property: function - area: "algebraic topology" - mathml: - - "Het*(X)" - urls: - - "https://en.wikipedia.org/wiki/%C3%89tale_cohomology" - - "https://ncatlab.org/nlab/show/etale+cohomology" - - "https://www.encyclopediaofmath.org/index.php/Etale_cohomology" - - - concept: euclid-number - arity: 1 - en: euclid number $1 - property: symbol - area: "number theory" - mathml: - - "Ex" - urls: - - "https://mathworld.wolfram.com/EuclidNumber.html" - - "https://en.wikipedia.org/wiki/Euclid_number" - - - concept: euclidean-distance - arity: 1 - en: euclidean distance of $1 - property: function - area: "geometry" - mathml: - - "dX" - - "dx" - urls: - - "https://en.wikipedia.org/wiki/Euclidean_distance" - alias: - - euclidean-metric - - - concept: euclidean-plane - arity: 0 + property: symbol + subject-area: "symbols" + mathml: + - "℮" + urls: + - "https://en.wikipedia.org/wiki/Estimation" + alias: + - estimated-sign + - e-mark + + - concept: etale-cohomology + arity: 1 + arguments: [a1] + speech: + en: etale cohomology of a1 + property: function + subject-area: "algebraic topology" + mathml: + - "Het*(X)" + urls: + - "https://en.wikipedia.org/wiki/%C3%89tale_cohomology" + - "https://ncatlab.org/nlab/show/etale+cohomology" + - "https://www.encyclopediaofmath.org/index.php/Etale_cohomology" + + - concept: euclid-number + arity: 1 + arguments: [a1] + speech: + en: euclid number a1 + property: symbol + subject-area: "number theory" + mathml: + - "Ex" + urls: + - "https://mathworld.wolfram.com/EuclidNumber.html" + - "https://en.wikipedia.org/wiki/Euclid_number" + + - concept: euclidean-distance + arity: 1 + arguments: [a1] + speech: + en: euclidean distance of a1 + property: function + subject-area: "geometry" + mathml: + - "dX" + - "dx" + urls: + - "https://en.wikipedia.org/wiki/Euclidean_distance" + alias: + - euclidean-metric + + - concept: euclidean-plane + arity: 0 + arguments: [] + speech: en: euclidean plane - property: symbol - area: "geometry" - mathml: - - "ℝ2" - urls: - - "https://mathworld.wolfram.com/EuclideanPlane.html" - alias: - - euclidean-space - - - concept: euler-characteristic - arity: 1 - en: euler characteristic of $1 - property: function - area: "algebraic topology" - mathml: - - "χ(x)" - urls: - - "https://mathworld.wolfram.com/EulerCharacteristic.html" - - "https://en.wikipedia.org/wiki/Euler_characteristic" - - "https://ncatlab.org/nlab/show/Euler+characteristic" - - "https://www.encyclopediaofmath.org/index.php/Euler_characteristic" - - - concept: euler-class - arity: 1 - en: euler class of $1 - property: function - area: "algebraic topology" - mathml: - - "e(x)" - urls: - - "https://en.wikipedia.org/wiki/Euler_class" - - "https://ncatlab.org/nlab/show/Euler+class" - - "https://www.encyclopediaofmath.org/index.php/Euler_class" - - - concept: euler-constant - arity: 0 + property: symbol + subject-area: "geometry" + mathml: + - "ℝ2" + urls: + - "https://mathworld.wolfram.com/EuclideanPlane.html" + alias: + - euclidean-space + + - concept: euler-characteristic + arity: 1 + arguments: [a1] + speech: + en: euler characteristic of a1 + property: function + subject-area: "algebraic topology" + mathml: + - "χ(x)" + urls: + - "https://mathworld.wolfram.com/EulerCharacteristic.html" + - "https://en.wikipedia.org/wiki/Euler_characteristic" + - "https://ncatlab.org/nlab/show/Euler+characteristic" + - "https://www.encyclopediaofmath.org/index.php/Euler_characteristic" + + - concept: euler-class + arity: 1 + arguments: [a1] + speech: + en: euler class of a1 + property: function + subject-area: "algebraic topology" + mathml: + - "e(x)" + urls: + - "https://en.wikipedia.org/wiki/Euler_class" + - "https://ncatlab.org/nlab/show/Euler+class" + - "https://www.encyclopediaofmath.org/index.php/Euler_class" + + - concept: euler-constant + arity: 0 + arguments: [] + speech: en: euler constant - property: symbol - area: "analysis" - mathml: - - "γ" - - "𝛾" - urls: - - "https://mathworld.wolfram.com/Euler-MascheroniConstant.html" - - "https://en.wikipedia.org/wiki/%CE%93%27(1)" - - "https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" - - "https://dlmf.nist.gov/5.2#E3" - - "https://www.encyclopediaofmath.org/index.php/Euler_constant" - alias: - - euler-mascheroni-constant - - - concept: euler-number - arity: 0 + property: symbol + subject-area: "analysis" + mathml: + - "γ" + - "𝛾" + urls: + - "https://mathworld.wolfram.com/Euler-MascheroniConstant.html" + - "https://en.wikipedia.org/wiki/%CE%93%27(1)" + - "https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" + - "https://dlmf.nist.gov/5.2#E3" + - "https://www.encyclopediaofmath.org/index.php/Euler_constant" + alias: + - euler-mascheroni-constant + + - concept: euler-number + arity: 0 + arguments: [] + speech: en: euler number - property: symbol - area: "physics" - mathml: - - "Eu" - - "e" - - "𝑒" - urls: - - "https://mathworld.wolfram.com/EulerNumber.html" - - "https://en.wikipedia.org/wiki/Euler_number" - - "https://en.wikipedia.org/wiki/Euler_number_(physics)" - - "https://dlmf.nist.gov/24.1#P2" - - "https://dlmf.nist.gov/24.2#ii" - - "https://ncatlab.org/nlab/show/Euler+number" - - "https://www.encyclopediaofmath.org/index.php/Euler_numbers" - alias: - - napier-constant - - - concept: euler-polynomial - arity: 1 - en: euler polynomial of $1 - property: function - area: "special-functions" - mathml: - - "Ex" - urls: - - "https://mathworld.wolfram.com/EulerPolynomial.html" - - "https://dlmf.nist.gov/24.1#P2" - - "https://dlmf.nist.gov/24.2#ii" - - "https://www.encyclopediaofmath.org/index.php/Euler_polynomials" - - - concept: euler-totient-function - arity: 1 - en: euler totient function of $1 - property: function - area: "number theory" - mathml: - - "φX" - - "ϕX" - urls: - - "https://mathworld.wolfram.com/EulerTotientFunction.html" - - "https://en.wikipedia.org/wiki/Euler%27s_totient_function" - alias: - - totient-function - - - concept: euler-mascheroni-constant - arity: 0 + property: symbol + subject-area: "physics" + mathml: + - "Eu" + - "e" + - "𝑒" + urls: + - "https://mathworld.wolfram.com/EulerNumber.html" + - "https://en.wikipedia.org/wiki/Euler_number" + - "https://en.wikipedia.org/wiki/Euler_number_(physics)" + - "https://dlmf.nist.gov/24.1#P2" + - "https://dlmf.nist.gov/24.2#ii" + - "https://ncatlab.org/nlab/show/Euler+number" + - "https://www.encyclopediaofmath.org/index.php/Euler_numbers" + alias: + - napier-constant + + - concept: euler-polynomial + arity: 1 + arguments: [a1] + speech: + en: euler polynomial of a1 + property: function + subject-area: "special-functions" + mathml: + - "Ex" + urls: + - "https://mathworld.wolfram.com/EulerPolynomial.html" + - "https://dlmf.nist.gov/24.1#P2" + - "https://dlmf.nist.gov/24.2#ii" + - "https://www.encyclopediaofmath.org/index.php/Euler_polynomials" + + - concept: euler-totient-function + arity: 1 + arguments: [a1] + speech: + en: euler totient function of a1 + property: function + subject-area: "number theory" + mathml: + - "φX" + - "ϕX" + urls: + - "https://mathworld.wolfram.com/EulerTotientFunction.html" + - "https://en.wikipedia.org/wiki/Euler%27s_totient_function" + alias: + - totient-function + + - concept: euler-mascheroni-constant + arity: 0 + arguments: [] + speech: en: euler mascheroni constant - property: constant - area: "number theory" - mathml: - - "γ" - urls: - - "https://mathworld.wolfram.com/Euler-MascheroniConstant.html" - - "https://en.wikipedia.org/wiki/%CE%93%27(1)" - - "https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" - - - concept: eulerian-number - arity: 1 - en: eulerian number of $1 - property: function - area: "combinatorics" - mathml: - - "A(x)" - urls: - - "https://mathworld.wolfram.com/EulerianNumber.html" - - "https://en.wikipedia.org/wiki/Eulerian_number" - - "https://dlmf.nist.gov/26.14#SS1.p3" - - - concept: exclusive-or - arity: 2 - en: $1 exclusive or $2 - property: infix - area: "logic" - mathml: - - "X⊻Y" - - "X⊕Y" - - "X↮Y" - - "X≢Y" - - "XXORY" - urls: - - "https://mathworld.wolfram.com/ExclusiveDisjunction.html" - - "https://ncatlab.org/nlab/show/exclusive+disjunction" - - "https://www.encyclopediaofmath.org/index.php/Exclusive_disjunction" - - "https://en.wikipedia.org/wiki/Exclusive_or" - alias: - - exclusive-disjunction - - xor - - - concept: expectation-value - arity: 1 - en: expectation value of $1 - property: fenced - area: "quantum physics" - mathml: - - "⟨X⟩" - urls: - - "https://mathworld.wolfram.com/ExpectationValue.html" - - "https://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)" - - "https://ncatlab.org/nlab/show/expectation+value" - - - concept: expected-value - arity: 1 - en: expected value of $1 - property: function - area: "probability theory" - mathml: - - "EX" - - "MX" - - "μx" - urls: - - "https://en.wikipedia.org/wiki/Expected_value#Notations" - alias: - - mathematical-expectation - - expectation - - mean - - average - - first-moment - - - concept: exponential-factorial - arity: 1 - en: exponential factorial of $1 - property: postfix - area: "number theory" - mathml: - - "x$" - urls: - - "https://mathworld.wolfram.com/ExponentialFactorial.html" - - "https://en.wikipedia.org/wiki/Exponential_factorial" - - - concept: exponential-integral - arity: 1 - en: exponential integral of $1 - property: - area: - mathml: - - "Ei(x)" - urls: - - "https://mathworld.wolfram.com/ExponentialIntegral.html" - - "https://en.wikipedia.org/wiki/Exponential_integral" - - "https://dlmf.nist.gov/6.2#i" - - "https://dlmf.nist.gov/6.2#E1" - - "https://dlmf.nist.gov/6.2#SS1.p3" - alias: - - ei - - - concept: exterior - arity: 1 - en: exterior of $1 - property: "function, msup" - area: "topology" - mathml: - - "extX" - - "Xe" - urls: - - "https://mathworld.wolfram.com/Exterior.html" - - "https://en.wikipedia.org/wiki/Exterior_(topology)" - - - concept: exterior-derivative - arity: 1 - en: exterior derivative of $1 - property: operator - area: "differential forms" - mathml: - - "d(x)" - urls: - - "https://mathworld.wolfram.com/ExteriorDerivative.html" - - "https://en.wikipedia.org/wiki/Exterior_derivative" - - - concept: exterior-algebra - arity: 1 - en: exterior algebra of $1 - property: function - area: "multilinear algebra" - mathml: - - "Λ(x)" - urls: - - "https://en.wikipedia.org/wiki/Exterior_algebra" - - - concept: exterior-product - arity: 2 - en: $1 exterior product $2 - property: infix - area: "multilinear algebra" - mathml: - - "X∧Y" - urls: - - "https://mathworld.wolfram.com/ExteriorProduct.html" - - "https://www.encyclopediaofmath.org/index.php/Exterior_product" - alias: - - wedge-product - - - concept: f-distribution - arity: 1 - en: f distribution of $1 - property: "indexed symbol" - area: "probability theory" - mathml: - - "Fx" - urls: - - "https://mathworld.wolfram.com/F-Distribution.html" - - "https://www.encyclopediaofmath.org/index.php/F-distribution" - - - concept: faber-polynomial - arity: 1 - en: $1th faber polynomial - property: function - area: "polynomials" - mathml: - - "Pn" - urls: - - "https://mathworld.wolfram.com/FaberPolynomial.html" - - "https://en.wikipedia.org/wiki/Faber_polynomials" - - "https://www.encyclopediaofmath.org/index.php/Faber_polynomials" - - - concept: falling-factorial - arity: 2 - en: falling factorial $1 $2 - property: mixfix - area: "combinatorics" - mathml: - - "(x)n" - - "xn_" - urls: - - "https://en.wikipedia.org/wiki/Falling_and_rising_factorials" - - "https://mathworld.wolfram.com/FallingFactorial.html" - - "https://dlmf.nist.gov/26.1#P1.p1" - alias: - - descending-factorial - - falling-sequential-product - - lower-factorial - - pochhammer-symbol - - - concept: fatou-set - arity: 1 - en: fatou set of $1 - property: function - area: "complex dynamics" - mathml: - - "F(x)" - urls: - - "https://en.wikipedia.org/wiki/Julia_set" - - - concept: farey-sequence - arity: 0 + property: constant + subject-area: "number theory" + mathml: + - "γ" + urls: + - "https://mathworld.wolfram.com/Euler-MascheroniConstant.html" + - "https://en.wikipedia.org/wiki/%CE%93%27(1)" + - "https://en.wikipedia.org/wiki/Euler%E2%80%93Mascheroni_constant" + + - concept: eulerian-number + arity: 1 + arguments: [a1] + speech: + en: eulerian number of a1 + property: function + subject-area: "combinatorics" + mathml: + - "A(x)" + urls: + - "https://mathworld.wolfram.com/EulerianNumber.html" + - "https://en.wikipedia.org/wiki/Eulerian_number" + - "https://dlmf.nist.gov/26.14#SS1.p3" + + - concept: exclusive-or + arity: 2 + arguments: [a1, a2] + speech: + en: a1 exclusive or a2 + property: infix + subject-area: "logic" + mathml: + - "X⊻Y" + - "X⊕Y" + - "X↮Y" + - "X≢Y" + - "XXORY" + urls: + - "https://mathworld.wolfram.com/ExclusiveDisjunction.html" + - "https://ncatlab.org/nlab/show/exclusive+disjunction" + - "https://www.encyclopediaofmath.org/index.php/Exclusive_disjunction" + - "https://en.wikipedia.org/wiki/Exclusive_or" + alias: + - exclusive-disjunction + - xor + + - concept: expectation-value + arity: 1 + arguments: [a1] + speech: + en: expectation value of a1 + property: fenced + subject-area: "quantum physics" + mathml: + - "⟨X⟩" + urls: + - "https://mathworld.wolfram.com/ExpectationValue.html" + - "https://en.wikipedia.org/wiki/Expectation_value_(quantum_mechanics)" + - "https://ncatlab.org/nlab/show/expectation+value" + + - concept: expected-value + arity: 1 + arguments: [a1] + speech: + en: expected value of a1 + property: function + subject-area: "probability theory" + mathml: + - "EX" + - "MX" + - "μx" + urls: + - "https://en.wikipedia.org/wiki/Expected_value#Notations" + alias: + - mathematical-expectation + - expectation + - mean + - average + - first-moment + + - concept: exponential-factorial + arity: 1 + arguments: [a1] + speech: + en: exponential factorial of a1 + property: postfix + subject-area: "number theory" + mathml: + - "x$" + urls: + - "https://mathworld.wolfram.com/ExponentialFactorial.html" + - "https://en.wikipedia.org/wiki/Exponential_factorial" + + - concept: exponential-integral + arity: 1 + arguments: [a1] + speech: + en: exponential integral of a1 + property: + subject-area: + mathml: + - "Ei(x)" + urls: + - "https://mathworld.wolfram.com/ExponentialIntegral.html" + - "https://en.wikipedia.org/wiki/Exponential_integral" + - "https://dlmf.nist.gov/6.2#i" + - "https://dlmf.nist.gov/6.2#E1" + - "https://dlmf.nist.gov/6.2#SS1.p3" + alias: + - ei + + - concept: exterior + arity: 1 + arguments: [a1] + speech: + en: exterior of a1 + property: "function, msup" + subject-area: "topology" + mathml: + - "extX" + - "Xe" + urls: + - "https://mathworld.wolfram.com/Exterior.html" + - "https://en.wikipedia.org/wiki/Exterior_(topology)" + + - concept: exterior-derivative + arity: 1 + arguments: [a1] + speech: + en: exterior derivative of a1 + property: operator + subject-area: "differential forms" + mathml: + - "d(x)" + urls: + - "https://mathworld.wolfram.com/ExteriorDerivative.html" + - "https://en.wikipedia.org/wiki/Exterior_derivative" + + - concept: exterior-algebra + arity: 1 + arguments: [a1] + speech: + en: exterior algebra of a1 + property: function + subject-area: "multilinear algebra" + mathml: + - "Λ(x)" + urls: + - "https://en.wikipedia.org/wiki/Exterior_algebra" + + - concept: exterior-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 exterior product a2 + property: infix + subject-area: "multilinear algebra" + mathml: + - "X∧Y" + urls: + - "https://mathworld.wolfram.com/ExteriorProduct.html" + - "https://www.encyclopediaofmath.org/index.php/Exterior_product" + alias: + - wedge-product + + - concept: f-distribution + arity: 1 + arguments: [a1] + speech: + en: f distribution of a1 + property: "indexed symbol" + subject-area: "probability theory" + mathml: + - "Fx" + urls: + - "https://mathworld.wolfram.com/F-Distribution.html" + - "https://www.encyclopediaofmath.org/index.php/F-distribution" + + - concept: faber-polynomial + arity: 1 + arguments: [a1] + speech: + en: a1th faber polynomial + property: function + subject-area: "polynomials" + mathml: + - "Pn" + urls: + - "https://mathworld.wolfram.com/FaberPolynomial.html" + - "https://en.wikipedia.org/wiki/Faber_polynomials" + - "https://www.encyclopediaofmath.org/index.php/Faber_polynomials" + + - concept: falling-factorial + arity: 2 + arguments: [a1, a2] + speech: + en: falling factorial a1 a2 + property: mixfix + subject-area: "combinatorics" + mathml: + - "(x)n" + - "xn_" + urls: + - "https://en.wikipedia.org/wiki/Falling_and_rising_factorials" + - "https://mathworld.wolfram.com/FallingFactorial.html" + - "https://dlmf.nist.gov/26.1#P1.p1" + alias: + - descending-factorial + - falling-sequential-product + - lower-factorial + - pochhammer-symbol + + - concept: fatou-set + arity: 1 + arguments: [a1] + speech: + en: fatou set of a1 + property: function + subject-area: "complex dynamics" + mathml: + - "F(x)" + urls: + - "https://en.wikipedia.org/wiki/Julia_set" + + - concept: farey-sequence + arity: 0 + arguments: [] + speech: en: farey sequence - property: symbol - area: "number theory" - mathml: - - "F" - urls: - - "https://mathworld.wolfram.com/FareySequence.html" - - "https://en.wikipedia.org/wiki/Farey_sequence" - - - concept: feferman-schutte-ordinal - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "F" + urls: + - "https://mathworld.wolfram.com/FareySequence.html" + - "https://en.wikipedia.org/wiki/Farey_sequence" + + - concept: feferman-schutte-ordinal + arity: 0 + arguments: [] + speech: en: feferman schutte ordinal - property: symbol - area: "ordinal numbers" - mathml: - - "Γ0" - urls: - - "https://en.wikipedia.org/wiki/Feferman%E2%80%93Sch%C3%BCtte_ordinal" - - - concept: feigenbaum-constant - arity: 0 + property: symbol + subject-area: "ordinal numbers" + mathml: + - "Γ0" + urls: + - "https://en.wikipedia.org/wiki/Feferman%E2%80%93Sch%C3%BCtte_ordinal" + + - concept: feigenbaum-constant + arity: 0 + arguments: [] + speech: en: feigenbaum constant - property: symbol - area: "chaos theory" - mathml: - - "δ" - urls: - - "https://mathworld.wolfram.com/FeigenbaumConstant.html" - - "https://en.wikipedia.org/wiki/Feigenbaum_constants" - - - concept: fermat-number - arity: 1 - en: $1th fermat number - property: "indexed symbol" - area: "number theory" - mathml: - - "Fx" - urls: - - "https://mathworld.wolfram.com/FermatNumber.html" - - "https://en.wikipedia.org/wiki/Fermat_number" - - - concept: fermat-quotient - arity: 1 - en: fermat quotient of $1 - property: function - area: "number theory" - mathml: - - "qx" - urls: - - "https://mathworld.wolfram.com/FermatQuotient.html" - - "https://en.wikipedia.org/wiki/Fermat_quotient" - - - concept: fermi-dirac-distribution - arity: 1 - en: fermi dirac distribution of $1 - property: function - area: "quantum statistics" - mathml: - - "n¯n" - urls: - - "https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_distribution" - alias: - - f-d-distribution - - - concept: feynman-slash - arity: 1 - en: feynman slash of $1 - property: menclose - area: "quantum field theory" - mathml: - - "A" - urls: - - "https://en.wikipedia.org/wiki/Feynman_slash_notation" - - - concept: fibonacci-number - arity: 1 - en: $1th fibonacci number - property: "indexed symbol" - area: "number theory" - mathml: - - "Fn" - urls: - - "https://mathworld.wolfram.com/FibonacciNumber.html" - - "https://en.wikipedia.org/wiki/Fibonacci_number" - - "https://en.wikipedia.org/wiki/Fibonacci_numbers_in_popular_culture" - - "https://dlmf.nist.gov/26.11#p4" - - "https://www.encyclopediaofmath.org/index.php/Fibonacci_numbers" - - - concept: fibonacci-polynomial - arity: 1 - en: fibonacci polynomial of $1 - property: "indexed function" - area: "polynomials" - mathml: - - "Fx" - urls: - - "https://mathworld.wolfram.com/FibonacciPolynomial.html" - - "https://en.wikipedia.org/wiki/Fibonacci_polynomials" - - "https://www.encyclopediaofmath.org/index.php/Fibonacci_polynomials" - - - concept: fibre-product - arity: 1 - en: fibre product of $1 - property: indexed infix - area: "category theory" - mathml: - - "×x" - urls: - - "https://en.wikipedia.org/wiki/Pullback_(category_theory)" - - "https://www.encyclopediaofmath.org/index.php/Fibre_product" - alias: - - pullback - - fiber-product - - cartesian-square - - - concept: field-extension - arity: 2 - en: $1 field extension $2 - property: infix - area: "algebra" - mathml: - - "X/Y" - urls: - - "https://mathworld.wolfram.com/FieldExtension.html" - - "https://en.wikipedia.org/wiki/Field_extension" - - "https://ncatlab.org/nlab/show/field+extension" - - "https://www.encyclopediaofmath.org/index.php/Field_extension" - - - concept: field-of-sets - arity: 2 + property: symbol + subject-area: "chaos theory" + mathml: + - "δ" + urls: + - "https://mathworld.wolfram.com/FeigenbaumConstant.html" + - "https://en.wikipedia.org/wiki/Feigenbaum_constants" + + - concept: fermat-number + arity: 1 + arguments: [a1] + speech: + en: a1th fermat number + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Fx" + urls: + - "https://mathworld.wolfram.com/FermatNumber.html" + - "https://en.wikipedia.org/wiki/Fermat_number" + + - concept: fermat-quotient + arity: 1 + arguments: [a1] + speech: + en: fermat quotient of a1 + property: function + subject-area: "number theory" + mathml: + - "qx" + urls: + - "https://mathworld.wolfram.com/FermatQuotient.html" + - "https://en.wikipedia.org/wiki/Fermat_quotient" + + - concept: fermi-dirac-distribution + arity: 1 + arguments: [a1] + speech: + en: fermi dirac distribution of a1 + property: function + subject-area: "quantum statistics" + mathml: + - "n¯n" + urls: + - "https://en.wikipedia.org/wiki/Fermi%E2%80%93Dirac_distribution" + alias: + - f-d-distribution + + - concept: feynman-slash + arity: 1 + arguments: [a1] + speech: + en: feynman slash of a1 + property: menclose + subject-area: "quantum field theory" + mathml: + - "A" + urls: + - "https://en.wikipedia.org/wiki/Feynman_slash_notation" + + - concept: fibonacci-number + arity: 1 + arguments: [a1] + speech: + en: a1th fibonacci number + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Fn" + urls: + - "https://mathworld.wolfram.com/FibonacciNumber.html" + - "https://en.wikipedia.org/wiki/Fibonacci_number" + - "https://en.wikipedia.org/wiki/Fibonacci_numbers_in_popular_culture" + - "https://dlmf.nist.gov/26.11#p4" + - "https://www.encyclopediaofmath.org/index.php/Fibonacci_numbers" + + - concept: fibonacci-polynomial + arity: 1 + arguments: [a1] + speech: + en: fibonacci polynomial of a1 + property: "indexed function" + subject-area: "polynomials" + mathml: + - "Fx" + urls: + - "https://mathworld.wolfram.com/FibonacciPolynomial.html" + - "https://en.wikipedia.org/wiki/Fibonacci_polynomials" + - "https://www.encyclopediaofmath.org/index.php/Fibonacci_polynomials" + + - concept: fibre-product + arity: 1 + arguments: [a1] + speech: + en: fibre product of a1 + property: indexed infix + subject-area: "category theory" + mathml: + - "×x" + urls: + - "https://en.wikipedia.org/wiki/Pullback_(category_theory)" + - "https://www.encyclopediaofmath.org/index.php/Fibre_product" + alias: + - pullback + - fiber-product + - cartesian-square + + - concept: field-extension + arity: 2 + arguments: [a1, a2] + speech: + en: a1 field extension a2 + property: infix + subject-area: "algebra" + mathml: + - "X/Y" + urls: + - "https://mathworld.wolfram.com/FieldExtension.html" + - "https://en.wikipedia.org/wiki/Field_extension" + - "https://ncatlab.org/nlab/show/field+extension" + - "https://www.encyclopediaofmath.org/index.php/Field_extension" + + - concept: field-of-sets + arity: 2 + arguments: [a1, a2] + speech: en: field of sets - property: fenced - area: "boolean algebra" - mathml: - - "(X,F)" - urls: - - "https://en.wikipedia.org/wiki/Field_of_sets" - - "https://www.encyclopediaofmath.org/index.php/Field_of_sets" - - - concept: first-isogonic-center - arity: 0 + property: fenced + subject-area: "boolean algebra" + mathml: + - "(X,F)" + urls: + - "https://en.wikipedia.org/wiki/Field_of_sets" + - "https://www.encyclopediaofmath.org/index.php/Field_of_sets" + + - concept: first-isogonic-center + arity: 0 + arguments: [] + speech: en: first isogonic center - property: symbol - area: "geometry" - mathml: - - "X(13)" - urls: - - "https://en.wikipedia.org/wiki/Fermat_point" - - - concept: fisher-information - arity: 1 - en: fisher information of $1 - property: function - area: "statistics" - mathml: - - "I(x)" - urls: - - "https://mathworld.wolfram.com/FisherInformation.html" - - "https://en.wikipedia.org/wiki/Fisher_information" - alias: - - information - - - concept: flattening - arity: 0 + property: symbol + subject-area: "geometry" + mathml: + - "X(13)" + urls: + - "https://en.wikipedia.org/wiki/Fermat_point" + + - concept: fisher-information + arity: 1 + arguments: [a1] + speech: + en: fisher information of a1 + property: function + subject-area: "statistics" + mathml: + - "I(x)" + urls: + - "https://mathworld.wolfram.com/FisherInformation.html" + - "https://en.wikipedia.org/wiki/Fisher_information" + alias: + - information + + - concept: flattening + arity: 0 + arguments: [] + speech: en: flattening - property: symbol - area: "celestial mechanics" - mathml: - - "f" - urls: - - "https://mathworld.wolfram.com/Flattening.html" - - "https://en.wikipedia.org/wiki/Flattening" - alias: - - ellipticity - - oblateness - - - concept: floor - arity: 1 - en: floor of $1 - property: fenced, function - area: "number theory" - mathml: - - "⌊X⌋" - - "⟦X⟧" - - "[X]" - - "floor(X)" - urls: - - "https://youtu.be/RxNs4SwP6lk" - - "https://youtu.be/RxNs4SwP6lk" - - "https://drive.google.com/file/d/1T3zc--Fbz0tFHaJq527Y_ZUyAvpOdSuM/view" - - - concept: fock-space - arity: 1 - en: fock space of $1 - property: function - area: "quantum mechanics" - mathml: - - "F(x)" - urls: - - "https://en.wikipedia.org/wiki/Fock_space" - - "https://ncatlab.org/nlab/show/Fock+space" - - "https://www.encyclopediaofmath.org/index.php/Fock_space" - - - concept: forward-difference - arity: 3 - en: $1th forward difference of $3 over $2 - property: operator - area: "numerical analysis" - mathml: - - "Δxnf(x)" - urls: - - "https://mathworld.wolfram.com/ForwardDifference.html)" - - "https://dlmf.nist.gov/18.1#EGx1" - - - concept: fourier-cosine-transform - arity: 1 - en: fourier cosine transform of $1 - property: operator - area: "functional analysis" - mathml: - - "ℱcf" - urls: - - "https://mathworld.wolfram.com/FourierCosineTransform.html" - - "https://dlmf.nist.gov/1.14#E9" - - "https://www.encyclopediaofmath.org/index.php/Fourier_cosine_transform" - - - concept: fourier-sine-transform - arity: 1 - en: fourier sine transform of $1 - property: operator - area: "functional analysis" - mathml: - - "ℱsf" - urls: - - "https://mathworld.wolfram.com/FourierSineTransform.html" - - "https://dlmf.nist.gov/1.14#E10" - - "https://www.encyclopediaofmath.org/index.php/Fourier_sine_transform" - - - concept: fourier-transform - arity: 1 - en: fourier transform of $1 - property: mover - area: "fourier analysis" - mathml: - - "f^" - urls: - - "https://mathworld.wolfram.com/FourierTransform.html" - - "https://en.wikipedia.org/wiki/%E2%84%B1" - - "https://en.wikipedia.org/wiki/Fourier_transform" - - "https://dlmf.nist.gov/1.14#E1" - - "https://ncatlab.org/nlab/show/Fourier+transform" - - "https://www.encyclopediaofmath.org/index.php/Fourier_transform" - - - concept: fox-derivative - arity: 1 - en: fox derivative of $1 - property: mfrac - area: "geometric topology" - mathml: - - "∂∂gi" - urls: - - "https://mathworld.wolfram.com/FoxDerivative.html" - - "https://en.wikipedia.org/wiki/Fox_derivative" - - "https://ncatlab.org/nlab/show/Fox+derivative" - - - concept: fox-wright-function - arity: 2 - en: fox wright function $1 $2 - property: mmultiscripts - area: "special functions" - mathml: - - "Ψqp" - urls: - - "https://en.wikipedia.org/wiki/Fox%E2%80%93Wright_function" - alias: - - wright-function - - - concept: fractional-derivative - arity: 1 - en: fractional derivative of $1 - property: operator - area: "fractional caclulus" - mathml: - - "Df" - urls: - - "https://mathworld.wolfram.com/FractionalDerivative.html" - - "https://dlmf.nist.gov/1.15#E51" - - - concept: fractional-integral - arity: 1 - en: fractional integral of $1 - property: operator - area: "fractional caclulus" - mathml: - - "If" - urls: - - "https://mathworld.wolfram.com/FractionalIntegral.html" - - "https://dlmf.nist.gov/1.15#E47" - - "https://dlmf.nist.gov/2.6#E33" - - - concept: fractional-part - arity: 1 - en: fractional part of $1 - property: "function, fenced" - area: "arithmetic" - mathml: - - "fracX" - - "⟦x⟧" - - "{x}" - urls: - - "https://mathworld.wolfram.com/FractionalPart.html" - - "https://en.wikipedia.org/wiki/Fractional_part" - - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions" - - "https://en.wikipedia.org/wiki/Phase_(waves)" - alias: - - decimal-part - - - concept: franel-number - arity: 1 - en: $1th franel number - property: "indexed symbol" - area: "combinatorics" - mathml: - - "Fr(x)" - urls: - - "https://mathworld.wolfram.com/FranelNumber.html" - - - concept: frattini-subgroup - arity: 1 - en: frattini subgroup of $1 - property: function - area: "group theory" - mathml: - - "φX" - - "ϕX" - urls: - - "https://mathworld.wolfram.com/FrattiniSubgroup.html" - - "https://en.wikipedia.org/wiki/Frattini_subgroup" - - "https://www.encyclopediaofmath.org/index.php/Frattini_subgroup" - - - concept: frechet-derivative - arity: 1 - en: frechet derivative of $1 - property: operator - area: "banach spaces" - mathml: - - "D(x)" - urls: - - "https://mathworld.wolfram.com/FrechetDerivative.html" - - "https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative" - - "https://www.encyclopediaofmath.org/index.php/Frechet_derivative" - - "https://www.encyclopediaofmath.org/index.php/Fréchet_derivative" - - - concept: frechet-topology - arity: 0 + property: symbol + subject-area: "celestial mechanics" + mathml: + - "f" + urls: + - "https://mathworld.wolfram.com/Flattening.html" + - "https://en.wikipedia.org/wiki/Flattening" + alias: + - ellipticity + - oblateness + + - concept: floor + arity: 1 + arguments: [a1] + speech: + en: floor of a1 + property: fenced, function + subject-area: "number theory" + mathml: + - "⌊X⌋" + - "⟦X⟧" + - "[X]" + - "floor(X)" + urls: + - "https://youtu.be/RxNs4SwP6lk" + - "https://youtu.be/RxNs4SwP6lk" + - "https://drive.google.com/file/d/1T3zc--Fbz0tFHaJq527Y_ZUyAvpOdSuM/view" + + - concept: fock-space + arity: 1 + arguments: [a1] + speech: + en: fock space of a1 + property: function + subject-area: "quantum mechanics" + mathml: + - "F(x)" + urls: + - "https://en.wikipedia.org/wiki/Fock_space" + - "https://ncatlab.org/nlab/show/Fock+space" + - "https://www.encyclopediaofmath.org/index.php/Fock_space" + + - concept: forward-difference + arity: 3 + arguments: [a1, a2, a3] + speech: + en: a1th forward difference of a3 over a2 + property: operator + subject-area: "numerical analysis" + mathml: + - "Δxnf(x)" + urls: + - "https://mathworld.wolfram.com/ForwardDifference.html)" + - "https://dlmf.nist.gov/18.1#EGx1" + + - concept: fourier-cosine-transform + arity: 1 + arguments: [a1] + speech: + en: fourier cosine transform of a1 + property: operator + subject-area: "functional analysis" + mathml: + - "ℱcf" + urls: + - "https://mathworld.wolfram.com/FourierCosineTransform.html" + - "https://dlmf.nist.gov/1.14#E9" + - "https://www.encyclopediaofmath.org/index.php/Fourier_cosine_transform" + + - concept: fourier-sine-transform + arity: 1 + arguments: [a1] + speech: + en: fourier sine transform of a1 + property: operator + subject-area: "functional analysis" + mathml: + - "ℱsf" + urls: + - "https://mathworld.wolfram.com/FourierSineTransform.html" + - "https://dlmf.nist.gov/1.14#E10" + - "https://www.encyclopediaofmath.org/index.php/Fourier_sine_transform" + + - concept: fourier-transform + arity: 1 + arguments: [a1] + speech: + en: fourier transform of a1 + property: mover + subject-area: "fourier analysis" + mathml: + - "f^" + urls: + - "https://mathworld.wolfram.com/FourierTransform.html" + - "https://en.wikipedia.org/wiki/%E2%84%B1" + - "https://en.wikipedia.org/wiki/Fourier_transform" + - "https://dlmf.nist.gov/1.14#E1" + - "https://ncatlab.org/nlab/show/Fourier+transform" + - "https://www.encyclopediaofmath.org/index.php/Fourier_transform" + + - concept: fox-derivative + arity: 1 + arguments: [a1] + speech: + en: fox derivative of a1 + property: mfrac + subject-area: "geometric topology" + mathml: + - "∂∂gi" + urls: + - "https://mathworld.wolfram.com/FoxDerivative.html" + - "https://en.wikipedia.org/wiki/Fox_derivative" + - "https://ncatlab.org/nlab/show/Fox+derivative" + + - concept: fox-wright-function + arity: 2 + arguments: [a1, a2] + speech: + en: fox wright function a1 a2 + property: mmultiscripts + subject-area: "special functions" + mathml: + - "Ψqp" + urls: + - "https://en.wikipedia.org/wiki/Fox%E2%80%93Wright_function" + alias: + - wright-function + + - concept: fractional-derivative + arity: 1 + arguments: [a1] + speech: + en: fractional derivative of a1 + property: operator + subject-area: "fractional caclulus" + mathml: + - "Df" + urls: + - "https://mathworld.wolfram.com/FractionalDerivative.html" + - "https://dlmf.nist.gov/1.15#E51" + + - concept: fractional-integral + arity: 1 + arguments: [a1] + speech: + en: fractional integral of a1 + property: operator + subject-area: "fractional caclulus" + mathml: + - "If" + urls: + - "https://mathworld.wolfram.com/FractionalIntegral.html" + - "https://dlmf.nist.gov/1.15#E47" + - "https://dlmf.nist.gov/2.6#E33" + + - concept: fractional-part + arity: 1 + arguments: [a1] + speech: + en: fractional part of a1 + property: "function, fenced" + subject-area: "arithmetic" + mathml: + - "fracX" + - "⟦x⟧" + - "{x}" + urls: + - "https://mathworld.wolfram.com/FractionalPart.html" + - "https://en.wikipedia.org/wiki/Fractional_part" + - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions" + - "https://en.wikipedia.org/wiki/Phase_(waves)" + alias: + - decimal-part + + - concept: franel-number + arity: 1 + arguments: [a1] + speech: + en: a1th franel number + property: "indexed symbol" + subject-area: "combinatorics" + mathml: + - "Fr(x)" + urls: + - "https://mathworld.wolfram.com/FranelNumber.html" + + - concept: frattini-subgroup + arity: 1 + arguments: [a1] + speech: + en: frattini subgroup of a1 + property: function + subject-area: "group theory" + mathml: + - "φX" + - "ϕX" + urls: + - "https://mathworld.wolfram.com/FrattiniSubgroup.html" + - "https://en.wikipedia.org/wiki/Frattini_subgroup" + - "https://www.encyclopediaofmath.org/index.php/Frattini_subgroup" + + - concept: frechet-derivative + arity: 1 + arguments: [a1] + speech: + en: frechet derivative of a1 + property: operator + subject-area: "banach spaces" + mathml: + - "D(x)" + urls: + - "https://mathworld.wolfram.com/FrechetDerivative.html" + - "https://en.wikipedia.org/wiki/Fr%C3%A9chet_derivative" + - "https://www.encyclopediaofmath.org/index.php/Frechet_derivative" + - "https://www.encyclopediaofmath.org/index.php/Fréchet_derivative" + + - concept: frechet-topology + arity: 0 + arguments: [] + speech: en: frechet topology - property: constant - area: "topology" - mathml: - - "T1" - urls: - - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions" - alias: - - tikhonov-space - - accessible-space - - - concept: fredholm-determinant - arity: 1 - en: fredholm determinant of $1 - property: function - area: "mathematical physics" - mathml: - - "det(x)" - urls: - - "https://en.wikipedia.org/wiki/Fredholm_determinant" - - "https://ncatlab.org/nlab/show/Fredholm+determinant" - - "https://ncatlab.org/nlab/show/Fredholm+determinant" - - - concept: free-algebra - arity: 2 - en: free algebra $1 $2 - property: mixfix - area: "ring theory" - mathml: - - "R⟨X⟩" - urls: - - "https://mathworld.wolfram.com/FreeAlgebra.html" - - "https://en.wikipedia.org/wiki/Free_algebra" - - "https://www.encyclopediaofmath.org/index.php/Free_algebra" - - - concept: free-module - arity: 2 - en: $1 free module on $2 - property: mixfix, msup - area: "module theory" - mathml: - - "R{E}" - - "R(E)" - urls: - - "https://mathworld.wolfram.com/FreeModule.html" - - "https://en.wikipedia.org/wiki/Free_module" - - "https://ncatlab.org/nlab/show/free+module" - - "https://www.encyclopediaofmath.org/index.php/Free_module" - - - concept: free-monoid - arity: 1 - en: free monoid of $1 - property: msup - area: "abstract algebra" - mathml: - - "X*" - urls: - - "https://en.wikipedia.org/wiki/Free_monoid" - - "https://en.wikipedia.org/wiki/Monoid_factorisation" - - "https://ncatlab.org/nlab/show/free+monoid" - - - concept: free-product - arity: 2 - en: $1 free product $2 - property: infix - area: "group theory" - mathml: - - "X*Y" - urls: - - "https://mathworld.wolfram.com/FreeProduct.html" - - "https://en.wikipedia.org/wiki/Free_product" - - "https://www.encyclopediaofmath.org/index.php/Free_product" - - - concept: fresnel-integral - arity: 1 - en: fresnel integral of $1 - property: operator - area: "special functions" - mathml: - - "ℱX" - - "CX" - - "SX" - urls: - - "https://mathworld.wolfram.com/FresnelIntegrals.html" - - "https://en.wikipedia.org/wiki/Fresnel_integral" - - "https://dlmf.nist.gov/7.2#iii" - - "https://dlmf.nist.gov/7.2#E7" - - "https://dlmf.nist.gov/7.2#E6" - - "https://dlmf.nist.gov/7.2#E8" - - "https://www.encyclopediaofmath.org/index.php/Fresnel_integrals" - - - concept: frobenius-norm - arity: 1 - en: frobenius norm of $1 - property: indexed fenced - area: "linear algebra" - mathml: - - "‖A‖F" - urls: - - "https://mathworld.wolfram.com/FrobeniusNorm.html" - - "https://www.encyclopediaofmath.org/index.php/Frobenius_matrix_norm" - alias: - - euclidean-norm - - frobenius-matrix-norm - - - concept: frolicher-nijenhuis-bracket - arity: 2 + property: constant + subject-area: "topology" + mathml: + - "T1" + urls: + - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions" + alias: + - tikhonov-space + - accessible-space + + - concept: fredholm-determinant + arity: 1 + arguments: [a1] + speech: + en: fredholm determinant of a1 + property: function + subject-area: "mathematical physics" + mathml: + - "det(x)" + urls: + - "https://en.wikipedia.org/wiki/Fredholm_determinant" + - "https://ncatlab.org/nlab/show/Fredholm+determinant" + - "https://ncatlab.org/nlab/show/Fredholm+determinant" + + - concept: free-algebra + arity: 2 + arguments: [a1, a2] + speech: + en: free algebra a1 a2 + property: mixfix + subject-area: "ring theory" + mathml: + - "R⟨X⟩" + urls: + - "https://mathworld.wolfram.com/FreeAlgebra.html" + - "https://en.wikipedia.org/wiki/Free_algebra" + - "https://www.encyclopediaofmath.org/index.php/Free_algebra" + + - concept: free-module + arity: 2 + arguments: [a1, a2] + speech: + en: a1 free module on a2 + property: mixfix, msup + subject-area: "module theory" + mathml: + - "R{E}" + - "R(E)" + urls: + - "https://mathworld.wolfram.com/FreeModule.html" + - "https://en.wikipedia.org/wiki/Free_module" + - "https://ncatlab.org/nlab/show/free+module" + - "https://www.encyclopediaofmath.org/index.php/Free_module" + + - concept: free-monoid + arity: 1 + arguments: [a1] + speech: + en: free monoid of a1 + property: msup + subject-area: "abstract algebra" + mathml: + - "X*" + urls: + - "https://en.wikipedia.org/wiki/Free_monoid" + - "https://en.wikipedia.org/wiki/Monoid_factorisation" + - "https://ncatlab.org/nlab/show/free+monoid" + + - concept: free-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 free product a2 + property: infix + subject-area: "group theory" + mathml: + - "X*Y" + urls: + - "https://mathworld.wolfram.com/FreeProduct.html" + - "https://en.wikipedia.org/wiki/Free_product" + - "https://www.encyclopediaofmath.org/index.php/Free_product" + + - concept: fresnel-integral + arity: 1 + arguments: [a1] + speech: + en: fresnel integral of a1 + property: operator + subject-area: "special functions" + mathml: + - "ℱX" + - "CX" + - "SX" + urls: + - "https://mathworld.wolfram.com/FresnelIntegrals.html" + - "https://en.wikipedia.org/wiki/Fresnel_integral" + - "https://dlmf.nist.gov/7.2#iii" + - "https://dlmf.nist.gov/7.2#E7" + - "https://dlmf.nist.gov/7.2#E6" + - "https://dlmf.nist.gov/7.2#E8" + - "https://www.encyclopediaofmath.org/index.php/Fresnel_integrals" + + - concept: frobenius-norm + arity: 1 + arguments: [a1] + speech: + en: frobenius norm of a1 + property: indexed fenced + subject-area: "linear algebra" + mathml: + - "‖A‖F" + urls: + - "https://mathworld.wolfram.com/FrobeniusNorm.html" + - "https://www.encyclopediaofmath.org/index.php/Frobenius_matrix_norm" + alias: + - euclidean-norm + - frobenius-matrix-norm + + - concept: frolicher-nijenhuis-bracket + arity: 2 + arguments: [a1, a2] + speech: en: frolicher nijenhuis bracket - property: fenced - area: "differntial geometry" - mathml: - - "[a,b]" - urls: - - "https://en.wikipedia.org/wiki/Fr%C3%B6licher%E2%80%93Nijenhuis_bracket" - - "https://encyclopediaofmath.org/wiki/Fr%C3%B6licher-Nijenhuis_bracket" - - - concept: functional-congruence - arity: 3 - en: functional congruence of $1 and $2 mod $3 - property: mixfix - area: "number theory" - mathml: - - "f≡g(modn)" - urls: - - "https://mathworld.wolfram.com/FunctionalCongruence.html" - alias: - - identical-congruence - - - concept: functor-category - arity: 2 + property: fenced + subject-area: "differntial geometry" + mathml: + - "[a,b]" + urls: + - "https://en.wikipedia.org/wiki/Fr%C3%B6licher%E2%80%93Nijenhuis_bracket" + - "https://encyclopediaofmath.org/wiki/Fr%C3%B6licher-Nijenhuis_bracket" + + - concept: functional-congruence + arity: 3 + arguments: [a1, a2, a3] + speech: + en: functional congruence of a1 and a2 mod a3 + property: mixfix + subject-area: "number theory" + mathml: + - "f≡g(modn)" + urls: + - "https://mathworld.wolfram.com/FunctionalCongruence.html" + alias: + - identical-congruence + + - concept: functor-category + arity: 2 + arguments: [a1, a2] + speech: en: functor category - property: msup, fenced - area: "category theory" - mathml: - - "fg" - - "[f,g]" - urls: - - "https://en.wikipedia.org/wiki/Functor_category" - - "https://ncatlab.org/nlab/show/functor+category" - - - concept: fundamental-matrix - arity: 0 + property: msup, fenced + subject-area: "category theory" + mathml: + - "fg" + - "[f,g]" + urls: + - "https://en.wikipedia.org/wiki/Functor_category" + - "https://ncatlab.org/nlab/show/functor+category" + + - concept: fundamental-matrix + arity: 0 + arguments: [] + speech: en: fundamental matrix - property: symbol - area: "computer vision" - mathml: - - "F" - urls: - - "https://en.wikipedia.org/wiki/Fundamental_matrix_(computer_vision)" - - - concept: g-function - arity: 1 - en: g function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "G(x)" - urls: - - "https://mathworld.wolfram.com/G-Function.html" - - "https://en.wikipedia.org/wiki/Meijer_G-function" - alias: - - meijer-g-function - - - concept: gabor-transform - arity: 1 - en: gabor transform of $1 - property: operator - area: "integral transforms" - mathml: - - "G(x)" - urls: - - "https://en.wikipedia.org/wiki/Gabor_transform" - - "https://en.wikipedia.org/wiki/Gabor%E2%80%93Wigner_transform" - - "https://www.encyclopediaofmath.org/index.php/Gabor_transform" - - - concept: gain-function - arity: 1 - en: gain function of $1 - property: function - area: "graph theory" - mathml: - - "φ(x)" - urls: - - "https://en.wikipedia.org/wiki/Gain_graph" - - "https://en.wikipedia.org/wiki/Gain_group" - - "https://www.encyclopediaofmath.org/index.php/Gain_function" - - - concept: galilean-transformation - arity: 1 - en: galilean transformation of $1 - property: function - area: "physics" - mathml: - - "G(x)" - urls: - - "https://mathworld.wolfram.com/GalileanTransformation.html" - - "https://en.wikipedia.org/wiki/Galilean_transformation" - - "https://www.encyclopediaofmath.org/index.php/Galilean_transformation" - - - concept: galois-field - arity: 1 - en: galois field of $1 - property: function - area: "finite fields" - mathml: - - "GF(p)" - - "Fp" - - "𝔽p" - urls: - - "https://mathworld.wolfram.com/GaloisField.html" - - "https://en.wikipedia.org/wiki/Finite_field" - - "https://www.encyclopediaofmath.org/index.php/Galois_field" - alias: - - finite-field - - - concept: galois-group - arity: 1 - en: galois group of $1 - property: function - area: "abstract algebra" - mathml: - - "GalG" - urls: - - "https://mathworld.wolfram.com/GaloisGroup.html" - - "https://en.wikipedia.org/wiki/Galois_group" - - "https://ncatlab.org/nlab/show/Galois+group" - - "https://www.encyclopediaofmath.org/index.php/Galois_group" - - - concept: gamma-distribution - arity: 0 + property: symbol + subject-area: "computer vision" + mathml: + - "F" + urls: + - "https://en.wikipedia.org/wiki/Fundamental_matrix_(computer_vision)" + + - concept: g-function + arity: 1 + arguments: [a1] + speech: + en: g function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "G(x)" + urls: + - "https://mathworld.wolfram.com/G-Function.html" + - "https://en.wikipedia.org/wiki/Meijer_G-function" + alias: + - meijer-g-function + + - concept: gabor-transform + arity: 1 + arguments: [a1] + speech: + en: gabor transform of a1 + property: operator + subject-area: "integral transforms" + mathml: + - "G(x)" + urls: + - "https://en.wikipedia.org/wiki/Gabor_transform" + - "https://en.wikipedia.org/wiki/Gabor%E2%80%93Wigner_transform" + - "https://www.encyclopediaofmath.org/index.php/Gabor_transform" + + - concept: gain-function + arity: 1 + arguments: [a1] + speech: + en: gain function of a1 + property: function + subject-area: "graph theory" + mathml: + - "φ(x)" + urls: + - "https://en.wikipedia.org/wiki/Gain_graph" + - "https://en.wikipedia.org/wiki/Gain_group" + - "https://www.encyclopediaofmath.org/index.php/Gain_function" + + - concept: galilean-transformation + arity: 1 + arguments: [a1] + speech: + en: galilean transformation of a1 + property: function + subject-area: "physics" + mathml: + - "G(x)" + urls: + - "https://mathworld.wolfram.com/GalileanTransformation.html" + - "https://en.wikipedia.org/wiki/Galilean_transformation" + - "https://www.encyclopediaofmath.org/index.php/Galilean_transformation" + + - concept: galois-field + arity: 1 + arguments: [a1] + speech: + en: galois field of a1 + property: function + subject-area: "finite fields" + mathml: + - "GF(p)" + - "Fp" + - "𝔽p" + urls: + - "https://mathworld.wolfram.com/GaloisField.html" + - "https://en.wikipedia.org/wiki/Finite_field" + - "https://www.encyclopediaofmath.org/index.php/Galois_field" + alias: + - finite-field + + - concept: galois-group + arity: 1 + arguments: [a1] + speech: + en: galois group of a1 + property: function + subject-area: "abstract algebra" + mathml: + - "GalG" + urls: + - "https://mathworld.wolfram.com/GaloisGroup.html" + - "https://en.wikipedia.org/wiki/Galois_group" + - "https://ncatlab.org/nlab/show/Galois+group" + - "https://www.encyclopediaofmath.org/index.php/Galois_group" + + - concept: gamma-distribution + arity: 0 + arguments: [] + speech: en: gamma distribution - property: symbol - area: "probability theory" - mathml: - - "Γ" - urls: - - "https://mathworld.wolfram.com/GammaDistribution.html" - - "https://en.wikipedia.org/wiki/Gamma_distribution" - - - concept: gamma-function - arity: 1 - en: gamma function of $1 - property: operator - area: "special functions" - mathml: - - "Γ(x)" - urls: - - "https://mathworld.wolfram.com/GammaFunction.html" - - "https://en.wikipedia.org/wiki/%CE%93(x)" - - "https://en.wikipedia.org/wiki/Gamma_function" - - "https://dlmf.nist.gov/5#PT2" - - "https://dlmf.nist.gov/5.2#E1" - - "https://ncatlab.org/nlab/show/Gamma+function" - alias: - - euler-integral-of-the-second-kind - - - concept: gateaux-derivative - arity: 3 - en: gateaux derivative of $1 at $2 ; £3 - property: mixfix - area: "differential calculus" - mathml: - - "dF(u;ψ))" - urls: - - "https://mathworld.wolfram.com/GateauxDerivative.html" - - "https://en.wikipedia.org/wiki/G%C3%A2teaux_derivative" - - "https://www.encyclopediaofmath.org/index.php/Gateaux_derivative" - alias: - - gateaux-differential - - - concept: gauss - arity: 1 - en: gauss of $1 - property: unit - area: "physics" - mathml: - - "G(x)" - urls: - - "https://en.wikipedia.org/wiki/Gauss_(unit)" - - - concept: gaussian-distribution - arity: 0 + property: symbol + subject-area: "probability theory" + mathml: + - "Γ" + urls: + - "https://mathworld.wolfram.com/GammaDistribution.html" + - "https://en.wikipedia.org/wiki/Gamma_distribution" + + - concept: gamma-function + arity: 1 + arguments: [a1] + speech: + en: gamma function of a1 + property: operator + subject-area: "special functions" + mathml: + - "Γ(x)" + urls: + - "https://mathworld.wolfram.com/GammaFunction.html" + - "https://en.wikipedia.org/wiki/%CE%93(x)" + - "https://en.wikipedia.org/wiki/Gamma_function" + - "https://dlmf.nist.gov/5#PT2" + - "https://dlmf.nist.gov/5.2#E1" + - "https://ncatlab.org/nlab/show/Gamma+function" + alias: + - euler-integral-of-the-second-kind + + - concept: gateaux-derivative + arity: 3 + arguments: [a1, a2, a3] + speech: + en: gateaux derivative of a1 at a2 ; £3 + property: mixfix + subject-area: "differential calculus" + mathml: + - "dF(u;ψ))" + urls: + - "https://mathworld.wolfram.com/GateauxDerivative.html" + - "https://en.wikipedia.org/wiki/G%C3%A2teaux_derivative" + - "https://www.encyclopediaofmath.org/index.php/Gateaux_derivative" + alias: + - gateaux-differential + + - concept: gauss + arity: 1 + arguments: [a1] + speech: + en: gauss of a1 + property: unit + subject-area: "physics" + mathml: + - "G(x)" + urls: + - "https://en.wikipedia.org/wiki/Gauss_(unit)" + + - concept: gaussian-distribution + arity: 0 + arguments: [] + speech: en: gaussian distribution - property: symbol - area: "probability theory" - mathml: - - "𝒩" - urls: - - "https://en.wikipedia.org/wiki/Normal_distribution" - alias: - - normal-distribution - - gauss-distribution - - laplace-gauss-distribution - - - concept: gaussian-curvature - arity: 1 - en: gaussian curvature of $1 - property: function - area: "differential geometry" - mathml: - - "Κ(x)" - urls: - - "https://mathworld.wolfram.com/GaussianCurvature.html" - - "https://en.wikipedia.org/wiki/Gaussian_curvature" - - "https://www.encyclopediaofmath.org/index.php/Gaussian_curvature" - - - concept: gaussian-integers - arity: 0 + property: symbol + subject-area: "probability theory" + mathml: + - "𝒩" + urls: + - "https://en.wikipedia.org/wiki/Normal_distribution" + alias: + - normal-distribution + - gauss-distribution + - laplace-gauss-distribution + + - concept: gaussian-curvature + arity: 1 + arguments: [a1] + speech: + en: gaussian curvature of a1 + property: function + subject-area: "differential geometry" + mathml: + - "Κ(x)" + urls: + - "https://mathworld.wolfram.com/GaussianCurvature.html" + - "https://en.wikipedia.org/wiki/Gaussian_curvature" + - "https://www.encyclopediaofmath.org/index.php/Gaussian_curvature" + + - concept: gaussian-integers + arity: 0 + arguments: [] + speech: en: gaussian integers - property: constant - area: "number theory" - mathml: - - "ℤ[i]" - urls: - - "https://mathworld.wolfram.com/GaussianInteger.html" - - "https://en.wikipedia.org/wiki/Gaussian_integer" - - "https://en.wikipedia.org/wiki/Gaussian_prime" - - - concept: gegenbauer-polynomial - arity: 2 + property: constant + subject-area: "number theory" + mathml: + - "ℤ[i]" + urls: + - "https://mathworld.wolfram.com/GaussianInteger.html" + - "https://en.wikipedia.org/wiki/Gaussian_integer" + - "https://en.wikipedia.org/wiki/Gaussian_prime" + + - concept: gegenbauer-polynomial + arity: 2 + arguments: [a1, a2] + speech: en: gegenbauer polynomial - property: "indexed function" - area: "orthogonal polynomials" - mathml: - - "Cn(α)(x)" - notation: "msubsup C $1 ($2" - urls: - - "https://mathworld.wolfram.com/GegenbauerPolynomial.html" - - "https://en.wikipedia.org/wiki/Gegenbauer_polynomials" - - "https://www.encyclopediaofmath.org/index.php/Gegenbauer_polynomials" - - "https://dlmf.nist.gov/18.3#T1.t1.r3" - - - concept: gelfand-triple - arity: 3 - en: gelfand triple of $1, $2 and $3 - property: fenced - area: "functional analysis" - mathml: - - "(a,b,c)" - urls: - - "https://en.wikipedia.org/wiki/Rigged_Hilbert_space#Formal_definition_(Gelfand_triple)" - - - concept: gelfond-constant - arity: 0 + property: "indexed function" + subject-area: "orthogonal polynomials" + mathml: + - "Cn(α)(x)" + notation: "msubsup C a1 (a2" + urls: + - "https://mathworld.wolfram.com/GegenbauerPolynomial.html" + - "https://en.wikipedia.org/wiki/Gegenbauer_polynomials" + - "https://www.encyclopediaofmath.org/index.php/Gegenbauer_polynomials" + - "https://dlmf.nist.gov/18.3#T1.t1.r3" + + - concept: gelfand-triple + arity: 3 + arguments: [a1, a2, a3] + speech: + en: gelfand triple of a1, a2 and a3 + property: fenced + subject-area: "functional analysis" + mathml: + - "(a,b,c)" + urls: + - "https://en.wikipedia.org/wiki/Rigged_Hilbert_space#Formal_definition_(Gelfand_triple)" + + - concept: gelfond-constant + arity: 0 + arguments: [] + speech: en: gelfond constant - property: constant - area: "transcendental constants" - mathml: - - "eπ" - urls: - - "https://mathworld.wolfram.com/GelfondsConstant.html" - - "https://en.wikipedia.org/wiki/Gelfond%27s_constant" - - - concept: gelfond-schneider-constant - arity: 0 + property: constant + subject-area: "transcendental constants" + mathml: + - "eπ" + urls: + - "https://mathworld.wolfram.com/GelfondsConstant.html" + - "https://en.wikipedia.org/wiki/Gelfond%27s_constant" + + - concept: gelfond-schneider-constant + arity: 0 + arguments: [] + speech: en: gelfond schneider constant - property: constant - area: "transcendental constants" - mathml: - - "22" - urls: - - "https://mathworld.wolfram.com/Gelfond-SchneiderConstant.html" - - "https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constant" - - - concept: gell-mann-matrix - arity: 0 + property: constant + subject-area: "transcendental constants" + mathml: + - "22" + urls: + - "https://mathworld.wolfram.com/Gelfond-SchneiderConstant.html" + - "https://en.wikipedia.org/wiki/Gelfond%E2%80%93Schneider_constant" + + - concept: gell-mann-matrix + arity: 0 + arguments: [] + speech: en: gell mann matrix - property: symbol - area: "particle physics" - mathml: - - "λ" - urls: - - "https://mathworld.wolfram.com/Gell-MannMatrix.html" - - "https://en.wikipedia.org/wiki/Gell-Mann_matrices" - - "https://www.encyclopediaofmath.org/index.php/Gell-Mann_matrices" - - - concept: general-linear-group - arity: 1 - en: general linear group of $1 - property: function - area: "group theory" - mathml: - - "GLX" - - "AutX" - urls: - - "https://mathworld.wolfram.com/GeneralLinearGroup.html" - - "https://en.wikipedia.org/wiki/General_linear_group" - - "https://en.wikipedia.org/wiki/GL(n,C)" - - "https://ncatlab.org/nlab/show/general+linear+group" - - "https://www.encyclopediaofmath.org/index.php/General_linear_group" - - - concept: generalized-hypergeometric-function - arity: 2 - en: generalized hypergeometric function $1 $2 - property: mmultiscripts - area: "special functions" - mathml: - - "Fqp" - urls: - - "https://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html" - - "https://en.wikipedia.org/wiki/Generalized_hypergeometric_function" - - "https://dlmf.nist.gov/16.2#i" - - "https://dlmf.nist.gov/16.2#E1" - - "https://dlmf.nist.gov/16.5#p4" - - "https://dlmf.nist.gov/16.2#E1" - - "https://dlmf.nist.gov/16.5#p4" - - "https://dlmf.nist.gov/16.2#E1" - - "https://dlmf.nist.gov/16.5#p4" - - "https://dlmf.nist.gov/16.2#E1" - - "https://dlmf.nist.gov/16.5#p4" - - - concept: generalized-mean - arity: 1 - en: generalized mean of $1 - property: function - area: "means" - mathml: - - "Mx" - urls: - - "https://mathworld.wolfram.com/GeneralizedMean.html" - - "https://en.wikipedia.org/wiki/Generalized_mean" - - "https://en.wikipedia.org/wiki/Power_mean" - alias: - - hoelder-mean - - power-mean - - - concept: genocchi-number - arity: 1 + property: symbol + subject-area: "particle physics" + mathml: + - "λ" + urls: + - "https://mathworld.wolfram.com/Gell-MannMatrix.html" + - "https://en.wikipedia.org/wiki/Gell-Mann_matrices" + - "https://www.encyclopediaofmath.org/index.php/Gell-Mann_matrices" + + - concept: general-linear-group + arity: 1 + arguments: [a1] + speech: + en: general linear group of a1 + property: function + subject-area: "group theory" + mathml: + - "GLX" + - "AutX" + urls: + - "https://mathworld.wolfram.com/GeneralLinearGroup.html" + - "https://en.wikipedia.org/wiki/General_linear_group" + - "https://en.wikipedia.org/wiki/GL(n,C)" + - "https://ncatlab.org/nlab/show/general+linear+group" + - "https://www.encyclopediaofmath.org/index.php/General_linear_group" + + - concept: generalized-hypergeometric-function + arity: 2 + arguments: [a1, a2] + speech: + en: generalized hypergeometric function a1 a2 + property: mmultiscripts + subject-area: "special functions" + mathml: + - "Fqp" + urls: + - "https://mathworld.wolfram.com/GeneralizedHypergeometricFunction.html" + - "https://en.wikipedia.org/wiki/Generalized_hypergeometric_function" + - "https://dlmf.nist.gov/16.2#i" + - "https://dlmf.nist.gov/16.2#E1" + - "https://dlmf.nist.gov/16.5#p4" + - "https://dlmf.nist.gov/16.2#E1" + - "https://dlmf.nist.gov/16.5#p4" + - "https://dlmf.nist.gov/16.2#E1" + - "https://dlmf.nist.gov/16.5#p4" + - "https://dlmf.nist.gov/16.2#E1" + - "https://dlmf.nist.gov/16.5#p4" + + - concept: generalized-mean + arity: 1 + arguments: [a1] + speech: + en: generalized mean of a1 + property: function + subject-area: "means" + mathml: + - "Mx" + urls: + - "https://mathworld.wolfram.com/GeneralizedMean.html" + - "https://en.wikipedia.org/wiki/Generalized_mean" + - "https://en.wikipedia.org/wiki/Power_mean" + alias: + - hoelder-mean + - power-mean + + - concept: genocchi-number + arity: 1 + arguments: [a1] + speech: en: genocchi number - property: symbol - area: "integer sequences" - mathml: - - "Gx" - urls: - - "https://mathworld.wolfram.com/GenocchiNumber.html" - - "https://en.wikipedia.org/wiki/Genocchi_number" - - "https://en.wikipedia.org/wiki/Genocchi_prime" - - "https://dlmf.nist.gov/24.15#i" - - - concept: geodesic-curvature - arity: 0 + property: symbol + subject-area: "integer sequences" + mathml: + - "Gx" + urls: + - "https://mathworld.wolfram.com/GenocchiNumber.html" + - "https://en.wikipedia.org/wiki/Genocchi_number" + - "https://en.wikipedia.org/wiki/Genocchi_prime" + - "https://dlmf.nist.gov/24.15#i" + + - concept: geodesic-curvature + arity: 0 + arguments: [] + speech: en: geodesic curvature - property: symbol - area: "riemannian geometry" - mathml: - - "kg" - urls: - - "https://mathworld.wolfram.com/GeodesicCurvature.html" - - "https://en.wikipedia.org/wiki/Geodesic_curvature" - - "https://www.encyclopediaofmath.org/index.php/Geodesic_curvature" - - - concept: geodesic-distance - arity: 1 - en: geodesic distance of $1 - property: function - area: "graph theory" - mathml: - - "d(x)" - urls: - - "https://en.wikipedia.org/wiki/Distance_(graph_theory)" - - "https://en.wikipedia.org/wiki/Diameter_(graph_theory)" - - "https://en.wikipedia.org/wiki/Radius_(graph_theory)" - - "https://www.encyclopediaofmath.org/index.php/Geodesic_distance" - alias: - - distance - - - concept: geometric-genus - arity: 1 - en: geometric genus of $1 - property: function - area: "algebraic geometry" - mathml: - - "pg" - urls: - - "https://mathworld.wolfram.com/GeometricGenus.html" - - "https://en.wikipedia.org/wiki/Geometric_genus" - - "https://www.encyclopediaofmath.org/index.php/Geometric_genus" - - - concept: geometric-integral - arity: 2 - en: geometric integral over $1 $2 - property: indexed - area: "calculus" - mathml: - - "Πab" - urls: - - "https://en.wikipedia.org/wiki/Product_integral" - - - concept: geometric-mean - arity: 1 - en: geometric mean of $1 - property: function - area: "means" - mathml: - - "GM(x)" - urls: - - "https://mathworld.wolfram.com/GeometricMean.html" - - "https://en.wikipedia.org/wiki/Geometric_mean" - - "https://www.encyclopediaofmath.org/index.php/Geometric_mean" - - - concept: geometric-product - arity: 2 - en: $1 geometric product $2 - property: infix - area: "geometric algebra" - mathml: - - "X⁢Y" - urls: - - "https://en.wikipedia.org/wiki/Geometric_algebra" - - - concept: germ - arity: 2 - en: germ of $1 at $2 - property: mixfix - area: "topology" - mathml: - - "[S]x" - urls: - - "https://en.wikipedia.org/wiki/Germ_(mathematics)" - - "https://ncatlab.org/nlab/show/germ" - - "https://www.encyclopediaofmath.org/index.php/Germ" - - - concept: glaisher-constant - arity: 0 + property: symbol + subject-area: "riemannian geometry" + mathml: + - "kg" + urls: + - "https://mathworld.wolfram.com/GeodesicCurvature.html" + - "https://en.wikipedia.org/wiki/Geodesic_curvature" + - "https://www.encyclopediaofmath.org/index.php/Geodesic_curvature" + + - concept: geodesic-distance + arity: 1 + arguments: [a1] + speech: + en: geodesic distance of a1 + property: function + subject-area: "graph theory" + mathml: + - "d(x)" + urls: + - "https://en.wikipedia.org/wiki/Distance_(graph_theory)" + - "https://en.wikipedia.org/wiki/Diameter_(graph_theory)" + - "https://en.wikipedia.org/wiki/Radius_(graph_theory)" + - "https://www.encyclopediaofmath.org/index.php/Geodesic_distance" + alias: + - distance + + - concept: geometric-genus + arity: 1 + arguments: [a1] + speech: + en: geometric genus of a1 + property: function + subject-area: "algebraic geometry" + mathml: + - "pg" + urls: + - "https://mathworld.wolfram.com/GeometricGenus.html" + - "https://en.wikipedia.org/wiki/Geometric_genus" + - "https://www.encyclopediaofmath.org/index.php/Geometric_genus" + + - concept: geometric-integral + arity: 2 + arguments: [a1, a2] + speech: + en: geometric integral over a1 a2 + property: indexed + subject-area: "calculus" + mathml: + - "Πab" + urls: + - "https://en.wikipedia.org/wiki/Product_integral" + + - concept: geometric-mean + arity: 1 + arguments: [a1] + speech: + en: geometric mean of a1 + property: function + subject-area: "means" + mathml: + - "GM(x)" + urls: + - "https://mathworld.wolfram.com/GeometricMean.html" + - "https://en.wikipedia.org/wiki/Geometric_mean" + - "https://www.encyclopediaofmath.org/index.php/Geometric_mean" + + - concept: geometric-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 geometric product a2 + property: infix + subject-area: "geometric algebra" + mathml: + - "X⁢Y" + urls: + - "https://en.wikipedia.org/wiki/Geometric_algebra" + + - concept: germ + arity: 2 + arguments: [a1, a2] + speech: + en: germ of a1 at a2 + property: mixfix + subject-area: "topology" + mathml: + - "[S]x" + urls: + - "https://en.wikipedia.org/wiki/Germ_(mathematics)" + - "https://ncatlab.org/nlab/show/germ" + - "https://www.encyclopediaofmath.org/index.php/Germ" + + - concept: glaisher-constant + arity: 0 + arguments: [] + speech: en: glaisher constant - property: constant - area: "number theory" - mathml: - - "A" - urls: - - "https://mathworld.wolfram.com/GlaisherConstant.html" - - "https://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constant" - - "https://dlmf.nist.gov/5.17#E6" - alias: - - glaisher-kinkelin-constant - - - concept: global-dimension - arity: 1 - en: global dimension of $1 - property: function - area: "ring theory" - mathml: - - "gl dim(A)" - urls: - - "https://en.wikipedia.org/wiki/Global_dimension" - alias: - - global-homological-dimension - - homological-dimension - - - concept: golden-ratio - arity: 0 + property: constant + subject-area: "number theory" + mathml: + - "A" + urls: + - "https://mathworld.wolfram.com/GlaisherConstant.html" + - "https://en.wikipedia.org/wiki/Glaisher%E2%80%93Kinkelin_constant" + - "https://dlmf.nist.gov/5.17#E6" + alias: + - glaisher-kinkelin-constant + + - concept: global-dimension + arity: 1 + arguments: [a1] + speech: + en: global dimension of a1 + property: function + subject-area: "ring theory" + mathml: + - "gl dim(A)" + urls: + - "https://en.wikipedia.org/wiki/Global_dimension" + alias: + - global-homological-dimension + - homological-dimension + + - concept: golden-ratio + arity: 0 + arguments: [] + speech: en: golden ratio - property: constant - area: "geometry" - mathml: - - "φ" - - "ϕ" - urls: - - "https://mathworld.wolfram.com/GoldenRatio.html" - - "https://en.wikipedia.org/wiki/Golden_ratio" - - "https://en.wikipedia.org/wiki/List_of_works_designed_with_the_golden_ratio" - - "https://www.encyclopediaofmath.org/index.php/Golden_ratio" - alias: - - golden-number - - golden-mean - - golden-section - - medial-section - - divine-proportion - - divine-section - - golden-proportion - - golden-cut - - - concept: graham-number - arity: 0 + property: constant + subject-area: "geometry" + mathml: + - "φ" + - "ϕ" + urls: + - "https://mathworld.wolfram.com/GoldenRatio.html" + - "https://en.wikipedia.org/wiki/Golden_ratio" + - "https://en.wikipedia.org/wiki/List_of_works_designed_with_the_golden_ratio" + - "https://www.encyclopediaofmath.org/index.php/Golden_ratio" + alias: + - golden-number + - golden-mean + - golden-section + - medial-section + - divine-proportion + - divine-section + - golden-proportion + - golden-cut + + - concept: graham-number + arity: 0 + arguments: [] + speech: en: graham number - property: constant - area: "ramsey theory" - mathml: - - "G64" - urls: - - "https://mathworld.wolfram.com/GrahamsNumber.html" - - "https://en.wikipedia.org/wiki/Graham%27s_number" - - - concept: gram-determinant - arity: 1 - en: gram determinant of $1 - property: function - area: "linear algebra" - mathml: - - "GX" - - "ΓX" - urls: - - "https://mathworld.wolfram.com/GramDeterminant.html" - - "https://www.encyclopediaofmath.org/index.php/Gram_determinant" - - - concept: gram-matrix - arity: 0 + property: constant + subject-area: "ramsey theory" + mathml: + - "G64" + urls: + - "https://mathworld.wolfram.com/GrahamsNumber.html" + - "https://en.wikipedia.org/wiki/Graham%27s_number" + + - concept: gram-determinant + arity: 1 + arguments: [a1] + speech: + en: gram determinant of a1 + property: function + subject-area: "linear algebra" + mathml: + - "GX" + - "ΓX" + urls: + - "https://mathworld.wolfram.com/GramDeterminant.html" + - "https://www.encyclopediaofmath.org/index.php/Gram_determinant" + + - concept: gram-matrix + arity: 0 + arguments: [] + speech: en: gram matrix - property: symbol - area: "linear algebra" - mathml: - - "G" - urls: - - "https://mathworld.wolfram.com/GramMatrix.html" - - "https://en.wikipedia.org/wiki/Gramian_matrix" - - "https://www.encyclopediaofmath.org/index.php/Gram_matrix" - alias: - - gramian-matrix - - gramian - - - concept: grassmannian - arity: 1 - en: grassmannian of $1 - property: function - area: "differential geometry" - mathml: - - "Gr(x)" - urls: - - "https://mathworld.wolfram.com/Grassmannian.html" - - "https://en.wikipedia.org/wiki/Grassmannian" - - "https://ncatlab.org/nlab/show/Grassmannian" - - - concept: green-function - arity: 1 - en: green function of $1 - property: function - area: "mathematical physics" - mathml: - - "G(x)" - urls: - - "https://mathworld.wolfram.com/GreensFunction.html" - - "https://en.wikipedia.org/wiki/Green%27s_function_(many-body_theory)" - - "https://en.wikipedia.org/wiki/Green%27s_function" - - "https://en.wikipedia.org/wiki/Propagator" - - "https://www.encyclopediaofmath.org/index.php/Green_function" - - - concept: grobner-basis - arity: 0 + property: symbol + subject-area: "linear algebra" + mathml: + - "G" + urls: + - "https://mathworld.wolfram.com/GramMatrix.html" + - "https://en.wikipedia.org/wiki/Gramian_matrix" + - "https://www.encyclopediaofmath.org/index.php/Gram_matrix" + alias: + - gramian-matrix + - gramian + + - concept: grassmannian + arity: 1 + arguments: [a1] + speech: + en: grassmannian of a1 + property: function + subject-area: "differential geometry" + mathml: + - "Gr(x)" + urls: + - "https://mathworld.wolfram.com/Grassmannian.html" + - "https://en.wikipedia.org/wiki/Grassmannian" + - "https://ncatlab.org/nlab/show/Grassmannian" + + - concept: green-function + arity: 1 + arguments: [a1] + speech: + en: green function of a1 + property: function + subject-area: "mathematical physics" + mathml: + - "G(x)" + urls: + - "https://mathworld.wolfram.com/GreensFunction.html" + - "https://en.wikipedia.org/wiki/Green%27s_function_(many-body_theory)" + - "https://en.wikipedia.org/wiki/Green%27s_function" + - "https://en.wikipedia.org/wiki/Propagator" + - "https://www.encyclopediaofmath.org/index.php/Green_function" + + - concept: grobner-basis + arity: 0 + arguments: [] + speech: en: grobner basis - property: symbol - area: "computer algebra" - mathml: - - "G" - urls: - - "https://mathworld.wolfram.com/GroebnerBasis.html" - - "https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis" - - "https://www.encyclopediaofmath.org/index.php/Gröbner_basis" - - - concept: group-algebra - arity: 2 - en: group algebra $2 over $1 - property: mixfix - area: "ring theory" - mathml: - - "R[G]" - - "RG" - urls: - - "https://mathworld.wolfram.com/GroupAlgebra.html" - - "https://en.wikipedia.org/wiki/Group_algebra" - - "https://ncatlab.org/nlab/show/group+algebra" - - "https://www.encyclopediaofmath.org/index.php/Group_algebra" - - - concept: group-of-units - arity: 1 - en: group of units of $1 - property: msup, function - area: "ring theory" - mathml: - - "X*" - - "X×" - - "U(x)" - urls: - - "https://ncatlab.org/nlab/show/group+of+units" - - "https://ncatlab.org/nlab/show/group+of+units" - - - concept: group-ring - arity: 2 - en: group ring $2 over $1 - property: mixfix, infix - area: "ring theory" - mathml: - - "R[G]" - - "RG" - urls: - - "https://mathworld.wolfram.com/GroupRing.html" - - "https://en.wikipedia.org/wiki/Group_ring" - - - concept: gudermannian-function - arity: 1 - en: gudermannian function of $1 - property: function - area: "trigonometry" - mathml: - - "gd(x)" - urls: - - "https://mathworld.wolfram.com/GudermannianFunction.html" - - "https://en.wikipedia.org/wiki/Gudermannian_function" - - "https://dlmf.nist.gov/4.23#E39" - alias: - - gudermannian - - - concept: hadamard-product - arity: 2 - en: $1 hadamard product $2 - property: infix - area: "algebra" - mathml: - - "X∘Y" - - "X⊙Y" - urls: - - "https://mathworld.wolfram.com/HadamardProduct.html" - - "https://en.wikipedia.org/wiki/Hadamard_product_(matrices)" - alias: - - elementwise-product - - entrywise-product - - schur-product - - - concept: hahn-polynomial - arity: 1 - en: hahn polynomial of $1 - property: function - area: "orthogonal polynomials" - mathml: - - "qx" - urls: - - "https://mathworld.wolfram.com/HahnPolynomial.html" - - "https://en.wikipedia.org/wiki/Hahn_polynomials" - - "https://dlmf.nist.gov/18.19#T1.t1.r3" - - - concept: hamiltonian - arity: 1 - en: hamiltonian of $1 - property: operator - area: "quantum mechanics" - mathml: - - "HX" - notationc: "mover H ˇ" - notationb: "mover H ^" - notationa: "mrow < H >" - urls: - - "https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)" - - "https://en.wikipedia.org/wiki/Hamiltonian_vector_field" - - "https://en.wikipedia.org/wiki/Hamiltonian_(control_theory)" - - "https://ncatlab.org/nlab/show/Hamiltonian" - - "https://www.encyclopediaofmath.org/index.php/Hamiltonian" - - - concept: hankel-function - arity: 1 - en: hankel function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "H(x)" - urls: - - "https://mathworld.wolfram.com/HankelFunction.html" - - "https://dlmf.nist.gov/10.1" - - "https://www.encyclopediaofmath.org/index.php/Hankel_functions" - - - concept: hardy-class - arity: 1 - en: hardy class of $1 - property: "indexed symbol" - area: "complex analysis" - mathml: - - "Hx" - urls: - - "https://en.wikipedia.org/wiki/Hardy_space" - - "https://www.encyclopediaofmath.org/index.php/Hardy_classes" - alias: - - hardy-space - - - concept: hardy-space - arity: 1 - en: hardy space of $1 - property: mixfix - area: "complex analysis" - mathml: - - "Hp" - urls: - - "https://mathworld.wolfram.com/HardySpace.html" - - "https://en.wikipedia.org/wiki/Hardy_space" - - "https://www.encyclopediaofmath.org/index.php/Hardy_spaces" - - - concept: hardy-littlewood-maximal-operator - arity: 1 - en: hardy littlewood maximal operator of $1 - property: operator - area: "real analysis" - mathml: - - "M(x)" - urls: - - "https://en.wikipedia.org/wiki/Hardy%E2%80%93Littlewood_maximal_function" - alias: - - hardy-littlewood-maximal-function - - - concept: harmonic-mean - arity: 1 - en: harmonic mean of $1 - property: function - area: "means" - mathml: - - "H(x)" - urls: - - "https://mathworld.wolfram.com/HarmonicMean.html" - - "https://en.wikipedia.org/wiki/Harmonic_mean" - - "https://en.wikipedia.org/wiki/Subcontrary_mean" - alias: - - subcontrary-mean - - - concept: hausdorff-measure - arity: 1 - en: hausdorff measure of $1 - property: "indexed function" - area: "metric geometry" - mathml: - - "Hd" - urls: - - "https://mathworld.wolfram.com/HausdorffMeasure.html" - - "https://en.wikipedia.org/wiki/Hausdorff_measure" - - - concept: hausdorff-metric - arity: 2 - en: hausdorff distance $1 $2 - property: function - area: "metric geometry" - mathml: - - "dH(X,Y)" - urls: - - "https://en.wikipedia.org/wiki/Hausdorff_distance" - - "https://ncatlab.org/nlab/show/Hausdorff+metric" - - - concept: hausdorff-space - arity: 0 + property: symbol + subject-area: "computer algebra" + mathml: + - "G" + urls: + - "https://mathworld.wolfram.com/GroebnerBasis.html" + - "https://en.wikipedia.org/wiki/Gr%C3%B6bner_basis" + - "https://www.encyclopediaofmath.org/index.php/Gröbner_basis" + + - concept: group-algebra + arity: 2 + arguments: [a1, a2] + speech: + en: group algebra a2 over a1 + property: mixfix + subject-area: "ring theory" + mathml: + - "R[G]" + - "RG" + urls: + - "https://mathworld.wolfram.com/GroupAlgebra.html" + - "https://en.wikipedia.org/wiki/Group_algebra" + - "https://ncatlab.org/nlab/show/group+algebra" + - "https://www.encyclopediaofmath.org/index.php/Group_algebra" + + - concept: group-of-units + arity: 1 + arguments: [a1] + speech: + en: group of units of a1 + property: msup, function + subject-area: "ring theory" + mathml: + - "X*" + - "X×" + - "U(x)" + urls: + - "https://ncatlab.org/nlab/show/group+of+units" + - "https://ncatlab.org/nlab/show/group+of+units" + + - concept: group-ring + arity: 2 + arguments: [a1, a2] + speech: + en: group ring a2 over a1 + property: mixfix, infix + subject-area: "ring theory" + mathml: + - "R[G]" + - "RG" + urls: + - "https://mathworld.wolfram.com/GroupRing.html" + - "https://en.wikipedia.org/wiki/Group_ring" + + - concept: gudermannian-function + arity: 1 + arguments: [a1] + speech: + en: gudermannian function of a1 + property: function + subject-area: "trigonometry" + mathml: + - "gd(x)" + urls: + - "https://mathworld.wolfram.com/GudermannianFunction.html" + - "https://en.wikipedia.org/wiki/Gudermannian_function" + - "https://dlmf.nist.gov/4.23#E39" + alias: + - gudermannian + + - concept: hadamard-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 hadamard product a2 + property: infix + subject-area: "algebra" + mathml: + - "X∘Y" + - "X⊙Y" + urls: + - "https://mathworld.wolfram.com/HadamardProduct.html" + - "https://en.wikipedia.org/wiki/Hadamard_product_(matrices)" + alias: + - elementwise-product + - entrywise-product + - schur-product + + - concept: hahn-polynomial + arity: 1 + arguments: [a1] + speech: + en: hahn polynomial of a1 + property: function + subject-area: "orthogonal polynomials" + mathml: + - "qx" + urls: + - "https://mathworld.wolfram.com/HahnPolynomial.html" + - "https://en.wikipedia.org/wiki/Hahn_polynomials" + - "https://dlmf.nist.gov/18.19#T1.t1.r3" + + - concept: hamiltonian + arity: 1 + arguments: [a1] + speech: + en: hamiltonian of a1 + property: operator + subject-area: "quantum mechanics" + mathml: + - "HX" + notationc: "mover H ˇ" + notationb: "mover H ^" + notationa: "mrow < H >" + urls: + - "https://en.wikipedia.org/wiki/Hamiltonian_(quantum_mechanics)" + - "https://en.wikipedia.org/wiki/Hamiltonian_vector_field" + - "https://en.wikipedia.org/wiki/Hamiltonian_(control_theory)" + - "https://ncatlab.org/nlab/show/Hamiltonian" + - "https://www.encyclopediaofmath.org/index.php/Hamiltonian" + + - concept: hankel-function + arity: 1 + arguments: [a1] + speech: + en: hankel function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "H(x)" + urls: + - "https://mathworld.wolfram.com/HankelFunction.html" + - "https://dlmf.nist.gov/10.1" + - "https://www.encyclopediaofmath.org/index.php/Hankel_functions" + + - concept: hardy-class + arity: 1 + arguments: [a1] + speech: + en: hardy class of a1 + property: "indexed symbol" + subject-area: "complex analysis" + mathml: + - "Hx" + urls: + - "https://en.wikipedia.org/wiki/Hardy_space" + - "https://www.encyclopediaofmath.org/index.php/Hardy_classes" + alias: + - hardy-space + + - concept: hardy-space + arity: 1 + arguments: [a1] + speech: + en: hardy space of a1 + property: mixfix + subject-area: "complex analysis" + mathml: + - "Hp" + urls: + - "https://mathworld.wolfram.com/HardySpace.html" + - "https://en.wikipedia.org/wiki/Hardy_space" + - "https://www.encyclopediaofmath.org/index.php/Hardy_spaces" + + - concept: hardy-littlewood-maximal-operator + arity: 1 + arguments: [a1] + speech: + en: hardy littlewood maximal operator of a1 + property: operator + subject-area: "real analysis" + mathml: + - "M(x)" + urls: + - "https://en.wikipedia.org/wiki/Hardy%E2%80%93Littlewood_maximal_function" + alias: + - hardy-littlewood-maximal-function + + - concept: harmonic-mean + arity: 1 + arguments: [a1] + speech: + en: harmonic mean of a1 + property: function + subject-area: "means" + mathml: + - "H(x)" + urls: + - "https://mathworld.wolfram.com/HarmonicMean.html" + - "https://en.wikipedia.org/wiki/Harmonic_mean" + - "https://en.wikipedia.org/wiki/Subcontrary_mean" + alias: + - subcontrary-mean + + - concept: hausdorff-measure + arity: 1 + arguments: [a1] + speech: + en: hausdorff measure of a1 + property: "indexed function" + subject-area: "metric geometry" + mathml: + - "Hd" + urls: + - "https://mathworld.wolfram.com/HausdorffMeasure.html" + - "https://en.wikipedia.org/wiki/Hausdorff_measure" + + - concept: hausdorff-metric + arity: 2 + arguments: [a1, a2] + speech: + en: hausdorff distance a1 a2 + property: function + subject-area: "metric geometry" + mathml: + - "dH(X,Y)" + urls: + - "https://en.wikipedia.org/wiki/Hausdorff_distance" + - "https://ncatlab.org/nlab/show/Hausdorff+metric" + + - concept: hausdorff-space + arity: 0 + arguments: [] + speech: en: hausdorff space - property: constant - area: "topology" - mathml: - - "T2" - urls: - - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions" - alias: - - separated-space - - - concept: hazard-function - arity: 1 - en: hazard function of $1 - property: function - area: "engineering" - mathml: - - "h(x)" - urls: - - "https://mathworld.wolfram.com/HazardFunction.html" - alias: - - failure-rate - - - concept: heaviside-function - arity: 1 - en: heaviside function of $1 - property: function - area: "special functions" - mathml: - - "H(x)" - urls: - - "https://dlmf.nist.gov/1.16#E13)[https://en.wikipedia.org/wiki/Heaviside_step_function" - - "https://en.wikipedia.org/wiki/Heaviside_step_function" - alias: - - heaviside-step-function - - unit-step-function - - - concept: heawood-number - arity: 1 - en: heawood number of $1 - property: function - area: "topological graph theory" - mathml: - - "H(x)" - urls: - - "https://en.wikipedia.org/wiki/Heawood_number" - - - concept: hecke-operator - arity: 1 - en: hecke operator of $1 - property: operator - area: "modular forms" - mathml: - - "Tx" - urls: - - "https://mathworld.wolfram.com/HeckeOperator.html" - - "https://en.wikipedia.org/wiki/Hecke_operator" - - - concept: height-function - arity: 1 - en: height function of $1 - property: function - area: "algebra" - mathml: - - "HX" - - "hX" - urls: - - "https://en.wikipedia.org/wiki/Height_of_a_polynomial" - - - concept: height-of-abelian-group - arity: 1 - en: height of abelian group of $1 - property: function - area: "group theory" - mathml: - - "hx" - urls: - - "https://en.wikipedia.org/wiki/Height_(abelian_group)" - - - concept: height-of-prime-ideal - arity: 1 - en: height of prime ideal of $1 - property: function - area: "commutative algebra" - mathml: - - "ht(x)" - urls: - - "https://en.wikipedia.org/wiki/Krull_dimension#height" - alias: - - codimension-of-prime-ideal - - rank-of-prime-ideal - - altitude-of-prime-ideal - - - concept: heisenberg-group - arity: 1 + property: constant + subject-area: "topology" + mathml: + - "T2" + urls: + - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions" + alias: + - separated-space + + - concept: hazard-function + arity: 1 + arguments: [a1] + speech: + en: hazard function of a1 + property: function + subject-area: "engineering" + mathml: + - "h(x)" + urls: + - "https://mathworld.wolfram.com/HazardFunction.html" + alias: + - failure-rate + + - concept: heaviside-function + arity: 1 + arguments: [a1] + speech: + en: heaviside function of a1 + property: function + subject-area: "special functions" + mathml: + - "H(x)" + urls: + - "https://dlmf.nist.gov/1.16#E13)[https://en.wikipedia.org/wiki/Heaviside_step_function" + - "https://en.wikipedia.org/wiki/Heaviside_step_function" + alias: + - heaviside-step-function + - unit-step-function + + - concept: heawood-number + arity: 1 + arguments: [a1] + speech: + en: heawood number of a1 + property: function + subject-area: "topological graph theory" + mathml: + - "H(x)" + urls: + - "https://en.wikipedia.org/wiki/Heawood_number" + + - concept: hecke-operator + arity: 1 + arguments: [a1] + speech: + en: hecke operator of a1 + property: operator + subject-area: "modular forms" + mathml: + - "Tx" + urls: + - "https://mathworld.wolfram.com/HeckeOperator.html" + - "https://en.wikipedia.org/wiki/Hecke_operator" + + - concept: height-function + arity: 1 + arguments: [a1] + speech: + en: height function of a1 + property: function + subject-area: "algebra" + mathml: + - "HX" + - "hX" + urls: + - "https://en.wikipedia.org/wiki/Height_of_a_polynomial" + + - concept: height-of-abelian-group + arity: 1 + arguments: [a1] + speech: + en: height of abelian group of a1 + property: function + subject-area: "group theory" + mathml: + - "hx" + urls: + - "https://en.wikipedia.org/wiki/Height_(abelian_group)" + + - concept: height-of-prime-ideal + arity: 1 + arguments: [a1] + speech: + en: height of prime ideal of a1 + property: function + subject-area: "commutative algebra" + mathml: + - "ht(x)" + urls: + - "https://en.wikipedia.org/wiki/Krull_dimension#height" + alias: + - codimension-of-prime-ideal + - rank-of-prime-ideal + - altitude-of-prime-ideal + + - concept: heisenberg-group + arity: 1 + arguments: [a1] + speech: en: heisenberg group - property: symbol - area: "group theory" - mathml: - - "H(x)" - urls: - - "https://mathworld.wolfram.com/HeisenbergGroup.html" - - "https://en.wikipedia.org/wiki/Heisenberg_group" - - "https://ncatlab.org/nlab/show/Heisenberg+group" - - - concept: hermite-polynomial - arity: 1 - en: hermite polynomial of $1 - property: function - area: "special functions" - mathml: - - "HX" - - "HeX" - urls: - - "https://mathworld.wolfram.com/HermitePolynomial.html" - - "https://en.wikipedia.org/wiki/Hermite_polynomials" - - "https://dlmf.nist.gov/18.3" - - "https://dlmf.nist.gov/18.3#T1.t1.r28" - - "https://dlmf.nist.gov/18.3#T1.t1.r29" - - - concept: hermitian-adjoint - arity: 1 - en: hermitian adjoint of $1 - property: msup - area: "functional analysis" - mathml: - - "A†" - - "A*" - urls: - - "https://en.wikipedia.org/wiki/Hermitian_adjoint" - alias: - - adjoint-operator - - - concept: hermitian-conjugate - arity: 1 - en: hermitian conjugate of $1 - property: msup - area: "linear algebra" - mathml: - - "AH" - urls: - - "https://mathworld.wolfram.com/HermitianConjugate.html" - - "https://en.wikipedia.org/wiki/Conjugate_transpose" - alias: - - adjoint-matrix - - - concept: heronian-mean - arity: 1 - en: heronian mean of $1 - property: function - area: "means" - mathml: - - "H(x)" - urls: - - "https://mathworld.wolfram.com/HeronianMean.html" - - "https://en.wikipedia.org/wiki/Heronian_mean" - - - concept: hessian - arity: 1 - en: hessian of $1 - property: operator - area: "differential operators" - mathml: - - "H(x)" - urls: - - "https://mathworld.wolfram.com/Hessian.html" - - "https://en.wikipedia.org/wiki/Hessian_matrix" - - "https://ncatlab.org/nlab/show/Hessian" - alias: - - hessian-matrix - - - concept: heun-function - arity: 1 - en: heun function of $1 - property: function - area: "special functions" - mathml: - - "HfX" - - "H⁢ℓX" - urls: - - "https://en.wikipedia.org/wiki/Heun_function" - - "https://dlmf.nist.gov/31.1" - - "https://dlmf.nist.gov/31.4#p1" - - "https://dlmf.nist.gov/31.3#E1" - - - concept: heun-polynomial - arity: 1 - en: heun polynomial of $1 - property: function - area: "special functions" - mathml: - - "Hp(x)" - urls: - - "https://en.wikipedia.org/wiki/Heun_function" - - "https://dlmf.nist.gov/31.5#p1" - - "https://dlmf.nist.gov/31.5#E2" - - - concept: hexadecimal - arity: 1 - en: hexadecimal of $1 - property: unit - area: "arithmetic" - mathml: - - "hexX" - notationb: "msub $1 hex" - notationa: "msub $1 16" - urls: - - "https://mathworld.wolfram.com/Hexadecimal.html" - - "https://en.wikipedia.org/wiki/Hexadecimal" - - - concept: hilbert-symbol - arity: 2 + property: symbol + subject-area: "group theory" + mathml: + - "H(x)" + urls: + - "https://mathworld.wolfram.com/HeisenbergGroup.html" + - "https://en.wikipedia.org/wiki/Heisenberg_group" + - "https://ncatlab.org/nlab/show/Heisenberg+group" + + - concept: hermite-polynomial + arity: 1 + arguments: [a1] + speech: + en: hermite polynomial of a1 + property: function + subject-area: "special functions" + mathml: + - "HX" + - "HeX" + urls: + - "https://mathworld.wolfram.com/HermitePolynomial.html" + - "https://en.wikipedia.org/wiki/Hermite_polynomials" + - "https://dlmf.nist.gov/18.3" + - "https://dlmf.nist.gov/18.3#T1.t1.r28" + - "https://dlmf.nist.gov/18.3#T1.t1.r29" + + - concept: hermitian-adjoint + arity: 1 + arguments: [a1] + speech: + en: hermitian adjoint of a1 + property: msup + subject-area: "functional analysis" + mathml: + - "A†" + - "A*" + urls: + - "https://en.wikipedia.org/wiki/Hermitian_adjoint" + alias: + - adjoint-operator + + - concept: hermitian-conjugate + arity: 1 + arguments: [a1] + speech: + en: hermitian conjugate of a1 + property: msup + subject-area: "linear algebra" + mathml: + - "AH" + urls: + - "https://mathworld.wolfram.com/HermitianConjugate.html" + - "https://en.wikipedia.org/wiki/Conjugate_transpose" + alias: + - adjoint-matrix + + - concept: heronian-mean + arity: 1 + arguments: [a1] + speech: + en: heronian mean of a1 + property: function + subject-area: "means" + mathml: + - "H(x)" + urls: + - "https://mathworld.wolfram.com/HeronianMean.html" + - "https://en.wikipedia.org/wiki/Heronian_mean" + + - concept: hessian + arity: 1 + arguments: [a1] + speech: + en: hessian of a1 + property: operator + subject-area: "differential operators" + mathml: + - "H(x)" + urls: + - "https://mathworld.wolfram.com/Hessian.html" + - "https://en.wikipedia.org/wiki/Hessian_matrix" + - "https://ncatlab.org/nlab/show/Hessian" + alias: + - hessian-matrix + + - concept: heun-function + arity: 1 + arguments: [a1] + speech: + en: heun function of a1 + property: function + subject-area: "special functions" + mathml: + - "HfX" + - "H⁢ℓX" + urls: + - "https://en.wikipedia.org/wiki/Heun_function" + - "https://dlmf.nist.gov/31.1" + - "https://dlmf.nist.gov/31.4#p1" + - "https://dlmf.nist.gov/31.3#E1" + + - concept: heun-polynomial + arity: 1 + arguments: [a1] + speech: + en: heun polynomial of a1 + property: function + subject-area: "special functions" + mathml: + - "Hp(x)" + urls: + - "https://en.wikipedia.org/wiki/Heun_function" + - "https://dlmf.nist.gov/31.5#p1" + - "https://dlmf.nist.gov/31.5#E2" + + - concept: hexadecimal + arity: 1 + arguments: [a1] + speech: + en: hexadecimal of a1 + property: unit + subject-area: "arithmetic" + mathml: + - "hexX" + notationb: "msub a1 hex" + notationa: "msub a1 16" + urls: + - "https://mathworld.wolfram.com/Hexadecimal.html" + - "https://en.wikipedia.org/wiki/Hexadecimal" + + - concept: hilbert-symbol + arity: 2 + arguments: [a1, a2] + speech: en: hilbert symbol - property: fenced - area: "quadratic forms" - mathml: - - "(x,y)" - urls: - - "https://mathworld.wolfram.com/HilbertSymbol.html" - - "https://en.wikipedia.org/wiki/Hilbert_symbol" - - - concept: hilbert-schmidt-norm - arity: 1 - en: hilbert schmidt norm of $1 - property: fenced - area: "matrix norms" - mathml: - - "|X|HS" - notation: "msub mrow | $1 | HS" - urls: - - "https://mathworld.wolfram.com/Hilbert-SchmidtNorm.html" - - "https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt_operator" - alias: - - - concept: hit-or-miss-transform - arity: 2 - en: $1 hit or miss transform $2 - property: infix - area: "mathematical morphology" - mathml: - - "X⊙Y" - urls: - - "https://en.wikipedia.org/wiki/Hit-or-miss_transform" - - - concept: hodge-star-operator - arity: 1 - en: hodge star operator of $1 - property: prefix - area: "differential geometry" - mathml: - - "⋆x" - urls: - - "https://en.wikipedia.org/wiki/Hodge_dual" - - "https://ncatlab.org/nlab/show/Hodge+star+operator" - - - concept: holomorph - arity: 1 - en: holomorph of $1 - property: function - area: "group theory" - mathml: - - "Hol(x)" - urls: - - "https://en.wikipedia.org/wiki/Holomorph_(mathematics)" - - "https://ncatlab.org/nlab/show/holomorph" - - - concept: holonomy-group - arity: 1 - en: holonomy group of $1 - property: "indexed symbol" - area: "differential geometry" - mathml: - - "Hol(x)" - urls: - - "https://mathworld.wolfram.com/Holonomy.html" - - "https://en.wikipedia.org/wiki/Holonomy" - - "https://ncatlab.org/nlab/show/holonomy" - - - concept: home-prime - arity: 1 - en: home prime of $1 - property: function - area: "number theory" - mathml: - - "HP(x)" - urls: - - "https://mathworld.wolfram.com/HomePrime.html" - - "https://en.wikipedia.org/wiki/Home_prime" - - - concept: homology-group - arity: 1 - en: homology group of $1 - property: function - area: "homology theory" - mathml: - - "Hx" - urls: - - "https://mathworld.wolfram.com/HomologyGroup.html" - - "https://en.wikipedia.org/wiki/Singular_homology" - - - concept: homomorphic-product - arity: 2 - en: $1 homomorphic product $2 - property: infix - area: "graph theory" - mathml: - - "X⋉Y" - urls: - - "https://en.wikipedia.org/wiki/Graph_product" - - - - concept: homotopy-category - arity: 1 - en: homotopy category of $1 - property: function - area: "category theory" - mathml: - - "Ho(x)" - urls: - - "https://ncatlab.org/nlab/show/homotopy+category" - - - concept: horsepower-mechanical - arity: 1 - en: $1 horsepower - property: unit - area: "imperial unit" - mathml: - - "x hp" - urls: - - "https://en.wikipedia.org/wiki/Horsepower" - alias: - - horsepower - - - concept: horsepower-metric - arity: 1 - en: horsepower metric of $1 - property: unit - area: "metric unit" - mathml: - - "PSX" - - "cvX" - - "hkX" - - "pkX" - - "ksX" - - "chX" - urls: - - "https://en.wikipedia.org/wiki/Metric_horsepower" - alias: - - horsepower - - - concept: hurwitz-zeta-function - arity: 1 - en: hurwitz zeta function of $1 - property: function - area: "special functions" - mathml: - - "ζ(x)" - urls: - - "https://mathworld.wolfram.com/HurwitzZetaFunction.html" - - "https://en.wikipedia.org/wiki/Hurwitz_zeta_function" - - "https://dlmf.nist.gov/25.11" - - "https://dlmf.nist.gov/25.11#E1" - - - concept: hvat - arity: 1 - en: hvat of $1 - property: unit - area: "customary units" - mathml: - - "hvat(x)" - urls: - - "https://en.wikipedia.org/wiki/Kubni_hvat" - - "https://en.wikipedia.org/wiki/%C4%8Cetvorni_hvat" - - "https://en.wikipedia.org/wiki/Hvat" - - "https://en.wikipedia.org/wiki/Kvadratni_hvat" - - - concept: hydrated-compound - arity: 2 - en: $1 hydrated compound $2 - property: infix - area: "chemistry" - mathml: - - "X⋅Y" - - "X•Y" - urls: - - "https://en.wikipedia.org/wiki/Hydrate" - - "https://en.wikipedia.org/wiki/Cobalt(II)_chloride" - - "https://www.youtube.com/watch?v=PV_3WBTDyJc" - - - concept: hyperbolic-cosine-integral - arity: 1 - en: hyperbolic cosine integral of $1 - property: function - area: "special functions" - mathml: - - "Chi(x)" - urls: - - "https://mathworld.wolfram.com/HyperbolicCosineIntegral.html" - - "https://dlmf.nist.gov/6.2#E16" - - - concept: hyperbolic-plane - arity: 0 + property: fenced + subject-area: "quadratic forms" + mathml: + - "(x,y)" + urls: + - "https://mathworld.wolfram.com/HilbertSymbol.html" + - "https://en.wikipedia.org/wiki/Hilbert_symbol" + + - concept: hilbert-schmidt-norm + arity: 1 + arguments: [a1] + speech: + en: hilbert schmidt norm of a1 + property: fenced + subject-area: "matrix norms" + mathml: + - "|X|HS" + notation: "msub mrow | a1 | HS" + urls: + - "https://mathworld.wolfram.com/Hilbert-SchmidtNorm.html" + - "https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt_operator" + alias: + + - concept: hit-or-miss-transform + arity: 2 + arguments: [a1, a2] + speech: + en: a1 hit or miss transform a2 + property: infix + subject-area: "mathematical morphology" + mathml: + - "X⊙Y" + urls: + - "https://en.wikipedia.org/wiki/Hit-or-miss_transform" + + - concept: hodge-star-operator + arity: 1 + arguments: [a1] + speech: + en: hodge star operator of a1 + property: prefix + subject-area: "differential geometry" + mathml: + - "⋆x" + urls: + - "https://en.wikipedia.org/wiki/Hodge_dual" + - "https://ncatlab.org/nlab/show/Hodge+star+operator" + + - concept: holomorph + arity: 1 + arguments: [a1] + speech: + en: holomorph of a1 + property: function + subject-area: "group theory" + mathml: + - "Hol(x)" + urls: + - "https://en.wikipedia.org/wiki/Holomorph_(mathematics)" + - "https://ncatlab.org/nlab/show/holomorph" + + - concept: holonomy-group + arity: 1 + arguments: [a1] + speech: + en: holonomy group of a1 + property: "indexed symbol" + subject-area: "differential geometry" + mathml: + - "Hol(x)" + urls: + - "https://mathworld.wolfram.com/Holonomy.html" + - "https://en.wikipedia.org/wiki/Holonomy" + - "https://ncatlab.org/nlab/show/holonomy" + + - concept: home-prime + arity: 1 + arguments: [a1] + speech: + en: home prime of a1 + property: function + subject-area: "number theory" + mathml: + - "HP(x)" + urls: + - "https://mathworld.wolfram.com/HomePrime.html" + - "https://en.wikipedia.org/wiki/Home_prime" + + - concept: homology-group + arity: 1 + arguments: [a1] + speech: + en: homology group of a1 + property: function + subject-area: "homology theory" + mathml: + - "Hx" + urls: + - "https://mathworld.wolfram.com/HomologyGroup.html" + - "https://en.wikipedia.org/wiki/Singular_homology" + + - concept: homomorphic-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 homomorphic product a2 + property: infix + subject-area: "graph theory" + mathml: + - "X⋉Y" + urls: + - "https://en.wikipedia.org/wiki/Graph_product" + + + - concept: homotopy-category + arity: 1 + arguments: [a1] + speech: + en: homotopy category of a1 + property: function + subject-area: "category theory" + mathml: + - "Ho(x)" + urls: + - "https://ncatlab.org/nlab/show/homotopy+category" + + - concept: horsepower-mechanical + arity: 1 + arguments: [a1] + speech: + en: a1 horsepower + property: unit + subject-area: "imperial unit" + mathml: + - "x hp" + urls: + - "https://en.wikipedia.org/wiki/Horsepower" + alias: + - horsepower + + - concept: horsepower-metric + arity: 1 + arguments: [a1] + speech: + en: horsepower metric of a1 + property: unit + subject-area: "metric unit" + mathml: + - "PSX" + - "cvX" + - "hkX" + - "pkX" + - "ksX" + - "chX" + urls: + - "https://en.wikipedia.org/wiki/Metric_horsepower" + alias: + - horsepower + + - concept: hurwitz-zeta-function + arity: 1 + arguments: [a1] + speech: + en: hurwitz zeta function of a1 + property: function + subject-area: "special functions" + mathml: + - "ζ(x)" + urls: + - "https://mathworld.wolfram.com/HurwitzZetaFunction.html" + - "https://en.wikipedia.org/wiki/Hurwitz_zeta_function" + - "https://dlmf.nist.gov/25.11" + - "https://dlmf.nist.gov/25.11#E1" + + - concept: hvat + arity: 1 + arguments: [a1] + speech: + en: hvat of a1 + property: unit + subject-area: "customary units" + mathml: + - "hvat(x)" + urls: + - "https://en.wikipedia.org/wiki/Kubni_hvat" + - "https://en.wikipedia.org/wiki/%C4%8Cetvorni_hvat" + - "https://en.wikipedia.org/wiki/Hvat" + - "https://en.wikipedia.org/wiki/Kvadratni_hvat" + + - concept: hydrated-compound + arity: 2 + arguments: [a1, a2] + speech: + en: a1 hydrated compound a2 + property: infix + subject-area: "chemistry" + mathml: + - "X⋅Y" + - "X•Y" + urls: + - "https://en.wikipedia.org/wiki/Hydrate" + - "https://en.wikipedia.org/wiki/Cobalt(II)_chloride" + - "https://www.youtube.com/watch?v=PV_3WBTDyJc" + + - concept: hyperbolic-cosine-integral + arity: 1 + arguments: [a1] + speech: + en: hyperbolic cosine integral of a1 + property: function + subject-area: "special functions" + mathml: + - "Chi(x)" + urls: + - "https://mathworld.wolfram.com/HyperbolicCosineIntegral.html" + - "https://dlmf.nist.gov/6.2#E16" + + - concept: hyperbolic-plane + arity: 0 + arguments: [] + speech: en: hyperbolic plane - property: symbol - area: "non-euclidean geometry" - mathml: - - "ℍ2" - urls: - - "https://mathworld.wolfram.com/HyperbolicPlane.html" - - "https://ncatlab.org/nlab/show/hyperbolic+plane" - - - concept: hyperbolic-sine-integral - arity: 1 - en: hyperbolic sine integral of $1 - property: function - area: "special functions" - mathml: - - "Shi(x)" - urls: - - "https://mathworld.wolfram.com/HyperbolicSineIntegral.html" - - "https://dlmf.nist.gov/6.2#E15" - - - concept: hyperbolic-space - arity: 1 + property: symbol + subject-area: "non-euclidean geometry" + mathml: + - "ℍ2" + urls: + - "https://mathworld.wolfram.com/HyperbolicPlane.html" + - "https://ncatlab.org/nlab/show/hyperbolic+plane" + + - concept: hyperbolic-sine-integral + arity: 1 + arguments: [a1] + speech: + en: hyperbolic sine integral of a1 + property: function + subject-area: "special functions" + mathml: + - "Shi(x)" + urls: + - "https://mathworld.wolfram.com/HyperbolicSineIntegral.html" + - "https://dlmf.nist.gov/6.2#E15" + + - concept: hyperbolic-space + arity: 1 + arguments: [a1] + speech: en: hyperbolic space - property: symbol - area: "non-euclidean geometry" - mathml: - - "Hn" - urls: - - "https://mathworld.wolfram.com/HyperbolicSpace.html" - - "https://en.wikipedia.org/wiki/Hyperbolic_space" - - - concept: hyperbolic-umbilic-canonical-integral-function - arity: 1 - en: hyperbolic umbilic canonical integral function of $1 - property: function - area: "special functions" - mathml: - - "Ψ(E)z" - urls: - - "https://dlmf.nist.gov/36.2#E11" - - "https://dlmf.nist.gov/36.3#i" - - "https://dlmf.nist.gov/36.3#ii" - - - concept: hyperdeterminant - arity: 1 - en: hyperdeterminant of $1 - property: "function, fenced" - area: "multilinear algebra" - mathml: - - "detX" - - "|x|" - urls: - - "https://mathworld.wolfram.com/Hyperdeterminant.html" - - "https://en.wikipedia.org/wiki/Hyperdeterminant" - - "https://ncatlab.org/nlab/show/hyperdeterminant" - - - concept: hypertorus - arity: 1 - en: $1th hypertorus - property: "indexed symbol" - area: "topology" - mathml: - - "Tn" - urls: - - "https://en.wikipedia.org/wiki/Torus#n-dimensional_torus" - alias: - - n-torus - - n-dimensional-torus - - - concept: identity-element - arity: 0 + property: symbol + subject-area: "non-euclidean geometry" + mathml: + - "Hn" + urls: + - "https://mathworld.wolfram.com/HyperbolicSpace.html" + - "https://en.wikipedia.org/wiki/Hyperbolic_space" + + - concept: hyperbolic-umbilic-canonical-integral-function + arity: 1 + arguments: [a1] + speech: + en: hyperbolic umbilic canonical integral function of a1 + property: function + subject-area: "special functions" + mathml: + - "Ψ(E)z" + urls: + - "https://dlmf.nist.gov/36.2#E11" + - "https://dlmf.nist.gov/36.3#i" + - "https://dlmf.nist.gov/36.3#ii" + + - concept: hyperdeterminant + arity: 1 + arguments: [a1] + speech: + en: hyperdeterminant of a1 + property: "function, fenced" + subject-area: "multilinear algebra" + mathml: + - "detX" + - "|x|" + urls: + - "https://mathworld.wolfram.com/Hyperdeterminant.html" + - "https://en.wikipedia.org/wiki/Hyperdeterminant" + - "https://ncatlab.org/nlab/show/hyperdeterminant" + + - concept: hypertorus + arity: 1 + arguments: [a1] + speech: + en: a1th hypertorus + property: "indexed symbol" + subject-area: "topology" + mathml: + - "Tn" + urls: + - "https://en.wikipedia.org/wiki/Torus#n-dimensional_torus" + alias: + - n-torus + - n-dimensional-torus + + - concept: identity-element + arity: 0 + arguments: [] + speech: en: identity element - property: symbol - area: "group theory" - mathml: - - "e" - - "I" - - "E" - notationa: "mn 1" - urls: - - "https://mathworld.wolfram.com/IdentityElement.html" - - "https://en.wikipedia.org/wiki/Identity_element" - - "https://ncatlab.org/nlab/show/identity+element" - alias: - - identity - - two-sided-identity - - - concept: identity-function - arity: 1 - en: identity function of $1 - property: function - area: "algebra" - mathml: - - "idX" - - "idx" - - "Ix" - urls: - - "https://mathworld.wolfram.com/IdentityFunction.html" - - "https://en.wikipedia.org/wiki/Identity_function" - - "https://ncatlab.org/nlab/show/identity+function" - alias: - - identity-map - - identity-relation - - identity-transformation - - - concept: identity-functor - arity: 1 - en: identity functor of $1 - property: function - area: "category theory" - mathml: - - "1x" - - "Ix" - - "Idx" - urls: - - "https://ncatlab.org/nlab/show/identity+functor" - - "https://en.wikipedia.org/wiki/Functor" - - - concept: identity-matrix - arity: 0 + property: symbol + subject-area: "group theory" + mathml: + - "e" + - "I" + - "E" + notationa: "mn 1" + urls: + - "https://mathworld.wolfram.com/IdentityElement.html" + - "https://en.wikipedia.org/wiki/Identity_element" + - "https://ncatlab.org/nlab/show/identity+element" + alias: + - identity + - two-sided-identity + + - concept: identity-function + arity: 1 + arguments: [a1] + speech: + en: identity function of a1 + property: function + subject-area: "algebra" + mathml: + - "idX" + - "idx" + - "Ix" + urls: + - "https://mathworld.wolfram.com/IdentityFunction.html" + - "https://en.wikipedia.org/wiki/Identity_function" + - "https://ncatlab.org/nlab/show/identity+function" + alias: + - identity-map + - identity-relation + - identity-transformation + + - concept: identity-functor + arity: 1 + arguments: [a1] + speech: + en: identity functor of a1 + property: function + subject-area: "category theory" + mathml: + - "1x" + - "Ix" + - "Idx" + urls: + - "https://ncatlab.org/nlab/show/identity+functor" + - "https://en.wikipedia.org/wiki/Functor" + + - concept: identity-matrix + arity: 0 + arguments: [] + speech: en: identity matrix - property: symbol - area: "linear algebra" - mathml: - - "I" - urls: - - "https://mathworld.wolfram.com/IdentityMatrix.html" - - "https://en.wikipedia.org/wiki/Identity_matrix" - alias: - - unit-matrix - - - concept: image - arity: 1 - en: image $1 - property: mixfix - area: "set theory" - mathml: - - "Image(f)" - - "f(D)" - - "X→" - urls: - - "https://mathworld.wolfram.com/Image.html" - - "https://en.wikipedia.org/wiki/Image_(mathematics)" - - "https://en.wikipedia.org/wiki/Range_(mathematics)" - - "https://en.wikipedia.org/wiki/Image_(category_theory)" - - "https://en.wikipedia.org/wiki/Image" - - "https://ncatlab.org/nlab/show/image" - - - concept: incenter - arity: 0 + property: symbol + subject-area: "linear algebra" + mathml: + - "I" + urls: + - "https://mathworld.wolfram.com/IdentityMatrix.html" + - "https://en.wikipedia.org/wiki/Identity_matrix" + alias: + - unit-matrix + + - concept: image + arity: 1 + arguments: [a1] + speech: + en: image a1 + property: mixfix + subject-area: "set theory" + mathml: + - "Image(f)" + - "f(D)" + - "X→" + urls: + - "https://mathworld.wolfram.com/Image.html" + - "https://en.wikipedia.org/wiki/Image_(mathematics)" + - "https://en.wikipedia.org/wiki/Range_(mathematics)" + - "https://en.wikipedia.org/wiki/Image_(category_theory)" + - "https://en.wikipedia.org/wiki/Image" + - "https://ncatlab.org/nlab/show/image" + + - concept: incenter + arity: 0 + arguments: [] + speech: en: incenter - property: symbol - area: "geometry" - mathml: - - "I" - urls: - - "https://mathworld.wolfram.com/Incenter.html" - - "https://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle" - - "https://en.wikipedia.org/wiki/Gergonne_point" - - "https://en.wikipedia.org/wiki/Incentre" - - - concept: incidence-relation - arity: 2 - en: $1 incidence relation $2 - property: infix - area: "projective geometry" - mathml: - - "XIY" - urls: - - "https://en.wikipedia.org/wiki/Incidence_(geometry)" - - "https://en.wikipedia.org/wiki/Incidence_(epidemiology)" - - "https://www.encyclopediaofmath.org/index.php/Incidence" - - - concept: incidence-structure - arity: 3 - en: incidence structure of $1, $2 and $3 - property: fenced - area: "incidence geometry" - mathml: - - "(P,L,I)" - urls: - - "https://en.wikipedia.org/wiki/Incidence_structure" - - - concept: inclusion-map - arity: 1 - en: inclusion map of $1 - property: function - area: "set theory" - mathml: - - "ι(x)" - urls: - - "https://en.wikipedia.org/wiki/Inclusion_map" - alias: - - inclusion-function - - insertion - - canonical-injection - - - concept: incomparability - arity: 2 - en: $1 incomparable to $2 - property: infix - area: "order theory" - mathml: - - "X⪋̸Y" - urls: - - "https://en.wikipedia.org/wiki/Comparability" - alias: - - incomparable - - - concept: incomplete-beta-function - arity: 1 - en: incomplete beta function of $1 - property: function - area: "special functions" - mathml: - - "B(x)" - urls: - - "https://mathworld.wolfram.com/IncompleteBetaFunction.html" - - "https://dlmf.nist.gov/8.17" - - "https://dlmf.nist.gov/8.17#E1" - - "https://dlmf.nist.gov/8.17#E2" - - - concept: incomplete-elliptic-integral-of-the-first-kind - arity: 1 - en: incomplete elliptic integral of the first kind of $1 - property: function - area: "elliptic functions" - mathml: - - "F(x)" - urls: - - "https://mathworld.wolfram.com/EllipticIntegral.html" - - "https://en.wikipedia.org/wiki/Elliptic_integral" - - "https://www.encyclopediaofmath.org/index.php/Elliptic_integral" - - - concept: incomplete-elliptic-integral-of-the-second-kind - arity: 1 - en: incomplete elliptic integral of the second kind of $1 - property: function - area: "elliptic functions" - mathml: - - "E(x)" - urls: - - "https://mathworld.wolfram.com/EllipticIntegral.html" - - "https://en.wikipedia.org/wiki/Elliptic_integral" - - "https://www.encyclopediaofmath.org/index.php/Elliptic_integral" - - - concept: incomplete-gamma-function - arity: 1 - en: incomplete gamma function of $1 - property: function - area: "special functions" - mathml: - - "Γ(x)" - urls: - - "https://mathworld.wolfram.com/IncompleteGammaFunction.html" - - "https://en.wikipedia.org/wiki/Incomplete_gamma_function" - - "https://en.wikipedia.org/wiki/Regularized_Gamma_function" - - "https://dlmf.nist.gov/8#PT2" - - "https://dlmf.nist.gov/8.2#E2" - - "https://dlmf.nist.gov/8.2#E1" - - "https://dlmf.nist.gov/8.2#E6" - - - concept: increase - arity: 1 - en: increase of $1 - property: postfix - area: "physics" - mathml: - - "x↑" - urls: - - "https://youtu.be/HZ7a9YkF204?t=4606" - - - concept: increase-tends-to - arity: 2 - en: $1 increase tends to $2 - property: infix - area: "calculus" - mathml: - - "X↗Y" - urls: - - "https://math.stackexchange.com/questions/1886232/what-does-this-notation-mean-limes-from-left-right" - - "http://pi.math.cornell.edu/~web6720/MATH%206710%20notes.pdf" - - - concept: independent - arity: 2 - en: $1 independent $2 - property: infix - area: "probability theory" - mathml: - - "X⟂Y" - - "X⫫Y" - urls: - - "https://en.wikipedia.org/wiki/Independence_(probability_theory)" - - "https://en.wikipedia.org/wiki/Independence_(mathematical_logic)" - - "https://www.encyclopediaofmath.org/index.php/Independence" - - - concept: index-of-subgroup - arity: 2 + property: symbol + subject-area: "geometry" + mathml: + - "I" + urls: + - "https://mathworld.wolfram.com/Incenter.html" + - "https://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle" + - "https://en.wikipedia.org/wiki/Gergonne_point" + - "https://en.wikipedia.org/wiki/Incentre" + + - concept: incidence-relation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 incidence relation a2 + property: infix + subject-area: "projective geometry" + mathml: + - "XIY" + urls: + - "https://en.wikipedia.org/wiki/Incidence_(geometry)" + - "https://en.wikipedia.org/wiki/Incidence_(epidemiology)" + - "https://www.encyclopediaofmath.org/index.php/Incidence" + + - concept: incidence-structure + arity: 3 + arguments: [a1, a2, a3] + speech: + en: incidence structure of a1, a2 and a3 + property: fenced + subject-area: "incidence geometry" + mathml: + - "(P,L,I)" + urls: + - "https://en.wikipedia.org/wiki/Incidence_structure" + + - concept: inclusion-map + arity: 1 + arguments: [a1] + speech: + en: inclusion map of a1 + property: function + subject-area: "set theory" + mathml: + - "ι(x)" + urls: + - "https://en.wikipedia.org/wiki/Inclusion_map" + alias: + - inclusion-function + - insertion + - canonical-injection + + - concept: incomparability + arity: 2 + arguments: [a1, a2] + speech: + en: a1 incomparable to a2 + property: infix + subject-area: "order theory" + mathml: + - "X⪋̸Y" + urls: + - "https://en.wikipedia.org/wiki/Comparability" + alias: + - incomparable + + - concept: incomplete-beta-function + arity: 1 + arguments: [a1] + speech: + en: incomplete beta function of a1 + property: function + subject-area: "special functions" + mathml: + - "B(x)" + urls: + - "https://mathworld.wolfram.com/IncompleteBetaFunction.html" + - "https://dlmf.nist.gov/8.17" + - "https://dlmf.nist.gov/8.17#E1" + - "https://dlmf.nist.gov/8.17#E2" + + - concept: incomplete-elliptic-integral-of-the-first-kind + arity: 1 + arguments: [a1] + speech: + en: incomplete elliptic integral of the first kind of a1 + property: function + subject-area: "elliptic functions" + mathml: + - "F(x)" + urls: + - "https://mathworld.wolfram.com/EllipticIntegral.html" + - "https://en.wikipedia.org/wiki/Elliptic_integral" + - "https://www.encyclopediaofmath.org/index.php/Elliptic_integral" + + - concept: incomplete-elliptic-integral-of-the-second-kind + arity: 1 + arguments: [a1] + speech: + en: incomplete elliptic integral of the second kind of a1 + property: function + subject-area: "elliptic functions" + mathml: + - "E(x)" + urls: + - "https://mathworld.wolfram.com/EllipticIntegral.html" + - "https://en.wikipedia.org/wiki/Elliptic_integral" + - "https://www.encyclopediaofmath.org/index.php/Elliptic_integral" + + - concept: incomplete-gamma-function + arity: 1 + arguments: [a1] + speech: + en: incomplete gamma function of a1 + property: function + subject-area: "special functions" + mathml: + - "Γ(x)" + urls: + - "https://mathworld.wolfram.com/IncompleteGammaFunction.html" + - "https://en.wikipedia.org/wiki/Incomplete_gamma_function" + - "https://en.wikipedia.org/wiki/Regularized_Gamma_function" + - "https://dlmf.nist.gov/8#PT2" + - "https://dlmf.nist.gov/8.2#E2" + - "https://dlmf.nist.gov/8.2#E1" + - "https://dlmf.nist.gov/8.2#E6" + + - concept: increase + arity: 1 + arguments: [a1] + speech: + en: increase of a1 + property: postfix + subject-area: "physics" + mathml: + - "x↑" + urls: + - "https://youtu.be/HZ7a9YkF204?t=4606" + + - concept: increase-tends-to + arity: 2 + arguments: [a1, a2] + speech: + en: a1 increase tends to a2 + property: infix + subject-area: "calculus" + mathml: + - "X↗Y" + urls: + - "https://math.stackexchange.com/questions/1886232/what-does-this-notation-mean-limes-from-left-right" + - "http://pi.math.cornell.edu/~web6720/MATH%206710%20notes.pdf" + + - concept: independent + arity: 2 + arguments: [a1, a2] + speech: + en: a1 independent a2 + property: infix + subject-area: "probability theory" + mathml: + - "X⟂Y" + - "X⫫Y" + urls: + - "https://en.wikipedia.org/wiki/Independence_(probability_theory)" + - "https://en.wikipedia.org/wiki/Independence_(mathematical_logic)" + - "https://www.encyclopediaofmath.org/index.php/Independence" + + - concept: index-of-subgroup + arity: 2 + arguments: [a1, a2] + speech: en: index of subgroup - property: fenced - area: "group theory" - mathml: - - "[x:y]" - - "(x:y)" - - "|x:y|" - urls: - - "https://en.wikipedia.org/wiki/Index_of_a_subgroup" - - - concept: index-of-lie-algebra - arity: 1 - en: index of lie algebra of $1 - property: function - area: "lie algebra" - mathml: - - "ind(x)" - urls: - - "https://en.wikipedia.org/wiki/Index_of_a_Lie_algebra" - - - concept: infimum - arity: 1 - en: infimum of $1 - property: "function, largeop" - area: "order theory" - mathml: - - "infX" - - "⋀X" - urls: - - "https://mathworld.wolfram.com/Infimum.html" - - "https://en.wikipedia.org/wiki/Infimum_and_supremum" - alias: - - meet - - greatest-lower-bound - - - concept: infimum-limit - arity: 1 - en: infimum limit of $1 - property: indexed - area: "limits" - mathml: - - "lim inf(X)" - - "lim_(X)" - urls: - - "https://mathworld.wolfram.com/InfimumLimit.html" - - "https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior" - alias: - - limit-inferior - - limit-infimum - - liminf - - inferior-limit - - lower-limit - - inner-limit - - - concept: infinite-product - arity: 1 - en: infinite product of $1 - property: indexed - area: "mathematical analysis" - mathml: - - "Π1∞an" - urls: - - "https://mathworld.wolfram.com/InfiniteProduct.html" - - "https://en.wikipedia.org/wiki/Infinite_product" - - "https://www.encyclopediaofmath.org/index.php/Infinite_product" - - - concept: infinitely-many-concurrently-active-copies - arity: 1 - en: infinitely many concurrently active copies of $1 - property: prefix - area: "formal languages" - mathml: - - "!x" - urls: - - "https://arxiv.org/pdf/0903.3513.pdf" - - - concept: injection - arity: 3 - en: injection $1, from $2 to $3 - property: mixfix, - area: "set theory" - mathml: - - "f:X↣Y" - urls: - - "https://en.wikipedia.org/wiki/Bijection#Definition" - - - concept: inner-automorphism-group - arity: 1 - en: inner automorphism group of $1 - property: function - area: "abstract algebra" - mathml: - - "Inn(x)" - urls: - - "https://mathworld.wolfram.com/InnerAutomorphism.html" - - "https://en.wikipedia.org/wiki/Inner_automorphism" - - "https://ncatlab.org/nlab/show/inner+automorphism" - - "https://www.encyclopediaofmath.org/index.php/Inner_automorphism" - alias: - - inner-automorphism - - - concept: inner-jordan-measure - arity: 1 - en: inner jordan measure of $1 - property: function - area: "measure theory" - mathml: - - "m*(N)" - urls: - - "https://mathworld.wolfram.com/JordanMeasure.html" - - "https://en.wikipedia.org/wiki/Jordan_measure" - - "https://www.encyclopediaofmath.org/index.php/Jordan_measure" - - - concept: inner-product - arity: 2 - en: $1 inner product $2 - property: infix, fenced - area: "linear algebra" - mathml: - - "(x⋅y)" - - "[x,y]" - urls: - - "https://mathworld.wolfram.com/InnerProduct.html" - - "https://en.wikipedia.org/wiki/Dot_product" - - "https://en.wikipedia.org/wiki/Inner_product_space" - - "https://www.encyclopediaofmath.org/index.php/Inner_product" - - "https://mathoverflow.net/a/366118" - - - concept: instantaneous-activity - arity: 2 - en: instantaneous activity of $1 at $2 - property: mixfix - area: "chemistry" - mathml: - - "{X}t" - urls: - - "https://en.wikipedia.org/wiki/Reaction_quotient" - - - concept: integer-part - arity: 1 - en: integer part of $1 - property: "function, fenced" - area: "number theory" - mathml: - - "intX" - notationa: "[ $1 ]" - urls: - - "https://mathworld.wolfram.com/IntegerPart.html" - - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions" - - - concept: interior - arity: 1 - en: interior of $1 - property: msup - area: "topology" - mathml: - - "Xo" - - "X∘" - urls: - - "https://mathworld.wolfram.com/Interior.html" - - "https://en.wikipedia.org/wiki/Interior_(topology)" - - "https://ncatlab.org/nlab/show/interior" - - "https://www.encyclopediaofmath.org/index.php/Interior" - - - concept: interior-product - arity: 2 - en: interior product of $1 $2 - property: "infix, indexed function" - area: "differential forms" - mathml: - - "X⨼ω" - - "ιXω" - urls: - - "https://mathworld.wolfram.com/InteriorProduct.html" - - "https://en.wikipedia.org/wiki/Interior_product" - - - concept: intersection-number - arity: 2 - en: $1 intersection number $2 - property: infix - area: "algebraic geometry" - mathml: - - "X⋅Y" - urls: - - "https://en.wikipedia.org/wiki/Intersection_number" - - - concept: inverse-image - arity: 2 - en: inverse image $1 $2 - property: mixfix - area: "set theory" - mathml: - - "f−1[X)" - urls: - - "https://en.wikipedia.org/wiki/Image_(mathematics)" - - "https://ncatlab.org/nlab/show/inverse+image" - alias: - - preimage - - - concept: inverse-limit - arity: 1 - en: inverse limit of $1 - property: prefix - area: "category theory" - mathml: - - "lim←(Ai)" - urls: - - "https://mathworld.wolfram.com/InverseLimit.html" - - "https://en.wikipedia.org/wiki/Inverse_limit" - - "https://ncatlab.org/nlab/show/inverse+limit" - alias: - - projective limit - - - concept: inverse-moment-of-function - arity: 2 - en: $2th inverse moment of function $1 - property: "msub, mixfix" - area: "mathematics" - mathml: - - "E[X−n]" - urls: - - "https://en.wikipedia.org/wiki/Moment_(mathematics)" - alias: - - inverse-moment - - - concept: inverse-tangent-integral - arity: 1 - en: inverse tangent integral of $1 - property: "indexed function" - area: "special functions" - mathml: - - "Tix" - urls: - - "https://en.wikipedia.org/wiki/Polylogarithm" - - - concept: inverse-wishart-distribution - arity: 0 + property: fenced + subject-area: "group theory" + mathml: + - "[x:y]" + - "(x:y)" + - "|x:y|" + urls: + - "https://en.wikipedia.org/wiki/Index_of_a_subgroup" + + - concept: index-of-lie-algebra + arity: 1 + arguments: [a1] + speech: + en: index of lie algebra of a1 + property: function + subject-area: "lie algebra" + mathml: + - "ind(x)" + urls: + - "https://en.wikipedia.org/wiki/Index_of_a_Lie_algebra" + + - concept: infimum + arity: 1 + arguments: [a1] + speech: + en: infimum of a1 + property: "function, largeop" + subject-area: "order theory" + mathml: + - "infX" + - "⋀X" + urls: + - "https://mathworld.wolfram.com/Infimum.html" + - "https://en.wikipedia.org/wiki/Infimum_and_supremum" + alias: + - meet + - greatest-lower-bound + + - concept: infimum-limit + arity: 1 + arguments: [a1] + speech: + en: infimum limit of a1 + property: indexed + subject-area: "limits" + mathml: + - "lim inf(X)" + - "lim_(X)" + urls: + - "https://mathworld.wolfram.com/InfimumLimit.html" + - "https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior" + alias: + - limit-inferior + - limit-infimum + - liminf + - inferior-limit + - lower-limit + - inner-limit + + - concept: infinite-product + arity: 1 + arguments: [a1] + speech: + en: infinite product of a1 + property: indexed + subject-area: "mathematical analysis" + mathml: + - "Π1∞an" + urls: + - "https://mathworld.wolfram.com/InfiniteProduct.html" + - "https://en.wikipedia.org/wiki/Infinite_product" + - "https://www.encyclopediaofmath.org/index.php/Infinite_product" + + - concept: infinitely-many-concurrently-active-copies + arity: 1 + arguments: [a1] + speech: + en: infinitely many concurrently active copies of a1 + property: prefix + subject-area: "formal languages" + mathml: + - "!x" + urls: + - "https://arxiv.org/pdf/0903.3513.pdf" + + - concept: injection + arity: 3 + arguments: [a1, a2, a3] + speech: + en: injection a1, from a2 to a3 + property: mixfix, + subject-area: "set theory" + mathml: + - "f:X↣Y" + urls: + - "https://en.wikipedia.org/wiki/Bijection#Definition" + + - concept: inner-automorphism-group + arity: 1 + arguments: [a1] + speech: + en: inner automorphism group of a1 + property: function + subject-area: "abstract algebra" + mathml: + - "Inn(x)" + urls: + - "https://mathworld.wolfram.com/InnerAutomorphism.html" + - "https://en.wikipedia.org/wiki/Inner_automorphism" + - "https://ncatlab.org/nlab/show/inner+automorphism" + - "https://www.encyclopediaofmath.org/index.php/Inner_automorphism" + alias: + - inner-automorphism + + - concept: inner-jordan-measure + arity: 1 + arguments: [a1] + speech: + en: inner jordan measure of a1 + property: function + subject-area: "measure theory" + mathml: + - "m*(N)" + urls: + - "https://mathworld.wolfram.com/JordanMeasure.html" + - "https://en.wikipedia.org/wiki/Jordan_measure" + - "https://www.encyclopediaofmath.org/index.php/Jordan_measure" + + - concept: inner-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 inner product a2 + property: infix, fenced + subject-area: "linear algebra" + mathml: + - "(x⋅y)" + - "[x,y]" + urls: + - "https://mathworld.wolfram.com/InnerProduct.html" + - "https://en.wikipedia.org/wiki/Dot_product" + - "https://en.wikipedia.org/wiki/Inner_product_space" + - "https://www.encyclopediaofmath.org/index.php/Inner_product" + - "https://mathoverflow.net/a/366118" + + - concept: instantaneous-activity + arity: 2 + arguments: [a1, a2] + speech: + en: instantaneous activity of a1 at a2 + property: mixfix + subject-area: "chemistry" + mathml: + - "{X}t" + urls: + - "https://en.wikipedia.org/wiki/Reaction_quotient" + + - concept: integer-part + arity: 1 + arguments: [a1] + speech: + en: integer part of a1 + property: "function, fenced" + subject-area: "number theory" + mathml: + - "intX" + notationa: "[ a1 ]" + urls: + - "https://mathworld.wolfram.com/IntegerPart.html" + - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions" + + - concept: interior + arity: 1 + arguments: [a1] + speech: + en: interior of a1 + property: msup + subject-area: "topology" + mathml: + - "Xo" + - "X∘" + urls: + - "https://mathworld.wolfram.com/Interior.html" + - "https://en.wikipedia.org/wiki/Interior_(topology)" + - "https://ncatlab.org/nlab/show/interior" + - "https://www.encyclopediaofmath.org/index.php/Interior" + + - concept: interior-product + arity: 2 + arguments: [a1, a2] + speech: + en: interior product of a1 a2 + property: "infix, indexed function" + subject-area: "differential forms" + mathml: + - "X⨼ω" + - "ιXω" + urls: + - "https://mathworld.wolfram.com/InteriorProduct.html" + - "https://en.wikipedia.org/wiki/Interior_product" + + - concept: intersection-number + arity: 2 + arguments: [a1, a2] + speech: + en: a1 intersection number a2 + property: infix + subject-area: "algebraic geometry" + mathml: + - "X⋅Y" + urls: + - "https://en.wikipedia.org/wiki/Intersection_number" + + - concept: inverse-image + arity: 2 + arguments: [a1, a2] + speech: + en: inverse image a1 a2 + property: mixfix + subject-area: "set theory" + mathml: + - "f−1[X)" + urls: + - "https://en.wikipedia.org/wiki/Image_(mathematics)" + - "https://ncatlab.org/nlab/show/inverse+image" + alias: + - preimage + + - concept: inverse-limit + arity: 1 + arguments: [a1] + speech: + en: inverse limit of a1 + property: prefix + subject-area: "category theory" + mathml: + - "lim←(Ai)" + urls: + - "https://mathworld.wolfram.com/InverseLimit.html" + - "https://en.wikipedia.org/wiki/Inverse_limit" + - "https://ncatlab.org/nlab/show/inverse+limit" + alias: + - projective limit + + - concept: inverse-moment-of-function + arity: 2 + arguments: [a1, a2] + speech: + en: a2th inverse moment of function a1 + property: "msub, mixfix" + subject-area: "mathematics" + mathml: + - "E[X−n]" + urls: + - "https://en.wikipedia.org/wiki/Moment_(mathematics)" + alias: + - inverse-moment + + - concept: inverse-tangent-integral + arity: 1 + arguments: [a1] + speech: + en: inverse tangent integral of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Tix" + urls: + - "https://en.wikipedia.org/wiki/Polylogarithm" + + - concept: inverse-wishart-distribution + arity: 0 + arguments: [] + speech: en: inverse wishart distribution - property: symbol - area: "probability theory" - mathml: - - "Wp−1" - urls: - - "https://mathworld.wolfram.com/WishartDistribution.html" - - "https://en.wikipedia.org/wiki/Wishart_distribution" - - "https://www.encyclopediaofmath.org/index.php/Wishart_distribution" - - - concept: ionic-charge - arity: 2 + property: symbol + subject-area: "probability theory" + mathml: + - "Wp−1" + urls: + - "https://mathworld.wolfram.com/WishartDistribution.html" + - "https://en.wikipedia.org/wiki/Wishart_distribution" + - "https://www.encyclopediaofmath.org/index.php/Wishart_distribution" + + - concept: ionic-charge + arity: 2 + arguments: [a1, a2] + speech: en: ionic charge - property: msup - area: "chemistry" - mathml: - - "Fe2" - urls: - - "https://en.wikipedia.org/wiki/Ion#Chemistry" - - - concept: isogonal-conjugate - arity: 1 - en: isogonal conjugate of $1 - property: msup - area: "geometry" - mathml: - - "X-1" - urls: - - "https://mathworld.wolfram.com/IsogonalConjugate.html" - - "https://en.wikipedia.org/wiki/Isogonal_conjugate" - - - concept: isomorphism - arity: 2 - en: $1 isomorphism $2 - property: infix - area: "set theory" - mathml: - - "X↦∼Y" - - "X≅Y" - urls: - - "https://mathworld.wolfram.com/Isomorphism.html" - - "https://en.wikipedia.org/wiki/Isomorphism" - - "https://ncatlab.org/nlab/show/isomorphism" - - "https://www.encyclopediaofmath.org/index.php/Isomorphism" - alias: - - natural-isomorphism - - - concept: isotropy-group - arity: 2 + property: msup + subject-area: "chemistry" + mathml: + - "Fe2" + urls: + - "https://en.wikipedia.org/wiki/Ion#Chemistry" + + - concept: isogonal-conjugate + arity: 1 + arguments: [a1] + speech: + en: isogonal conjugate of a1 + property: msup + subject-area: "geometry" + mathml: + - "X-1" + urls: + - "https://mathworld.wolfram.com/IsogonalConjugate.html" + - "https://en.wikipedia.org/wiki/Isogonal_conjugate" + + - concept: isomorphism + arity: 2 + arguments: [a1, a2] + speech: + en: a1 isomorphism a2 + property: infix + subject-area: "set theory" + mathml: + - "X↦∼Y" + - "X≅Y" + urls: + - "https://mathworld.wolfram.com/Isomorphism.html" + - "https://en.wikipedia.org/wiki/Isomorphism" + - "https://ncatlab.org/nlab/show/isomorphism" + - "https://www.encyclopediaofmath.org/index.php/Isomorphism" + alias: + - natural-isomorphism + + - concept: isotropy-group + arity: 2 + arguments: [a1, a2] + speech: en: isotropy group - property: msub - area: "group theory" - mathml: - - "Gx" - urls: - - "https://mathworld.wolfram.com/IsotropyGroup.html" - - "https://www.encyclopediaofmath.org/index.php/Isotropy_group" - alias: - - little-group - - stabilizer-subgroup - - - concept: iverson-bracket - arity: 1 - en: iverson bracket of $1 - property: fenced - area: "set theory" - mathml: - - "[P]" - urls: - - "https://en.wikipedia.org/wiki/Iverson_bracket" - - - concept: j-invariant - arity: 1 - en: j invariant of $1 - property: function - area: "number theory" - mathml: - - "j(x)" - urls: - - "https://mathworld.wolfram.com/j-Invariant.html" - - "https://ncatlab.org/nlab/show/j-invariant" - - - concept: jacobi-matrix - arity: 1 - en: jacobi matrix of $1 - property: function - area: "operator theory" - mathml: - - "J(x)" - urls: - - "https://mathworld.wolfram.com/JacobiMatrix.html" - - "https://en.wikipedia.org/wiki/Jacobi_operator" - - "https://www.encyclopediaofmath.org/index.php/Jacobi_matrix" - alias: - - jacobi-operator - - - concept: jacobi-polynomial - arity: 2 - en: $1thjacobi polynomial of $2 - property: function - area: "orthogonal polynomials" - mathml: - - "Pnα,β(x)" - notation: "msubsup P" - urls: - - "https://mathworld.wolfram.com/JacobiPolynomial.html" - - "https://en.wikipedia.org/wiki/Heckman%E2%80%93Opdam_polynomials" - - "https://en.wikipedia.org/wiki/Jacobi_polynomials" - - "https://dlmf.nist.gov/18.3" - - "https://dlmf.nist.gov/18.3#T1.t1.r3" - - "https://www.encyclopediaofmath.org/index.php/Jacobi_polynomials" - - - concept: jacobi-symbol - arity: 2 + property: msub + subject-area: "group theory" + mathml: + - "Gx" + urls: + - "https://mathworld.wolfram.com/IsotropyGroup.html" + - "https://www.encyclopediaofmath.org/index.php/Isotropy_group" + alias: + - little-group + - stabilizer-subgroup + + - concept: iverson-bracket + arity: 1 + arguments: [a1] + speech: + en: iverson bracket of a1 + property: fenced + subject-area: "set theory" + mathml: + - "[P]" + urls: + - "https://en.wikipedia.org/wiki/Iverson_bracket" + + - concept: j-invariant + arity: 1 + arguments: [a1] + speech: + en: j invariant of a1 + property: function + subject-area: "number theory" + mathml: + - "j(x)" + urls: + - "https://mathworld.wolfram.com/j-Invariant.html" + - "https://ncatlab.org/nlab/show/j-invariant" + + - concept: jacobi-matrix + arity: 1 + arguments: [a1] + speech: + en: jacobi matrix of a1 + property: function + subject-area: "operator theory" + mathml: + - "J(x)" + urls: + - "https://mathworld.wolfram.com/JacobiMatrix.html" + - "https://en.wikipedia.org/wiki/Jacobi_operator" + - "https://www.encyclopediaofmath.org/index.php/Jacobi_matrix" + alias: + - jacobi-operator + + - concept: jacobi-polynomial + arity: 2 + arguments: [a1, a2] + speech: + en: a1thjacobi polynomial of a2 + property: function + subject-area: "orthogonal polynomials" + mathml: + - "Pnα,β(x)" + notation: "msubsup P" + urls: + - "https://mathworld.wolfram.com/JacobiPolynomial.html" + - "https://en.wikipedia.org/wiki/Heckman%E2%80%93Opdam_polynomials" + - "https://en.wikipedia.org/wiki/Jacobi_polynomials" + - "https://dlmf.nist.gov/18.3" + - "https://dlmf.nist.gov/18.3#T1.t1.r3" + - "https://www.encyclopediaofmath.org/index.php/Jacobi_polynomials" + + - concept: jacobi-symbol + arity: 2 + arguments: [a1, a2] + speech: en: jacobi symbol - property: mixfix - area: "number theory" - mathml: - - "(x|y)" - urls: - - "https://mathworld.wolfram.com/JacobiSymbol.html" - - "https://en.wikipedia.org/wiki/Jacobi_symbol" - - "https://dlmf.nist.gov/27.9#p3" - - "https://www.encyclopediaofmath.org/index.php/Jacobi_symbol" - - - concept: jacobi-theta-function - arity: 1 - en: jacobi theta function of $1 - property: function - area: "special-functions" - mathml: - - "ϑ(x)" - urls: - - "https://mathworld.wolfram.com/JacobiThetaFunctions.html" - - "https://en.wikipedia.org/wiki/Jacobi_theta_functions_(notational_variations)" - - - concept: jacobi-zeta-function - arity: 2 + property: mixfix + subject-area: "number theory" + mathml: + - "(x|y)" + urls: + - "https://mathworld.wolfram.com/JacobiSymbol.html" + - "https://en.wikipedia.org/wiki/Jacobi_symbol" + - "https://dlmf.nist.gov/27.9#p3" + - "https://www.encyclopediaofmath.org/index.php/Jacobi_symbol" + + - concept: jacobi-theta-function + arity: 1 + arguments: [a1] + speech: + en: jacobi theta function of a1 + property: function + subject-area: "special-functions" + mathml: + - "ϑ(x)" + urls: + - "https://mathworld.wolfram.com/JacobiThetaFunctions.html" + - "https://en.wikipedia.org/wiki/Jacobi_theta_functions_(notational_variations)" + + - concept: jacobi-zeta-function + arity: 2 + arguments: [a1, a2] + speech: en: jacobi zeta function - property: function - area: "special-functions" - mathml: - - "Z(x|k)" - urls: - - "https://mathworld.wolfram.com/JacobiZetaFunction.html" - - "https://en.wikipedia.org/wiki/Jacobi_zeta_function" - - "https://dlmf.nist.gov/22.16#iii" - - "https://dlmf.nist.gov/22.16#E32" - - - concept: jacobian-elliptic-function - arity: 1 - en: jacobian elliptic function of $1 - property: function - area: "special-functions" - mathml: - - "snX" - - "cnX" - - "dnX" - - "sdX" - - "cdX" - - "scX" - urls: - - "https://dlmf.nist.gov/22.2" - - "https://dlmf.nist.gov/22.2#E5" - - "https://dlmf.nist.gov/22.2#E6" - - "https://dlmf.nist.gov/22.2#E7" - - "https://dlmf.nist.gov/22.2#E8" - - "https://dlmf.nist.gov/22.2#E4" - - "https://dlmf.nist.gov/22.2#E9" - - - concept: jacobson-radical - arity: 1 - en: jacobson radical of $1 - property: function - area: "ring theory" - mathml: - - "JX" - - "radX" - urls: - - "https://mathworld.wolfram.com/JacobsonRadical.html" - - "https://en.wikipedia.org/wiki/Jacobson_radical" - - "https://ncatlab.org/nlab/show/Jacobson+radical" - - "https://www.encyclopediaofmath.org/index.php/Jacobson_radical" - - - concept: jacobsthal-number - arity: 0 + property: function + subject-area: "special-functions" + mathml: + - "Z(x|k)" + urls: + - "https://mathworld.wolfram.com/JacobiZetaFunction.html" + - "https://en.wikipedia.org/wiki/Jacobi_zeta_function" + - "https://dlmf.nist.gov/22.16#iii" + - "https://dlmf.nist.gov/22.16#E32" + + - concept: jacobian-elliptic-function + arity: 1 + arguments: [a1] + speech: + en: jacobian elliptic function of a1 + property: function + subject-area: "special-functions" + mathml: + - "snX" + - "cnX" + - "dnX" + - "sdX" + - "cdX" + - "scX" + urls: + - "https://dlmf.nist.gov/22.2" + - "https://dlmf.nist.gov/22.2#E5" + - "https://dlmf.nist.gov/22.2#E6" + - "https://dlmf.nist.gov/22.2#E7" + - "https://dlmf.nist.gov/22.2#E8" + - "https://dlmf.nist.gov/22.2#E4" + - "https://dlmf.nist.gov/22.2#E9" + + - concept: jacobson-radical + arity: 1 + arguments: [a1] + speech: + en: jacobson radical of a1 + property: function + subject-area: "ring theory" + mathml: + - "JX" + - "radX" + urls: + - "https://mathworld.wolfram.com/JacobsonRadical.html" + - "https://en.wikipedia.org/wiki/Jacobson_radical" + - "https://ncatlab.org/nlab/show/Jacobson+radical" + - "https://www.encyclopediaofmath.org/index.php/Jacobson_radical" + + - concept: jacobsthal-number + arity: 0 + arguments: [] + speech: en: jacobsthal number - property: symbol - area: "number theory" - mathml: - - "J" - urls: - - "https://mathworld.wolfram.com/JacobsthalNumber.html" - - "https://en.wikipedia.org/wiki/Jacobsthal_number" - - - concept: janko-group - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "J" + urls: + - "https://mathworld.wolfram.com/JacobsthalNumber.html" + - "https://en.wikipedia.org/wiki/Jacobsthal_number" + + - concept: janko-group + arity: 0 + arguments: [] + speech: en: janko group - property: symbol - area: "group theory" - mathml: - - "J1" - - "J2" - - "J3" - - "J4" - urls: - - "https://mathworld.wolfram.com/JankoGroups.html" - - "https://en.wikipedia.org/wiki/Janko_group" - - - concept: jet - arity: 3 - en: $1 jet of $3 at $2 - property: function - area: "differential geometry" - mathml: - - "Jxkf" - urls: - - "https://en.wikipedia.org/wiki/Jet_(mathematics)" - - "https://www.encyclopediaofmath.org/index.php/Jet" - - - concept: join - arity: 1 - en: join of $1 - property: indexed - area: "measure theory" - mathml: - - "⋁α∈𝒜Σα" - urls: - - "https://mathworld.wolfram.com/Join.html" - - "https://en.wikipedia.org/wiki/Join_(sigma_algebra)" - - "https://en.wikipedia.org/wiki/Join_(topology)" - - "https://ncatlab.org/nlab/show/join" - - "https://www.encyclopediaofmath.org/index.php/Join" - - - concept: jone-polynomial - arity: 1 - en: jone polynomial of $1 - property: function - area: "knot theory" - mathml: - - "V(x)" - urls: - - "https://mathworld.wolfram.com/JonesPolynomial.html" - - "https://en.wikipedia.org/wiki/Jones_polynomial" - - "https://ncatlab.org/nlab/show/Jones+polynomial" - - - concept: jordan-block - arity: 2 + property: symbol + subject-area: "group theory" + mathml: + - "J1" + - "J2" + - "J3" + - "J4" + urls: + - "https://mathworld.wolfram.com/JankoGroups.html" + - "https://en.wikipedia.org/wiki/Janko_group" + + - concept: jet + arity: 3 + arguments: [a1, a2, a3] + speech: + en: a1 jet of a3 at a2 + property: function + subject-area: "differential geometry" + mathml: + - "Jxkf" + urls: + - "https://en.wikipedia.org/wiki/Jet_(mathematics)" + - "https://www.encyclopediaofmath.org/index.php/Jet" + + - concept: join + arity: 1 + arguments: [a1] + speech: + en: join of a1 + property: indexed + subject-area: "measure theory" + mathml: + - "⋁α∈𝒜Σα" + urls: + - "https://mathworld.wolfram.com/Join.html" + - "https://en.wikipedia.org/wiki/Join_(sigma_algebra)" + - "https://en.wikipedia.org/wiki/Join_(topology)" + - "https://ncatlab.org/nlab/show/join" + - "https://www.encyclopediaofmath.org/index.php/Join" + + - concept: jone-polynomial + arity: 1 + arguments: [a1] + speech: + en: jone polynomial of a1 + property: function + subject-area: "knot theory" + mathml: + - "V(x)" + urls: + - "https://mathworld.wolfram.com/JonesPolynomial.html" + - "https://en.wikipedia.org/wiki/Jones_polynomial" + - "https://ncatlab.org/nlab/show/Jones+polynomial" + + - concept: jordan-block + arity: 2 + arguments: [a1, a2] + speech: en: jordan block - property: "indexed symbol" - area: "linear algebra" - mathml: - - "Jab" - urls: - - "https://mathworld.wolfram.com/JordanBlock.html" - - "https://en.wikipedia.org/wiki/Jordan_matrix" - alias: - - jordan-matrix - - - concept: jordan-measure - arity: 1 - en: jordan measure of $1 - property: function - area: "measure theory" - mathml: - - "m(x)" - urls: - - "https://mathworld.wolfram.com/JordanMeasure.html" - - "https://en.wikipedia.org/wiki/Jordan_measure" - - "https://www.encyclopediaofmath.org/index.php/Jordan_measure" - - - concept: jordan-totient-function - arity: 1 - en: jordan totient function of $1 - property: function - area: "number theory" - mathml: - - "Jx" - urls: - - "https://en.wikipedia.org/wiki/Jordan%27s_totient_function" - - - concept: julia-set - arity: 1 - en: julia set of $1 - property: function - area: "complex dynamics" - mathml: - - "J(x)" - urls: - - "https://mathworld.wolfram.com/JuliaSet.html" - - "https://en.wikipedia.org/wiki/Julia_set" - - "https://www.encyclopediaofmath.org/index.php/Julia_set" - - - concept: kaprekar-constant - arity: 0 + property: "indexed symbol" + subject-area: "linear algebra" + mathml: + - "Jab" + urls: + - "https://mathworld.wolfram.com/JordanBlock.html" + - "https://en.wikipedia.org/wiki/Jordan_matrix" + alias: + - jordan-matrix + + - concept: jordan-measure + arity: 1 + arguments: [a1] + speech: + en: jordan measure of a1 + property: function + subject-area: "measure theory" + mathml: + - "m(x)" + urls: + - "https://mathworld.wolfram.com/JordanMeasure.html" + - "https://en.wikipedia.org/wiki/Jordan_measure" + - "https://www.encyclopediaofmath.org/index.php/Jordan_measure" + + - concept: jordan-totient-function + arity: 1 + arguments: [a1] + speech: + en: jordan totient function of a1 + property: function + subject-area: "number theory" + mathml: + - "Jx" + urls: + - "https://en.wikipedia.org/wiki/Jordan%27s_totient_function" + + - concept: julia-set + arity: 1 + arguments: [a1] + speech: + en: julia set of a1 + property: function + subject-area: "complex dynamics" + mathml: + - "J(x)" + urls: + - "https://mathworld.wolfram.com/JuliaSet.html" + - "https://en.wikipedia.org/wiki/Julia_set" + - "https://www.encyclopediaofmath.org/index.php/Julia_set" + + - concept: kaprekar-constant + arity: 0 + arguments: [] + speech: en: kaprekar constant - property: symbol - area: "number theory" - mathml: - - "6174" - urls: - - "https://mathworld.wolfram.com/KaprekarConstant.html" - - "https://en.wikipedia.org/wiki/6174_(number)" - alias: - - kaprekar-number - - - concept: kauffman-bracket - arity: 1 - en: kauffman bracket of $1 - property: fenced - area: "knot theory" - mathml: - - "⟨x⟩" - urls: - - "https://en.wikipedia.org/wiki/Bracket_polynomial" - alias: - - bracket-polynomial - - - concept: kelvin-function - arity: 1 - en: $1th order kelvin function - property: function - area: "special functions" - mathml: - - "berv(x)" - - "beiv(x)" - urls: - - "https://mathworld.wolfram.com/KelvinFunctions.html" - - "https://en.wikipedia.org/wiki/Kelvin_functions" - - "https://dlmf.nist.gov/10#PT5" - - "https://dlmf.nist.gov/10.61#E1" - - "https://dlmf.nist.gov/10.61#E1" - - "https://dlmf.nist.gov/10.61#E2" - - "https://dlmf.nist.gov/10.61#E2" - - "https://www.encyclopediaofmath.org/index.php/Kelvin_functions" - - - concept: kernel - arity: 1 - en: kernel of $1 - property: function - area: "linear algebra" - mathml: - - "ker(x)" - urls: - - "https://mathworld.wolfram.com/Kernel.html" - - "https://en.wikipedia.org/wiki/Kernel_(algebra)" - - "https://en.wikipedia.org/wiki/Kernel_(set_theory)" - - "https://en.wikipedia.org/wiki/Sunflower_(mathematics)" - - "https://en.wikipedia.org/wiki/Kernel_(linear_algebra)" - - "https://en.wikipedia.org/wiki/Kernel_(category_theory)" - - "https://en.wikipedia.org/wiki/Kernel_(statistics)" - - "https://en.wikipedia.org/wiki/Covariance_function" - - "https://ncatlab.org/nlab/show/kernel" - alias: - - nullspace - - null-space - - - concept: khinchin-constant - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "6174" + urls: + - "https://mathworld.wolfram.com/KaprekarConstant.html" + - "https://en.wikipedia.org/wiki/6174_(number)" + alias: + - kaprekar-number + + - concept: kauffman-bracket + arity: 1 + arguments: [a1] + speech: + en: kauffman bracket of a1 + property: fenced + subject-area: "knot theory" + mathml: + - "⟨x⟩" + urls: + - "https://en.wikipedia.org/wiki/Bracket_polynomial" + alias: + - bracket-polynomial + + - concept: kelvin-function + arity: 1 + arguments: [a1] + speech: + en: a1th order kelvin function + property: function + subject-area: "special functions" + mathml: + - "berv(x)" + - "beiv(x)" + urls: + - "https://mathworld.wolfram.com/KelvinFunctions.html" + - "https://en.wikipedia.org/wiki/Kelvin_functions" + - "https://dlmf.nist.gov/10#PT5" + - "https://dlmf.nist.gov/10.61#E1" + - "https://dlmf.nist.gov/10.61#E1" + - "https://dlmf.nist.gov/10.61#E2" + - "https://dlmf.nist.gov/10.61#E2" + - "https://www.encyclopediaofmath.org/index.php/Kelvin_functions" + + - concept: kernel + arity: 1 + arguments: [a1] + speech: + en: kernel of a1 + property: function + subject-area: "linear algebra" + mathml: + - "ker(x)" + urls: + - "https://mathworld.wolfram.com/Kernel.html" + - "https://en.wikipedia.org/wiki/Kernel_(algebra)" + - "https://en.wikipedia.org/wiki/Kernel_(set_theory)" + - "https://en.wikipedia.org/wiki/Sunflower_(mathematics)" + - "https://en.wikipedia.org/wiki/Kernel_(linear_algebra)" + - "https://en.wikipedia.org/wiki/Kernel_(category_theory)" + - "https://en.wikipedia.org/wiki/Kernel_(statistics)" + - "https://en.wikipedia.org/wiki/Covariance_function" + - "https://ncatlab.org/nlab/show/kernel" + alias: + - nullspace + - null-space + + - concept: khinchin-constant + arity: 0 + arguments: [] + speech: en: khinchin constant - property: constant - area: "continued fractions" - mathml: - - "K" - notationa: "msub K 0" - urls: - - "https://mathworld.wolfram.com/KhinchinsConstant.html" - - "https://en.wikipedia.org/wiki/Khinchin%27s_constant" - - - concept: killing-form - arity: 1 - en: killing form of $1 - property: function - area: "lie algebra" - mathml: - - "B(x)" - urls: - - "https://mathworld.wolfram.com/KillingForm.html" - - "https://en.wikipedia.org/wiki/Killing_form" - - "https://ncatlab.org/nlab/show/Killing+form" - - "https://www.encyclopediaofmath.org/index.php/Killing_form" - - - concept: kleene-star - arity: 1 - en: kleene star of $1 - property: msup - area: "formal languages" - mathml: - - "x*" - urls: - - "https://en.wikipedia.org/wiki/Kleene_star" - - - concept: kleene-plus - arity: 1 - en: kleene plus of $1 - property: msup - area: "formal languages" - mathml: - - "x+" - urls: - - "https://en.wikipedia.org/wiki/Kleene_star" - - - concept: klein-four-group - arity: 0 + property: constant + subject-area: "continued fractions" + mathml: + - "K" + notationa: "msub K 0" + urls: + - "https://mathworld.wolfram.com/KhinchinsConstant.html" + - "https://en.wikipedia.org/wiki/Khinchin%27s_constant" + + - concept: killing-form + arity: 1 + arguments: [a1] + speech: + en: killing form of a1 + property: function + subject-area: "lie algebra" + mathml: + - "B(x)" + urls: + - "https://mathworld.wolfram.com/KillingForm.html" + - "https://en.wikipedia.org/wiki/Killing_form" + - "https://ncatlab.org/nlab/show/Killing+form" + - "https://www.encyclopediaofmath.org/index.php/Killing_form" + + - concept: kleene-star + arity: 1 + arguments: [a1] + speech: + en: kleene star of a1 + property: msup + subject-area: "formal languages" + mathml: + - "x*" + urls: + - "https://en.wikipedia.org/wiki/Kleene_star" + + - concept: kleene-plus + arity: 1 + arguments: [a1] + speech: + en: kleene plus of a1 + property: msup + subject-area: "formal languages" + mathml: + - "x+" + urls: + - "https://en.wikipedia.org/wiki/Kleene_star" + + - concept: klein-four-group + arity: 0 + arguments: [] + speech: en: klein four group - property: symbol - area: "group theory" - mathml: - - "V" - notationa: "msub K 4" - urls: - - "https://mathworld.wolfram.com/KleinFour-Group.html" - - "https://en.wikipedia.org/wiki/Klein_four-group" - - - concept: kloosterman-sum - arity: 1 - en: kloosterman sum of $1 - property: function - area: "analytic number theory" - mathml: - - "SX" - - "KX" - urls: - - "https://mathworld.wolfram.com/KloostermansSum.html" - - "https://en.wikipedia.org/wiki/Kloosterman_sum" - - - concept: kneser-graph - arity: 2 - en: kneser graph $1 $2 - property: "indexed symbol" - area: "graph theory" - mathml: - - "K(n,k)" - - "KGn,k" - urls: - - "https://mathworld.wolfram.com/KneserGraph.html" - - "https://en.wikipedia.org/wiki/Kneser_graph" - - - concept: knodel-number - arity: 1 - en: knodel number of $1 - property: "indexed symbol" - area: "number theory" - mathml: - - "K(x)" - urls: - - "https://mathworld.wolfram.com/KnoedelNumbers.html" - - "https://en.wikipedia.org/wiki/Kn%C3%B6del_number" - - - concept: kodaira-dimension - arity: 1 - en: kodaira dimension of $1 - property: function - area: "algebraic geometry" - mathml: - - "κ(x)" - urls: - - "https://en.wikipedia.org/wiki/Kodaira_dimension" - - "https://www.encyclopediaofmath.org/index.php/Kodaira_dimension" - - - concept: kolmogorov-complexity - arity: 1 - en: kolmogorov complexity of $1 - property: function - area: "information theory" - mathml: - - "K(x)" - urls: - - "https://mathworld.wolfram.com/KolmogorovComplexity.html" - - "https://en.wikipedia.org/wiki/Kolmogorov_complexity" - - - concept: kolmogorov-space - arity: 0 + property: symbol + subject-area: "group theory" + mathml: + - "V" + notationa: "msub K 4" + urls: + - "https://mathworld.wolfram.com/KleinFour-Group.html" + - "https://en.wikipedia.org/wiki/Klein_four-group" + + - concept: kloosterman-sum + arity: 1 + arguments: [a1] + speech: + en: kloosterman sum of a1 + property: function + subject-area: "analytic number theory" + mathml: + - "SX" + - "KX" + urls: + - "https://mathworld.wolfram.com/KloostermansSum.html" + - "https://en.wikipedia.org/wiki/Kloosterman_sum" + + - concept: kneser-graph + arity: 2 + arguments: [a1, a2] + speech: + en: kneser graph a1 a2 + property: "indexed symbol" + subject-area: "graph theory" + mathml: + - "K(n,k)" + - "KGn,k" + urls: + - "https://mathworld.wolfram.com/KneserGraph.html" + - "https://en.wikipedia.org/wiki/Kneser_graph" + + - concept: knodel-number + arity: 1 + arguments: [a1] + speech: + en: knodel number of a1 + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "K(x)" + urls: + - "https://mathworld.wolfram.com/KnoedelNumbers.html" + - "https://en.wikipedia.org/wiki/Kn%C3%B6del_number" + + - concept: kodaira-dimension + arity: 1 + arguments: [a1] + speech: + en: kodaira dimension of a1 + property: function + subject-area: "algebraic geometry" + mathml: + - "κ(x)" + urls: + - "https://en.wikipedia.org/wiki/Kodaira_dimension" + - "https://www.encyclopediaofmath.org/index.php/Kodaira_dimension" + + - concept: kolmogorov-complexity + arity: 1 + arguments: [a1] + speech: + en: kolmogorov complexity of a1 + property: function + subject-area: "information theory" + mathml: + - "K(x)" + urls: + - "https://mathworld.wolfram.com/KolmogorovComplexity.html" + - "https://en.wikipedia.org/wiki/Kolmogorov_complexity" + + - concept: kolmogorov-space + arity: 0 + arguments: [] + speech: en: kolmogorov space - property: constant - area: "topology" - mathml: - - "T0" - urls: - - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions" - - - concept: kontsevich-integral - arity: 1 - en: kontsevich integral of $1 - property: function - area: "knot theory" - mathml: - - "Z(x)" - urls: - - "https://mathworld.wolfram.com/KontsevichIntegral.html" - - "https://en.wikipedia.org/wiki/Kontsevich_invariant" - - "https://ncatlab.org/nlab/show/Kontsevich+integral" - - "https://www.encyclopediaofmath.org/index.php/Kontsevich_integral" - - - concept: krawtchouk-polynomial - arity: 1 - en: krawtchouk polynomial of $1 - property: function - area: "orthogonal polynomials" - mathml: - - "Kx" - urls: - - "https://mathworld.wolfram.com/KrawtchoukPolynomial.html" - - "https://en.wikipedia.org/wiki/Kravchuk_polynomials" - - "https://dlmf.nist.gov/18.19#T1.t1.r6" - - "https://www.encyclopediaofmath.org/index.php/Krawtchouk_polynomials" - - - concept: kripke-frame - arity: 2 + property: constant + subject-area: "topology" + mathml: + - "T0" + urls: + - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions" + + - concept: kontsevich-integral + arity: 1 + arguments: [a1] + speech: + en: kontsevich integral of a1 + property: function + subject-area: "knot theory" + mathml: + - "Z(x)" + urls: + - "https://mathworld.wolfram.com/KontsevichIntegral.html" + - "https://en.wikipedia.org/wiki/Kontsevich_invariant" + - "https://ncatlab.org/nlab/show/Kontsevich+integral" + - "https://www.encyclopediaofmath.org/index.php/Kontsevich_integral" + + - concept: krawtchouk-polynomial + arity: 1 + arguments: [a1] + speech: + en: krawtchouk polynomial of a1 + property: function + subject-area: "orthogonal polynomials" + mathml: + - "Kx" + urls: + - "https://mathworld.wolfram.com/KrawtchoukPolynomial.html" + - "https://en.wikipedia.org/wiki/Kravchuk_polynomials" + - "https://dlmf.nist.gov/18.19#T1.t1.r6" + - "https://www.encyclopediaofmath.org/index.php/Krawtchouk_polynomials" + + - concept: kripke-frame + arity: 2 + arguments: [a1, a2] + speech: en: kripke frame - property: fenced - area: "modal logic" - mathml: - - "⟨x,y⟩" - urls: - - "https://ncatlab.org/nlab/show/Kripke+frame" - - - concept: kronecker-delta - arity: 2 + property: fenced + subject-area: "modal logic" + mathml: + - "⟨x,y⟩" + urls: + - "https://ncatlab.org/nlab/show/Kripke+frame" + + - concept: kronecker-delta + arity: 2 + arguments: [a1, a2] + speech: en: kronecker delta - property: "indexed function" - area: "special functions" - mathml: - - "δij" - urls: - - "https://mathworld.wolfram.com/KroneckerDelta.html" - - "https://en.wikipedia.org/wiki/Kronecker_delta" - - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4" - - "https://ncatlab.org/nlab/show/Kronecker+delta" - - - concept: kronecker-product - arity: 2 - en: $1 kronecker product $2 - property: infix - area: "matrix theory" - mathml: - - "X⊗Y" - urls: - - "https://mathworld.wolfram.com/KroneckerProduct.html" - - "https://en.wikipedia.org/wiki/Khatri-Rao_product" - - "https://en.wikipedia.org/wiki/Kronecker_product" - - "https://en.wikipedia.org/wiki/Tracy-Singh_product" - - "https://www.encyclopediaofmath.org/index.php/Kronecker_product" - - - concept: kronecker-symbol - arity: 2 + property: "indexed function" + subject-area: "special functions" + mathml: + - "δij" + urls: + - "https://mathworld.wolfram.com/KroneckerDelta.html" + - "https://en.wikipedia.org/wiki/Kronecker_delta" + - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r4" + - "https://ncatlab.org/nlab/show/Kronecker+delta" + + - concept: kronecker-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 kronecker product a2 + property: infix + subject-area: "matrix theory" + mathml: + - "X⊗Y" + urls: + - "https://mathworld.wolfram.com/KroneckerProduct.html" + - "https://en.wikipedia.org/wiki/Khatri-Rao_product" + - "https://en.wikipedia.org/wiki/Kronecker_product" + - "https://en.wikipedia.org/wiki/Tracy-Singh_product" + - "https://www.encyclopediaofmath.org/index.php/Kronecker_product" + + - concept: kronecker-symbol + arity: 2 + arguments: [a1, a2] + speech: en: kronecker symbol - property: fenced, fenced stacked - area: "number theory" - mathml: - - "(x|y)" - - "(xy)" - urls: - - "https://mathworld.wolfram.com/KroneckerSymbol.html" - - "https://en.wikipedia.org/wiki/Kronecker_symbol" - - "https://www.encyclopediaofmath.org/index.php/Kronecker_symbol" - - - concept: krull-dimension - arity: 1 - en: krull dimension of $1 - property: function - area: "commutative algebra" - mathml: - - "dim(x)" - urls: - - "https://mathworld.wolfram.com/KrullDimension.html" - - "https://en.wikipedia.org/wiki/Krull_dimension" - - "https://en.wikipedia.org/wiki/Height_(ring_theory)" - - - concept: kulkarni-nomizu-product - arity: 2 - en: kulkarni nomizu product of $1 and $2 - property: embellished infix - area: "differential geometry" - mathml: - - "h∧k" - urls: - - "https://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_product" - - - concept: kullback-leibler-distance - arity: 1 - en: kullback leibler distance of $1 - property: function - area: "mathematical statistics" - mathml: - - "KLX" - notationa: "msub D KL" - urls: - - "http://users.monash.edu/~lloyd/tildeMML/KL/" - - "https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence" - alias: - - kl-distance - - kl-divergence - - kullback-leibler-divergence - - relative-entropy - - - concept: lagrange-bracket - arity: 4 - en: "lagrange bracket of $1, $2, canonical coordinates $3, $4" - property: indexed fenced - area: "classical mechanics" - mathml: - - "[u,v]p,q" - urls: - - "https://mathworld.wolfram.com/LagrangeBracket.html" - - "https://en.wikipedia.org/wiki/Lagrange_bracket" - - "https://www.encyclopediaofmath.org/index.php/Lagrange_bracket" - - - concept: lagrange-multiplier - arity: 0 + property: fenced, fenced stacked + subject-area: "number theory" + mathml: + - "(x|y)" + - "(xy)" + urls: + - "https://mathworld.wolfram.com/KroneckerSymbol.html" + - "https://en.wikipedia.org/wiki/Kronecker_symbol" + - "https://www.encyclopediaofmath.org/index.php/Kronecker_symbol" + + - concept: krull-dimension + arity: 1 + arguments: [a1] + speech: + en: krull dimension of a1 + property: function + subject-area: "commutative algebra" + mathml: + - "dim(x)" + urls: + - "https://mathworld.wolfram.com/KrullDimension.html" + - "https://en.wikipedia.org/wiki/Krull_dimension" + - "https://en.wikipedia.org/wiki/Height_(ring_theory)" + + - concept: kulkarni-nomizu-product + arity: 2 + arguments: [a1, a2] + speech: + en: kulkarni nomizu product of a1 and a2 + property: embellished infix + subject-area: "differential geometry" + mathml: + - "h∧k" + urls: + - "https://en.wikipedia.org/wiki/Kulkarni%E2%80%93Nomizu_product" + + - concept: kullback-leibler-distance + arity: 1 + arguments: [a1] + speech: + en: kullback leibler distance of a1 + property: function + subject-area: "mathematical statistics" + mathml: + - "KLX" + notationa: "msub D KL" + urls: + - "http://users.monash.edu/~lloyd/tildeMML/KL/" + - "https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence" + alias: + - kl-distance + - kl-divergence + - kullback-leibler-divergence + - relative-entropy + + - concept: lagrange-bracket + arity: 4 + arguments: [a1, a2, a3, a4] + speech: + en: "lagrange bracket of a1, a2, canonical coordinates a3, a4" + property: indexed fenced + subject-area: "classical mechanics" + mathml: + - "[u,v]p,q" + urls: + - "https://mathworld.wolfram.com/LagrangeBracket.html" + - "https://en.wikipedia.org/wiki/Lagrange_bracket" + - "https://www.encyclopediaofmath.org/index.php/Lagrange_bracket" + + - concept: lagrange-multiplier + arity: 0 + arguments: [] + speech: en: lagrange multiplier - property: symbol - area: "mathematical optimization" - mathml: - - "λ" - urls: - - "https://mathworld.wolfram.com/LagrangeMultiplier.html" - - "https://en.wikipedia.org/wiki/Lagrange_multiplier" - - "https://ncatlab.org/nlab/show/Lagrange+multiplier" - - "https://www.encyclopediaofmath.org/index.php/Lagrange_multipliers" - alias: - - lagrangian - - - concept: lagrange-point - arity: 0 + property: symbol + subject-area: "mathematical optimization" + mathml: + - "λ" + urls: + - "https://mathworld.wolfram.com/LagrangeMultiplier.html" + - "https://en.wikipedia.org/wiki/Lagrange_multiplier" + - "https://ncatlab.org/nlab/show/Lagrange+multiplier" + - "https://www.encyclopediaofmath.org/index.php/Lagrange_multipliers" + alias: + - lagrangian + + - concept: lagrange-point + arity: 0 + arguments: [] + speech: en: lagrange point - property: symbol - area: "celestial mechanics" - mathml: - - "L1" - - "L2" - - "L3" - - "L4" - - "L5" - urls: - - "https://en.wikipedia.org/wiki/Lagrange_point" - alias: - - lagrangian-point - - l-point - - libration-point - - - concept: laguerre-polynomial - arity: 1 - en: laguerre polynomial of $1 - property: "indexed function" - area: "orthogonal polynomials" - mathml: - - "L(x)" - urls: - - "https://mathworld.wolfram.com/LaguerrePolynomial.html" - - "https://en.wikipedia.org/wiki/Laguerre_polynomials" - - "https://dlmf.nist.gov/18.3" - - "https://dlmf.nist.gov/18.1#I1.ix7.p1" - - "https://dlmf.nist.gov/18.3#T1.t1.r27" - - "https://www.encyclopediaofmath.org/index.php/Laguerre_polynomials" - - - concept: landau-constant - arity: 0 + property: symbol + subject-area: "celestial mechanics" + mathml: + - "L1" + - "L2" + - "L3" + - "L4" + - "L5" + urls: + - "https://en.wikipedia.org/wiki/Lagrange_point" + alias: + - lagrangian-point + - l-point + - libration-point + + - concept: laguerre-polynomial + arity: 1 + arguments: [a1] + speech: + en: laguerre polynomial of a1 + property: "indexed function" + subject-area: "orthogonal polynomials" + mathml: + - "L(x)" + urls: + - "https://mathworld.wolfram.com/LaguerrePolynomial.html" + - "https://en.wikipedia.org/wiki/Laguerre_polynomials" + - "https://dlmf.nist.gov/18.3" + - "https://dlmf.nist.gov/18.1#I1.ix7.p1" + - "https://dlmf.nist.gov/18.3#T1.t1.r27" + - "https://www.encyclopediaofmath.org/index.php/Laguerre_polynomials" + + - concept: landau-constant + arity: 0 + arguments: [] + speech: en: landau constant - property: constant - area: "complex analysis" - mathml: - - "A" - - "B" - - "L" - urls: - - "https://mathworld.wolfram.com/LandauConstant.html" - - "https://en.wikipedia.org/wiki/Landau%27s_constants" - - - concept: laplace-operator - arity: 1 - en: laplace operator of $1 - property: "embellished operator" - area: "differential operators" - mathml: - - "∇2f" - - "∇·∇f" - - "Δ(f)" - urls: - - "https://en.wikipedia.org/wiki/Laplace_operator" - - "https://ncatlab.org/nlab/show/Laplace+operator" - - "https://www.encyclopediaofmath.org/index.php/Laplace_operator" - - - concept: laplace-transform - arity: 1 - en: laplace transform of $1 - property: operator - area: "integral transforms" - mathml: - - "ℒ⁡(x)" - urls: - - "https://mathworld.wolfram.com/LaplaceTransform.html" - - "https://en.wikipedia.org/wiki/Laplace_transform" - - "https://dlmf.nist.gov/1.14#E17" - - "https://www.encyclopediaofmath.org/index.php/Laplace_transform" - - - concept: laplacian-matrix - arity: 0 + property: constant + subject-area: "complex analysis" + mathml: + - "A" + - "B" + - "L" + urls: + - "https://mathworld.wolfram.com/LandauConstant.html" + - "https://en.wikipedia.org/wiki/Landau%27s_constants" + + - concept: laplace-operator + arity: 1 + arguments: [a1] + speech: + en: laplace operator of a1 + property: "embellished operator" + subject-area: "differential operators" + mathml: + - "∇2f" + - "∇·∇f" + - "Δ(f)" + urls: + - "https://en.wikipedia.org/wiki/Laplace_operator" + - "https://ncatlab.org/nlab/show/Laplace+operator" + - "https://www.encyclopediaofmath.org/index.php/Laplace_operator" + + - concept: laplace-transform + arity: 1 + arguments: [a1] + speech: + en: laplace transform of a1 + property: operator + subject-area: "integral transforms" + mathml: + - "ℒ⁡(x)" + urls: + - "https://mathworld.wolfram.com/LaplaceTransform.html" + - "https://en.wikipedia.org/wiki/Laplace_transform" + - "https://dlmf.nist.gov/1.14#E17" + - "https://www.encyclopediaofmath.org/index.php/Laplace_transform" + + - concept: laplacian-matrix + arity: 0 + arguments: [] + speech: en: laplacian matrix - property: symbol - area: "graph theory" - mathml: - - "L" - urls: - - "https://mathworld.wolfram.com/LaplacianMatrix.html" - - "https://en.wikipedia.org/wiki/Laplacian_matrix" - - - concept: latin-rectangle - arity: 1 - en: latin rectangle $1 - property: mtable - area: "combinatorial mathematics" - mathml: - - "012343401240321" + property: symbol + subject-area: "graph theory" + mathml: + - "L" + urls: + - "https://mathworld.wolfram.com/LaplacianMatrix.html" + - "https://en.wikipedia.org/wiki/Laplacian_matrix" + + - concept: latin-rectangle + arity: 1 + arguments: [a1] + speech: + en: latin rectangle a1 + property: mtable + subject-area: "combinatorial mathematics" + mathml: + - "012343401240321" - urls: - - "https://mathworld.wolfram.com/LatinRectangle.html" - - "https://en.wikipedia.org/wiki/Latin_rectangle" - - "https://www.encyclopediaofmath.org/index.php/Latin_rectangle" - - - concept: latin-square - arity: 1 - en: latin square $1 - property: mtable - area: "combinatorial mathematics" - mathml: - - "ABCCABBCA" - urls: - - "https://mathworld.wolfram.com/LatinSquare.html" - - "https://en.wikipedia.org/wiki/Latin_square" - - "https://en.wikipedia.org/wiki/Small_Latin_squares_and_quasigroups" - - "https://ncatlab.org/nlab/show/Latin+square" - - "https://www.encyclopediaofmath.org/index.php/Latin_square" - - - concept: least-prime-factor - arity: 1 - en: least prime factor of $1 - property: function - area: "number theory" - mathml: - - "lpf(x)" - urls: - - "https://mathworld.wolfram.com/LeastPrimeFactor.html" - - - concept: lebesgue-constant - arity: 1 - en: lebesgue constant of $1 - property: indexed constant - area: "fourier series" - mathml: - - "Lx" - urls: - - "https://mathworld.wolfram.com/LebesgueConstants.html" - - "https://en.wikipedia.org/wiki/Lebesgue_constant_(interpolation)" - - "https://dlmf.nist.gov/1.8#E8" - - "https://www.encyclopediaofmath.org/index.php/Lebesgue_constants" - - - concept: lebesgue-integral - arity: 1 - en: lebesgue integral of $1 - property: indexed - area: "measure theory" - mathml: - - "∫f" - urls: - - "https://mathworld.wolfram.com/LebesgueIntegral.html" - - "https://www.encyclopediaofmath.org/index.php/Lebesgue_integral" - - - concept: leech-lattice - arity: 0 + urls: + - "https://mathworld.wolfram.com/LatinRectangle.html" + - "https://en.wikipedia.org/wiki/Latin_rectangle" + - "https://www.encyclopediaofmath.org/index.php/Latin_rectangle" + + - concept: latin-square + arity: 1 + arguments: [a1] + speech: + en: latin square a1 + property: mtable + subject-area: "combinatorial mathematics" + mathml: + - "ABCCABBCA" + urls: + - "https://mathworld.wolfram.com/LatinSquare.html" + - "https://en.wikipedia.org/wiki/Latin_square" + - "https://en.wikipedia.org/wiki/Small_Latin_squares_and_quasigroups" + - "https://ncatlab.org/nlab/show/Latin+square" + - "https://www.encyclopediaofmath.org/index.php/Latin_square" + + - concept: least-prime-factor + arity: 1 + arguments: [a1] + speech: + en: least prime factor of a1 + property: function + subject-area: "number theory" + mathml: + - "lpf(x)" + urls: + - "https://mathworld.wolfram.com/LeastPrimeFactor.html" + + - concept: lebesgue-constant + arity: 1 + arguments: [a1] + speech: + en: lebesgue constant of a1 + property: indexed constant + subject-area: "fourier series" + mathml: + - "Lx" + urls: + - "https://mathworld.wolfram.com/LebesgueConstants.html" + - "https://en.wikipedia.org/wiki/Lebesgue_constant_(interpolation)" + - "https://dlmf.nist.gov/1.8#E8" + - "https://www.encyclopediaofmath.org/index.php/Lebesgue_constants" + + - concept: lebesgue-integral + arity: 1 + arguments: [a1] + speech: + en: lebesgue integral of a1 + property: indexed + subject-area: "measure theory" + mathml: + - "∫f" + urls: + - "https://mathworld.wolfram.com/LebesgueIntegral.html" + - "https://www.encyclopediaofmath.org/index.php/Lebesgue_integral" + + - concept: leech-lattice + arity: 0 + arguments: [] + speech: en: leech lattice - property: symbol - area: "group theory" - mathml: - - "Λ24" - urls: - - "https://mathworld.wolfram.com/LeechLattice.html" - - "https://en.wikipedia.org/wiki/Leech_lattice" - - "https://ncatlab.org/nlab/show/Leech+lattice" - - - concept: left-adjoint - arity: 2 - en: $1 left adjoint $2 - property: infix - area: "category theory" - mathml: - - "X⊣Y" - urls: - - "https://en.wikipedia.org/wiki/Adjoint_functors" - - - concept: left-composition - arity: 2 - en: $1 left composition $2 - property: infix - area: "algebra" - mathml: - - "X;Y" - urls: - - "https://en.wikipedia.org/wiki/Composition_of_relations" - alias: - - left-compose - - - concept: left-derivative - arity: 1 - en: left derivative of $1 - property: operator - area: "calculus" - mathml: - - "∂−f" - urls: - - "https://en.wikipedia.org/wiki/Left_and_right_derivative" - - - concept: legendre-chi-function - arity: 1 - en: legendre chi function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "χx" - urls: - - "https://en.wikipedia.org/wiki/Legendre_chi_function" - - "https://mathworld.wolfram.com/LegendresChi-Function.html" - - - concept: legendre-polynomial - arity: 1 - en: legendre polynomial of $1 - property: function - area: "orthogonal polynomials" - mathml: - - "Px" - urls: - - "https://mathworld.wolfram.com/LegendrePolynomial.html" - - "https://en.wikipedia.org/wiki/Legendre_polynomials" - - "https://dlmf.nist.gov/18.3" - - "https://dlmf.nist.gov/18.3#T1.t1.r25" - - "https://ncatlab.org/nlab/show/Legendre+polynomial" - - - concept: legendre-symbol - arity: 2 + property: symbol + subject-area: "group theory" + mathml: + - "Λ24" + urls: + - "https://mathworld.wolfram.com/LeechLattice.html" + - "https://en.wikipedia.org/wiki/Leech_lattice" + - "https://ncatlab.org/nlab/show/Leech+lattice" + + - concept: left-adjoint + arity: 2 + arguments: [a1, a2] + speech: + en: a1 left adjoint a2 + property: infix + subject-area: "category theory" + mathml: + - "X⊣Y" + urls: + - "https://en.wikipedia.org/wiki/Adjoint_functors" + + - concept: left-composition + arity: 2 + arguments: [a1, a2] + speech: + en: a1 left composition a2 + property: infix + subject-area: "algebra" + mathml: + - "X;Y" + urls: + - "https://en.wikipedia.org/wiki/Composition_of_relations" + alias: + - left-compose + + - concept: left-derivative + arity: 1 + arguments: [a1] + speech: + en: left derivative of a1 + property: operator + subject-area: "calculus" + mathml: + - "∂−f" + urls: + - "https://en.wikipedia.org/wiki/Left_and_right_derivative" + + - concept: legendre-chi-function + arity: 1 + arguments: [a1] + speech: + en: legendre chi function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "χx" + urls: + - "https://en.wikipedia.org/wiki/Legendre_chi_function" + - "https://mathworld.wolfram.com/LegendresChi-Function.html" + + - concept: legendre-polynomial + arity: 1 + arguments: [a1] + speech: + en: legendre polynomial of a1 + property: function + subject-area: "orthogonal polynomials" + mathml: + - "Px" + urls: + - "https://mathworld.wolfram.com/LegendrePolynomial.html" + - "https://en.wikipedia.org/wiki/Legendre_polynomials" + - "https://dlmf.nist.gov/18.3" + - "https://dlmf.nist.gov/18.3#T1.t1.r25" + - "https://ncatlab.org/nlab/show/Legendre+polynomial" + + - concept: legendre-symbol + arity: 2 + arguments: [a1, a2] + speech: en: legendre symbol - property: fenced, fenced stacked - area: "number theory" - mathml: - - "(a|p)" - - "(ap)" - urls: - - "https://mathworld.wolfram.com/LegendreSymbol.html" - - "https://en.wikipedia.org/wiki/Legendre_symbol" - - "https://dlmf.nist.gov/27.9" - - - concept: lehmer-mean - arity: 1 - en: lehmer mean of $1 - property: "indexed function" - area: "means" - mathml: - - "Lx" - urls: - - "https://mathworld.wolfram.com/LehmerMean.html" - - "https://en.wikipedia.org/wiki/Lehmer_mean" - - - concept: lehmer-number - arity: 1 - en: lehmer number of $1 - property: "indexed function" - area: "number theory" - mathml: - - "Ux" - urls: - - "https://mathworld.wolfram.com/LehmerNumber.html" - - "https://mathworld.wolfram.com/LehmersNumber.html" - - "https://en.wikipedia.org/wiki/Lehmer_number" - - - concept: level - arity: 1 - en: level of $1 - property: function - area: "scales of measurement" - mathml: - - "Lx" - urls: - - "https://en.wikipedia.org/wiki/Level_(logarithmic_quantity)" - - "https://en.wikipedia.org/wiki/Categorical_variable" - - "https://ncatlab.org/nlab/show/level" - - - concept: levi-civita-symbol - arity: 3 - en: levi civita symbol of $1, $2 and $3 - property: "indexed symbol" - area: "combinatorics" - mathml: - - "ϵijk" - urls: - - "https://mathworld.wolfram.com/Levi-CivitaSymbol.html" - - "https://en.wikipedia.org/wiki/Levi-Civita_symbol" - - "https://dlmf.nist.gov/1.6#E14" - alias: - - permutation-symbol - - - concept: levy-prokhorov-metric - arity: 1 - en: levy prokhorov metric of $1 - property: function - area: "measure theory" - mathml: - - "π(x)" - urls: - - "https://en.wikipedia.org/wiki/L%C3%A9vy%E2%80%93Prokhorov_metric" - - "https://encyclopediaofmath.org/wiki/L%C3%A9vy-Prokhorov_metric" - - - concept: lexicographic-product - arity: 2 - en: $1 lexicographic product $2 - property: infix, mixfix - area: "graph theory" - mathml: - - "G∙H" - urls: - - "https://en.wikipedia.org/wiki/Lexicographic_product_of_graphs" - alias: - - graph-composition - - - concept: lexicographic-order - arity: 2 - en: $1 lexicographic order $2 - property: infix - area: "discrete mathematics" - mathml: - - "X<Y" - urls: - - "https://en.wikipedia.org/wiki/Lexicographic_order" - - "https://mathworld.wolfram.com/LexicographicOrder.html" - - "https://ncatlab.org/nlab/show/lexicographic+order" - alias: - - dictionary-order - - - concept: lie-derivative - arity: 1 - en: lie derivative of $1 - property: "indexed operator" - area: "lie algebra" - mathml: - - "ℒx" - urls: - - "https://mathworld.wolfram.com/LieDerivative.html" - - "https://en.wikipedia.org/wiki/Lie_derivative" - - "https://ncatlab.org/nlab/show/Lie+derivative" - - - concept: lie-superbracket - arity: 2 + property: fenced, fenced stacked + subject-area: "number theory" + mathml: + - "(a|p)" + - "(ap)" + urls: + - "https://mathworld.wolfram.com/LegendreSymbol.html" + - "https://en.wikipedia.org/wiki/Legendre_symbol" + - "https://dlmf.nist.gov/27.9" + + - concept: lehmer-mean + arity: 1 + arguments: [a1] + speech: + en: lehmer mean of a1 + property: "indexed function" + subject-area: "means" + mathml: + - "Lx" + urls: + - "https://mathworld.wolfram.com/LehmerMean.html" + - "https://en.wikipedia.org/wiki/Lehmer_mean" + + - concept: lehmer-number + arity: 1 + arguments: [a1] + speech: + en: lehmer number of a1 + property: "indexed function" + subject-area: "number theory" + mathml: + - "Ux" + urls: + - "https://mathworld.wolfram.com/LehmerNumber.html" + - "https://mathworld.wolfram.com/LehmersNumber.html" + - "https://en.wikipedia.org/wiki/Lehmer_number" + + - concept: level + arity: 1 + arguments: [a1] + speech: + en: level of a1 + property: function + subject-area: "scales of measurement" + mathml: + - "Lx" + urls: + - "https://en.wikipedia.org/wiki/Level_(logarithmic_quantity)" + - "https://en.wikipedia.org/wiki/Categorical_variable" + - "https://ncatlab.org/nlab/show/level" + + - concept: levi-civita-symbol + arity: 3 + arguments: [a1, a2, a3] + speech: + en: levi civita symbol of a1, a2 and a3 + property: "indexed symbol" + subject-area: "combinatorics" + mathml: + - "ϵijk" + urls: + - "https://mathworld.wolfram.com/Levi-CivitaSymbol.html" + - "https://en.wikipedia.org/wiki/Levi-Civita_symbol" + - "https://dlmf.nist.gov/1.6#E14" + alias: + - permutation-symbol + + - concept: levy-prokhorov-metric + arity: 1 + arguments: [a1] + speech: + en: levy prokhorov metric of a1 + property: function + subject-area: "measure theory" + mathml: + - "π(x)" + urls: + - "https://en.wikipedia.org/wiki/L%C3%A9vy%E2%80%93Prokhorov_metric" + - "https://encyclopediaofmath.org/wiki/L%C3%A9vy-Prokhorov_metric" + + - concept: lexicographic-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 lexicographic product a2 + property: infix, mixfix + subject-area: "graph theory" + mathml: + - "G∙H" + urls: + - "https://en.wikipedia.org/wiki/Lexicographic_product_of_graphs" + alias: + - graph-composition + + - concept: lexicographic-order + arity: 2 + arguments: [a1, a2] + speech: + en: a1 lexicographic order a2 + property: infix + subject-area: "discrete mathematics" + mathml: + - "X<Y" + urls: + - "https://en.wikipedia.org/wiki/Lexicographic_order" + - "https://mathworld.wolfram.com/LexicographicOrder.html" + - "https://ncatlab.org/nlab/show/lexicographic+order" + alias: + - dictionary-order + + - concept: lie-derivative + arity: 1 + arguments: [a1] + speech: + en: lie derivative of a1 + property: "indexed operator" + subject-area: "lie algebra" + mathml: + - "ℒx" + urls: + - "https://mathworld.wolfram.com/LieDerivative.html" + - "https://en.wikipedia.org/wiki/Lie_derivative" + - "https://ncatlab.org/nlab/show/Lie+derivative" + + - concept: lie-superbracket + arity: 2 + arguments: [a1, a2] + speech: en: lie superbracket - property: fenced - area: "lie algebra" - mathml: - - "[x,y]" - urls: - - "https://en.wikipedia.org/wiki/Lie_superalgebra" - alias: - - supercommutator - - - concept: like-charge - arity: 2 - en: $1 like charge $2 - property: infix - area: "physics" - mathml: - - "X⇈Y" - urls: - - "https://youtu.be/HZ7a9YkF204?t=4719" - - - concept: line-graph - arity: 1 - en: line graph of $1 - property: function - area: "graph theory" - mathml: - - "L(x)" - urls: - - "https://mathworld.wolfram.com/LineGraph.html" - - "https://en.wikipedia.org/wiki/Line_graph" - - - concept: line-integral - arity: 1 - en: line integral of $1 - property: indexed - area: "analysis" - mathml: - - "∫f" - urls: - - "https://mathworld.wolfram.com/LineIntegral.html" - - "https://en.wikipedia.org/wiki/Line_integral" - - "https://ncatlab.org/nlab/show/line+integral" - alias: - - curve-integral - - path-integral - - curvilinear-integral - - contour-integral - - - concept: linear-span - arity: 1 - en: linear span of $1 - property: function - area: "linear algebra" - mathml: - - "span(x)" - urls: - - "https://mathworld.wolfram.com/LinearSpan.html" - - "https://en.wikipedia.org/wiki/Linear_span" - alias: - - span - - linear-hull - - - concept: link - arity: 1 - en: link of $1 - property: function - area: "graph theory" - mathml: - - "Lk(x)" - urls: - - "https://mathworld.wolfram.com/Link.html" - - - concept: gunter-link - arity: 1 - en: gunter link of $1 - property: unit - area: "units" - mathml: - - "l.X" - - "li.X" - - "lnk.X" - urls: - - "https://en.wikipedia.org/wiki/Link_(unit)" - - - concept: liouville-constant - arity: 0 + property: fenced + subject-area: "lie algebra" + mathml: + - "[x,y]" + urls: + - "https://en.wikipedia.org/wiki/Lie_superalgebra" + alias: + - supercommutator + + - concept: like-charge + arity: 2 + arguments: [a1, a2] + speech: + en: a1 like charge a2 + property: infix + subject-area: "physics" + mathml: + - "X⇈Y" + urls: + - "https://youtu.be/HZ7a9YkF204?t=4719" + + - concept: line-graph + arity: 1 + arguments: [a1] + speech: + en: line graph of a1 + property: function + subject-area: "graph theory" + mathml: + - "L(x)" + urls: + - "https://mathworld.wolfram.com/LineGraph.html" + - "https://en.wikipedia.org/wiki/Line_graph" + + - concept: line-integral + arity: 1 + arguments: [a1] + speech: + en: line integral of a1 + property: indexed + subject-area: "analysis" + mathml: + - "∫f" + urls: + - "https://mathworld.wolfram.com/LineIntegral.html" + - "https://en.wikipedia.org/wiki/Line_integral" + - "https://ncatlab.org/nlab/show/line+integral" + alias: + - curve-integral + - path-integral + - curvilinear-integral + - contour-integral + + - concept: linear-span + arity: 1 + arguments: [a1] + speech: + en: linear span of a1 + property: function + subject-area: "linear algebra" + mathml: + - "span(x)" + urls: + - "https://mathworld.wolfram.com/LinearSpan.html" + - "https://en.wikipedia.org/wiki/Linear_span" + alias: + - span + - linear-hull + + - concept: link + arity: 1 + arguments: [a1] + speech: + en: link of a1 + property: function + subject-area: "graph theory" + mathml: + - "Lk(x)" + urls: + - "https://mathworld.wolfram.com/Link.html" + + - concept: gunter-link + arity: 1 + arguments: [a1] + speech: + en: gunter link of a1 + property: unit + subject-area: "units" + mathml: + - "l.X" + - "li.X" + - "lnk.X" + urls: + - "https://en.wikipedia.org/wiki/Link_(unit)" + + - concept: liouville-constant + arity: 0 + arguments: [] + speech: en: liouville constant - property: constant - area: "number theory" - mathml: - - "L" - urls: - - "https://mathworld.wolfram.com/LiouvillesConstant.html" - alias: - - liouville-number - - - concept: liouville-function - arity: 1 - en: liouville function of $1 - property: function - area: "number theory" - mathml: - - "λ(x)" - urls: - - "https://mathworld.wolfram.com/LiouvilleFunction.html" - - "https://en.wikipedia.org/wiki/Liouville_function" - - "https://dlmf.nist.gov/27.2#E13" - - - concept: localization - arity: 2 - en: localization of $2 by $1 - property: mixfix - area: "module theory" - mathml: - - "S−1R" - urls: - - "https://mathworld.wolfram.com/Localization.html" - - "https://en.wikipedia.org/wiki/Localization_(algebra)" - - "https://en.wikipedia.org/wiki/Localization_of_a_ring" - - "https://ncatlab.org/nlab/show/localization" - - "https://ncatlab.org/nlab/show/localization+of+a+module" - - - concept: logarithmic-integral - arity: 1 - en: logarithmic integral of $1 - property: function - area: "special functions" - mathml: - - "li(x)" - urls: - - "https://mathworld.wolfram.com/LogarithmicIntegral.html" - - "https://dlmf.nist.gov/6.2#i" - - "https://dlmf.nist.gov/6.2#E8" - - - concept: logarithmic-moment-of-function - arity: 2 - en: $1th logarithmic moment of $2 - property: "mixfix" - area: "mathematics" - mathml: - - "E[lnn(X)]" - notation: "E [ msup ln $1 /msup ( $2 ) ]" - urls: - - "https://en.wikipedia.org/wiki/Moment_(mathematics)" - alias: - - logarithmic-moment - - - concept: logit - arity: 1 - en: logit of $1 - property: function - area: "statistics" - mathml: - - "logit(x)" - urls: - - "https://en.wikipedia.org/wiki/Logit" - - - concept: lommel-function - arity: 2 - en: $1 ,$2 lommel function - property: "indexed function" - area: "special functions" - mathml: - - "s(uv(z)" - urls: - - "https://mathworld.wolfram.com/LommelFunction.html" - - "https://en.wikipedia.org/wiki/Lommel_function" - - "https://dlmf.nist.gov/11.9" - - "https://dlmf.nist.gov/11.9#E5" - - "https://dlmf.nist.gov/11.9#E3" - - - concept: long-division - arity: 1 - en: long division of $1 by $2 - property: mfrac - area: "arithmetic" - comments: - - "long division display layout" - urls: - - "https://mathworld.wolfram.com/LongDivision.html" - - "https://en.wikipedia.org/wiki/Long_division" - - - concept: loop-space - arity: 1 - en: loop space of $1 - property: function - area: "topology" - mathml: - - "Ω(x)" - urls: - - "https://mathworld.wolfram.com/LoopSpace.html" - - "https://en.wikipedia.org/wiki/Loop_space" - - "https://ncatlab.org/nlab/show/loop+space" - - - concept: lower-closure-poset - arity: 1 - en: lower closure poset of $1 - property: prefix - area: "order theory" - mathml: - - "↓x" - urls: - - "https://en.wikipedia.org/wiki/Upper_set#Upper_closure_and_lower_closure" - - - concept: lower-darboux-integral - arity: 1 - en: lower darboux integral of $1 - property: indexed - area: "real analysis" - mathml: - - "∫ab_f" - notation: "munder ¯" - urls: - - "https://mathworld.wolfram.com/DarbouxIntegral.html" - - "https://en.wikipedia.org/wiki/Darboux_integral" - - "https://www.encyclopediaofmath.org/index.php/Darboux_integral" - - - concept: lower-dini-derivative - arity: 1 - en: lower dini derivative of $1 - property: decorated function - area: "analysis" - mathml: - - "f′-(t)" - urls: - - "https://mathworld.wolfram.com/DiniDerivative.html" - - "https://en.wikipedia.org/wiki/Dini_derivative" - - "https://www.encyclopediaofmath.org/index.php/Dini_derivative" - - - concept: lower-shadow - arity: 1 - en: lower shadow of $1 - property: function - area: "combinatorics" - mathml: - - "𝜕X" - notationa: "msub 𝜕 -" - urls: - - "http://qk206.user.srcf.net/notes/combinatorics.pdf" - alias: - - shadow - - - concept: lucas-number - arity: 1 - en: lucas number of $1 - property: "indexed symbol" - area: "integer sequences" - mathml: - - "Lx" - urls: - - "https://mathworld.wolfram.com/LucasNumber.html" - - "https://en.wikipedia.org/wiki/Lucas_number" - - "https://en.wikipedia.org/wiki/Lucas_prime" - - - concept: lucas-sequence - arity: 1 - en: lucas sequence of $1 - property: "indexed function" - area: "integer sequences" - mathml: - - "Ux" - - "Vx" - urls: - - "https://mathworld.wolfram.com/LucasSequence.html" - - "https://en.wikipedia.org/wiki/Lucas_sequence" - - - concept: lyapunov-candidate-function - arity: 1 - en: lyapunov candidate function of $1 - property: function - area: "stability theory" - mathml: - - "V(x)" - urls: - - "https://mathworld.wolfram.com/LyapunovFunction.html" - - "https://en.wikipedia.org/wiki/Lyapunov_function" - - "https://www.encyclopediaofmath.org/index.php/Lyapunov_function" - alias: - - lyapunov-function - - - concept: macdonald-polynomial - arity: 1 - en: macdonald polynomial of $1 - property: function - area: "orthogonal polynomials" - mathml: - - "Pλ(x;t,q)" - urls: - - "https://en.wikipedia.org/wiki/Macdonald_polynomials" - - "https://ncatlab.org/nlab/show/Macdonald+polynomial" - - - concept: mahler-measure - arity: 1 - en: mahler measure of $1 - property: function - area: "number theory" - mathml: - - "M(x)" - urls: - - "https://mathworld.wolfram.com/MahlerMeasure.html" - - "https://en.wikipedia.org/wiki/Mahler_measure" - - "https://www.encyclopediaofmath.org/index.php/Mahler_measure" - - - concept: mangoldt-function - arity: 1 - en: mangoldt function of $1 - property: function - area: "special functions" - mathml: - - "Λ(x)" - urls: - - "https://mathworld.wolfram.com/MangoldtFunction.html" - - "https://dlmf.nist.gov/27.2#E14" - - "https://www.encyclopediaofmath.org/index.php/Mangoldt_function" - alias: - - von-mangoldt-function - - - concept: mapping-class-group - arity: 1 - en: mapping class group of $1 - property: function - area: "geometric topology" - mathml: - - "MCG(x)" - urls: - - "https://en.wikipedia.org/wiki/Mapping_class_group" - - "https://ncatlab.org/nlab/show/mapping+class+group" - - - concept: mapping-cone - arity: 1 - en: mapping cone of $1 - property: "indexed symbol" - area: "homotopy theory" - mathml: - - "Cx" - notationa: "mrow C $1" - urls: - - "https://en.wikipedia.org/wiki/Mapping_cone_(topology)" - - "https://en.wikipedia.org/wiki/Mapping_cone_(homological_algebra)" - - "https://ncatlab.org/nlab/show/mapping+cone" - alias: - - homotopy-cofiber - - - concept: matching-polynomial - arity: 1 - en: matching polynomial of $1 - property: "indexed function" - area: "graph theory" - mathml: - - "mx" - - "Mx" - - "μx" - urls: - - "https://en.wikipedia.org/wiki/Matching_polynomial" - - - concept: mathieu-function-of-first-kind - arity: 1 - en: mathieu function of first kind of $1 - property: "indexed function" - area: "special functions" - mathml: - - "cex" - - "sex" - urls: - - "https://mathworld.wolfram.com/MathieuFunction.html" - - "https://en.wikipedia.org/wiki/Mathieu_function" - - "https://dlmf.nist.gov/28#PT2" - - "https://dlmf.nist.gov/28#PT3" - - "https://dlmf.nist.gov/28.2#SS6.p1" - - "https://dlmf.nist.gov/28.26#i" - - "https://dlmf.nist.gov/28.26#i" - - "https://dlmf.nist.gov/28.26#i" - - "https://dlmf.nist.gov/28.26#i" - - "https://dlmf.nist.gov/28.12#SS2.p2" - - "https://dlmf.nist.gov/28.2#SS6.p1" - - "https://www.encyclopediaofmath.org/index.php/Mathieu_functions" - alias: - - angular-mathieu-function - - mathieu-function - - - concept: mathieu-function-of-second-kind - arity: 1 - en: mathieu function of second kind of $1 - property: "indexed function" - area: "special functions" - mathml: - - "fex" - - "gex" - urls: - - "https://mathworld.wolfram.com/MathieuFunction.html" - - "https://en.wikipedia.org/wiki/Mathieu_function" - - "https://dlmf.nist.gov/28#PT2" - - "https://dlmf.nist.gov/28#PT3" - - "https://dlmf.nist.gov/28.2#SS6.p1" - - "https://dlmf.nist.gov/28.26#i" - - "https://dlmf.nist.gov/28.26#i" - - "https://dlmf.nist.gov/28.26#i" - - "https://dlmf.nist.gov/28.26#i" - - "https://dlmf.nist.gov/28.12#SS2.p2" - - "https://dlmf.nist.gov/28.2#SS6.p1" - - "https://www.encyclopediaofmath.org/index.php/Mathieu_functions" - alias: - - angular-mathieu-function - - mathieu-function - - - concept: mathieu-group - arity: 1 - en: mathieu group $1 - property: "indexed symbol" - area: "group theory" - mathml: - - "M11" - - "M12" - - "M22" - - "M23" - - "M24" - urls: - - "https://mathworld.wolfram.com/MathieuGroups.html" - - "https://en.wikipedia.org/wiki/Multiply_transitive_group" - - "https://en.wikipedia.org/wiki/Mathieu_group" - - "https://en.wikipedia.org/wiki/Mathieu_group_M11" - - "https://en.wikipedia.org/wiki/Mathieu_group_M12" - - "https://en.wikipedia.org/wiki/Mathieu_group_M22" - - "https://en.wikipedia.org/wiki/Mathieu_group_M23" - - "https://en.wikipedia.org/wiki/Mathieu_group_M24" - - "https://ncatlab.org/nlab/show/Mathieu+group" - - "https://www.encyclopediaofmath.org/index.php/Mathieu_group" - - - concept: matrix - arity: 1 - en: matrix $1 - property: mtable, fenced - area: "algebra" - mathml: - - "(......)" - - "[......]" - urls: - - "https://mathworld.wolfram.com/Matrix.html" - - "https://mathworld.wolfram.com/SquareBracket.html" - - "https://en.wikipedia.org/wiki/Matrix_(mathematics)" - - "https://en.wikipedia.org/wiki/List_of_matrices" - - "https://en.wikipedia.org/wiki/Skew-symmetric_matrix" - - "https://en.wikipedia.org/wiki/Prenex_normal_form" - - "https://en.wikipedia.org/wiki/Matrix_isolation" - - "https://ncatlab.org/nlab/show/matrix" - - "https://www.encyclopediaofmath.org/index.php/Matrix" - - - concept: matrix-ring - arity: 1 - en: matrix ring of $1 - property: function - area: "abstract algebra" - mathml: - - "Mx" - urls: - - "https://en.wikipedia.org/wiki/Matrix_ring" - - "https://www.encyclopediaofmath.org/index.php/Matrix_ring" - - - concept: maximum-degree - arity: 1 - en: maximum degree of $1 - property: function - area: "graph theory" - mathml: - - "Δ(x)" - urls: - - "https://mathworld.wolfram.com/MaximumDegree.html" - - "https://en.wikipedia.org/wiki/Degree_(graph_theory)" - - "https://en.wikipedia.org/wiki/Degree_sequence" - - - concept: mean-curvature - arity: 1 - en: mean curvature of $1 - property: function - area: "differential geometry" - mathml: - - "H(x)" - urls: - - "https://mathworld.wolfram.com/MeanCurvature.html" - - "https://en.wikipedia.org/wiki/Mean_curvature" - - "https://www.encyclopediaofmath.org/index.php/Mean_curvature" - - - concept: mean-squared-error - arity: 1 - en: mean squared error of $1 - property: function - area: "statistics" - mathml: - - "MSE(x)" - urls: - - "https://en.wikipedia.org/wiki/Mean_squared_error" - - - concept: meixner-pollaczek-polynomial - arity: 1 - en: meixner pollaczek polynomial of $1 - property: "indexed function" - area: "orthogonal polynomials" - mathml: - - "P(x)" - urls: - - "https://mathworld.wolfram.com/Meixner-PollaczekPolynomial.html" - - "https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek_polynomials" - - "https://dlmf.nist.gov/18.19#P3.p1" - - - concept: mellin-transform - arity: 1 - en: mellin transform of $1 - property: operator - area: "integral transforms" - mathml: - - "ℳ(x)" - urls: - - "https://mathworld.wolfram.com/MellinTransform.html" - - "https://en.wikipedia.org/wiki/Mellin_transform" - - "https://dlmf.nist.gov/1.14#E32" - - "https://www.encyclopediaofmath.org/index.php/Mellin_transform" - - - concept: meridian-radius-of-curvature - arity: 1 - en: meridian radius of curvature of $1 - property: function - area: "geodesy" - mathml: - - "M(x)" - urls: - - "https://en.wikipedia.org/wiki/Meridian_arc" - - "https://en.wikipedia.org/wiki/Meridian_arc" - - - concept: meridian-distance - arity: 1 - en: meridian distance of $1 - property: function - area: "geodesy" - mathml: - - "m(x)" - urls: - - "https://mathworld.wolfram.com/Meridian.html" - - - concept: mersenne-number - arity: 1 - en: mersenne number of $1 - property: "indexed symbol" - area: "number theory" - mathml: - - "Mx" - urls: - - "https://mathworld.wolfram.com/MersenneNumber.html" - - "https://www.encyclopediaofmath.org/index.php/Mersenne_number" - - - concept: mersenne-prime - arity: 1 - en: mersenne prime of $1 - property: "indexed symbol" - area: "number theory" - mathml: - - "Mx" - urls: - - "https://mathworld.wolfram.com/MersennePrime.html" - - "https://en.wikipedia.org/wiki/Mersenne_number" - - "https://en.wikipedia.org/wiki/Mersenne_prime" - - - concept: merten-function - arity: 1 - en: merten function of $1 - property: function - area: "number theory" - mathml: - - "M(x)" - urls: - - "https://mathworld.wolfram.com/MertensFunction.html" - - "https://en.wikipedia.org/wiki/Mertens_function" - - - concept: meson - arity: 1 - en: meson of $1 - property: - urls: - - "https://en.wikipedia.org/wiki/Meson" - - "https://en.wikipedia.org/wiki/List_of_mesons" - - "https://ncatlab.org/nlab/show/meson" - - - concept: metaplectic-group - arity: 1 + property: constant + subject-area: "number theory" + mathml: + - "L" + urls: + - "https://mathworld.wolfram.com/LiouvillesConstant.html" + alias: + - liouville-number + + - concept: liouville-function + arity: 1 + arguments: [a1] + speech: + en: liouville function of a1 + property: function + subject-area: "number theory" + mathml: + - "λ(x)" + urls: + - "https://mathworld.wolfram.com/LiouvilleFunction.html" + - "https://en.wikipedia.org/wiki/Liouville_function" + - "https://dlmf.nist.gov/27.2#E13" + + - concept: localization + arity: 2 + arguments: [a1, a2] + speech: + en: localization of a2 by a1 + property: mixfix + subject-area: "module theory" + mathml: + - "S−1R" + urls: + - "https://mathworld.wolfram.com/Localization.html" + - "https://en.wikipedia.org/wiki/Localization_(algebra)" + - "https://en.wikipedia.org/wiki/Localization_of_a_ring" + - "https://ncatlab.org/nlab/show/localization" + - "https://ncatlab.org/nlab/show/localization+of+a+module" + + - concept: logarithmic-integral + arity: 1 + arguments: [a1] + speech: + en: logarithmic integral of a1 + property: function + subject-area: "special functions" + mathml: + - "li(x)" + urls: + - "https://mathworld.wolfram.com/LogarithmicIntegral.html" + - "https://dlmf.nist.gov/6.2#i" + - "https://dlmf.nist.gov/6.2#E8" + + - concept: logarithmic-moment-of-function + arity: 2 + arguments: [a1, a2] + speech: + en: a1th logarithmic moment of a2 + property: "mixfix" + subject-area: "mathematics" + mathml: + - "E[lnn(X)]" + notation: "E [ msup ln a1 /msup ( a2 ) ]" + urls: + - "https://en.wikipedia.org/wiki/Moment_(mathematics)" + alias: + - logarithmic-moment + + - concept: logit + arity: 1 + arguments: [a1] + speech: + en: logit of a1 + property: function + subject-area: "statistics" + mathml: + - "logit(x)" + urls: + - "https://en.wikipedia.org/wiki/Logit" + + - concept: lommel-function + arity: 2 + arguments: [a1, a2] + speech: + en: a1 ,a2 lommel function + property: "indexed function" + subject-area: "special functions" + mathml: + - "s(uv(z)" + urls: + - "https://mathworld.wolfram.com/LommelFunction.html" + - "https://en.wikipedia.org/wiki/Lommel_function" + - "https://dlmf.nist.gov/11.9" + - "https://dlmf.nist.gov/11.9#E5" + - "https://dlmf.nist.gov/11.9#E3" + + - concept: long-division + arity: 1 + arguments: [a1] + speech: + en: long division of a1 by a2 + property: mfrac + subject-area: "arithmetic" + comments: + - "long division display layout" + urls: + - "https://mathworld.wolfram.com/LongDivision.html" + - "https://en.wikipedia.org/wiki/Long_division" + + - concept: loop-space + arity: 1 + arguments: [a1] + speech: + en: loop space of a1 + property: function + subject-area: "topology" + mathml: + - "Ω(x)" + urls: + - "https://mathworld.wolfram.com/LoopSpace.html" + - "https://en.wikipedia.org/wiki/Loop_space" + - "https://ncatlab.org/nlab/show/loop+space" + + - concept: lower-closure-poset + arity: 1 + arguments: [a1] + speech: + en: lower closure poset of a1 + property: prefix + subject-area: "order theory" + mathml: + - "↓x" + urls: + - "https://en.wikipedia.org/wiki/Upper_set#Upper_closure_and_lower_closure" + + - concept: lower-darboux-integral + arity: 1 + arguments: [a1] + speech: + en: lower darboux integral of a1 + property: indexed + subject-area: "real analysis" + mathml: + - "∫ab_f" + notation: "munder ¯" + urls: + - "https://mathworld.wolfram.com/DarbouxIntegral.html" + - "https://en.wikipedia.org/wiki/Darboux_integral" + - "https://www.encyclopediaofmath.org/index.php/Darboux_integral" + + - concept: lower-dini-derivative + arity: 1 + arguments: [a1] + speech: + en: lower dini derivative of a1 + property: decorated function + subject-area: "analysis" + mathml: + - "f′-(t)" + urls: + - "https://mathworld.wolfram.com/DiniDerivative.html" + - "https://en.wikipedia.org/wiki/Dini_derivative" + - "https://www.encyclopediaofmath.org/index.php/Dini_derivative" + + - concept: lower-shadow + arity: 1 + arguments: [a1] + speech: + en: lower shadow of a1 + property: function + subject-area: "combinatorics" + mathml: + - "𝜕X" + notationa: "msub 𝜕 -" + urls: + - "http://qk206.user.srcf.net/notes/combinatorics.pdf" + alias: + - shadow + + - concept: lucas-number + arity: 1 + arguments: [a1] + speech: + en: lucas number of a1 + property: "indexed symbol" + subject-area: "integer sequences" + mathml: + - "Lx" + urls: + - "https://mathworld.wolfram.com/LucasNumber.html" + - "https://en.wikipedia.org/wiki/Lucas_number" + - "https://en.wikipedia.org/wiki/Lucas_prime" + + - concept: lucas-sequence + arity: 1 + arguments: [a1] + speech: + en: lucas sequence of a1 + property: "indexed function" + subject-area: "integer sequences" + mathml: + - "Ux" + - "Vx" + urls: + - "https://mathworld.wolfram.com/LucasSequence.html" + - "https://en.wikipedia.org/wiki/Lucas_sequence" + + - concept: lyapunov-candidate-function + arity: 1 + arguments: [a1] + speech: + en: lyapunov candidate function of a1 + property: function + subject-area: "stability theory" + mathml: + - "V(x)" + urls: + - "https://mathworld.wolfram.com/LyapunovFunction.html" + - "https://en.wikipedia.org/wiki/Lyapunov_function" + - "https://www.encyclopediaofmath.org/index.php/Lyapunov_function" + alias: + - lyapunov-function + + - concept: macdonald-polynomial + arity: 1 + arguments: [a1] + speech: + en: macdonald polynomial of a1 + property: function + subject-area: "orthogonal polynomials" + mathml: + - "Pλ(x;t,q)" + urls: + - "https://en.wikipedia.org/wiki/Macdonald_polynomials" + - "https://ncatlab.org/nlab/show/Macdonald+polynomial" + + - concept: mahler-measure + arity: 1 + arguments: [a1] + speech: + en: mahler measure of a1 + property: function + subject-area: "number theory" + mathml: + - "M(x)" + urls: + - "https://mathworld.wolfram.com/MahlerMeasure.html" + - "https://en.wikipedia.org/wiki/Mahler_measure" + - "https://www.encyclopediaofmath.org/index.php/Mahler_measure" + + - concept: mangoldt-function + arity: 1 + arguments: [a1] + speech: + en: mangoldt function of a1 + property: function + subject-area: "special functions" + mathml: + - "Λ(x)" + urls: + - "https://mathworld.wolfram.com/MangoldtFunction.html" + - "https://dlmf.nist.gov/27.2#E14" + - "https://www.encyclopediaofmath.org/index.php/Mangoldt_function" + alias: + - von-mangoldt-function + + - concept: mapping-class-group + arity: 1 + arguments: [a1] + speech: + en: mapping class group of a1 + property: function + subject-area: "geometric topology" + mathml: + - "MCG(x)" + urls: + - "https://en.wikipedia.org/wiki/Mapping_class_group" + - "https://ncatlab.org/nlab/show/mapping+class+group" + + - concept: mapping-cone + arity: 1 + arguments: [a1] + speech: + en: mapping cone of a1 + property: "indexed symbol" + subject-area: "homotopy theory" + mathml: + - "Cx" + notationa: "mrow C a1" + urls: + - "https://en.wikipedia.org/wiki/Mapping_cone_(topology)" + - "https://en.wikipedia.org/wiki/Mapping_cone_(homological_algebra)" + - "https://ncatlab.org/nlab/show/mapping+cone" + alias: + - homotopy-cofiber + + - concept: matching-polynomial + arity: 1 + arguments: [a1] + speech: + en: matching polynomial of a1 + property: "indexed function" + subject-area: "graph theory" + mathml: + - "mx" + - "Mx" + - "μx" + urls: + - "https://en.wikipedia.org/wiki/Matching_polynomial" + + - concept: mathieu-function-of-first-kind + arity: 1 + arguments: [a1] + speech: + en: mathieu function of first kind of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "cex" + - "sex" + urls: + - "https://mathworld.wolfram.com/MathieuFunction.html" + - "https://en.wikipedia.org/wiki/Mathieu_function" + - "https://dlmf.nist.gov/28#PT2" + - "https://dlmf.nist.gov/28#PT3" + - "https://dlmf.nist.gov/28.2#SS6.p1" + - "https://dlmf.nist.gov/28.26#i" + - "https://dlmf.nist.gov/28.26#i" + - "https://dlmf.nist.gov/28.26#i" + - "https://dlmf.nist.gov/28.26#i" + - "https://dlmf.nist.gov/28.12#SS2.p2" + - "https://dlmf.nist.gov/28.2#SS6.p1" + - "https://www.encyclopediaofmath.org/index.php/Mathieu_functions" + alias: + - angular-mathieu-function + - mathieu-function + + - concept: mathieu-function-of-second-kind + arity: 1 + arguments: [a1] + speech: + en: mathieu function of second kind of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "fex" + - "gex" + urls: + - "https://mathworld.wolfram.com/MathieuFunction.html" + - "https://en.wikipedia.org/wiki/Mathieu_function" + - "https://dlmf.nist.gov/28#PT2" + - "https://dlmf.nist.gov/28#PT3" + - "https://dlmf.nist.gov/28.2#SS6.p1" + - "https://dlmf.nist.gov/28.26#i" + - "https://dlmf.nist.gov/28.26#i" + - "https://dlmf.nist.gov/28.26#i" + - "https://dlmf.nist.gov/28.26#i" + - "https://dlmf.nist.gov/28.12#SS2.p2" + - "https://dlmf.nist.gov/28.2#SS6.p1" + - "https://www.encyclopediaofmath.org/index.php/Mathieu_functions" + alias: + - angular-mathieu-function + - mathieu-function + + - concept: mathieu-group + arity: 1 + arguments: [a1] + speech: + en: mathieu group a1 + property: "indexed symbol" + subject-area: "group theory" + mathml: + - "M11" + - "M12" + - "M22" + - "M23" + - "M24" + urls: + - "https://mathworld.wolfram.com/MathieuGroups.html" + - "https://en.wikipedia.org/wiki/Multiply_transitive_group" + - "https://en.wikipedia.org/wiki/Mathieu_group" + - "https://en.wikipedia.org/wiki/Mathieu_group_M11" + - "https://en.wikipedia.org/wiki/Mathieu_group_M12" + - "https://en.wikipedia.org/wiki/Mathieu_group_M22" + - "https://en.wikipedia.org/wiki/Mathieu_group_M23" + - "https://en.wikipedia.org/wiki/Mathieu_group_M24" + - "https://ncatlab.org/nlab/show/Mathieu+group" + - "https://www.encyclopediaofmath.org/index.php/Mathieu_group" + + - concept: matrix + arity: 1 + arguments: [a1] + speech: + en: matrix a1 + property: mtable, fenced + subject-area: "algebra" + mathml: + - "(......)" + - "[......]" + urls: + - "https://mathworld.wolfram.com/Matrix.html" + - "https://mathworld.wolfram.com/SquareBracket.html" + - "https://en.wikipedia.org/wiki/Matrix_(mathematics)" + - "https://en.wikipedia.org/wiki/List_of_matrices" + - "https://en.wikipedia.org/wiki/Skew-symmetric_matrix" + - "https://en.wikipedia.org/wiki/Prenex_normal_form" + - "https://en.wikipedia.org/wiki/Matrix_isolation" + - "https://ncatlab.org/nlab/show/matrix" + - "https://www.encyclopediaofmath.org/index.php/Matrix" + + - concept: matrix-ring + arity: 1 + arguments: [a1] + speech: + en: matrix ring of a1 + property: function + subject-area: "abstract algebra" + mathml: + - "Mx" + urls: + - "https://en.wikipedia.org/wiki/Matrix_ring" + - "https://www.encyclopediaofmath.org/index.php/Matrix_ring" + + - concept: maximum-degree + arity: 1 + arguments: [a1] + speech: + en: maximum degree of a1 + property: function + subject-area: "graph theory" + mathml: + - "Δ(x)" + urls: + - "https://mathworld.wolfram.com/MaximumDegree.html" + - "https://en.wikipedia.org/wiki/Degree_(graph_theory)" + - "https://en.wikipedia.org/wiki/Degree_sequence" + + - concept: mean-curvature + arity: 1 + arguments: [a1] + speech: + en: mean curvature of a1 + property: function + subject-area: "differential geometry" + mathml: + - "H(x)" + urls: + - "https://mathworld.wolfram.com/MeanCurvature.html" + - "https://en.wikipedia.org/wiki/Mean_curvature" + - "https://www.encyclopediaofmath.org/index.php/Mean_curvature" + + - concept: mean-squared-error + arity: 1 + arguments: [a1] + speech: + en: mean squared error of a1 + property: function + subject-area: "statistics" + mathml: + - "MSE(x)" + urls: + - "https://en.wikipedia.org/wiki/Mean_squared_error" + + - concept: meixner-pollaczek-polynomial + arity: 1 + arguments: [a1] + speech: + en: meixner pollaczek polynomial of a1 + property: "indexed function" + subject-area: "orthogonal polynomials" + mathml: + - "P(x)" + urls: + - "https://mathworld.wolfram.com/Meixner-PollaczekPolynomial.html" + - "https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek_polynomials" + - "https://dlmf.nist.gov/18.19#P3.p1" + + - concept: mellin-transform + arity: 1 + arguments: [a1] + speech: + en: mellin transform of a1 + property: operator + subject-area: "integral transforms" + mathml: + - "ℳ(x)" + urls: + - "https://mathworld.wolfram.com/MellinTransform.html" + - "https://en.wikipedia.org/wiki/Mellin_transform" + - "https://dlmf.nist.gov/1.14#E32" + - "https://www.encyclopediaofmath.org/index.php/Mellin_transform" + + - concept: meridian-radius-of-curvature + arity: 1 + arguments: [a1] + speech: + en: meridian radius of curvature of a1 + property: function + subject-area: "geodesy" + mathml: + - "M(x)" + urls: + - "https://en.wikipedia.org/wiki/Meridian_arc" + - "https://en.wikipedia.org/wiki/Meridian_arc" + + - concept: meridian-distance + arity: 1 + arguments: [a1] + speech: + en: meridian distance of a1 + property: function + subject-area: "geodesy" + mathml: + - "m(x)" + urls: + - "https://mathworld.wolfram.com/Meridian.html" + + - concept: mersenne-number + arity: 1 + arguments: [a1] + speech: + en: mersenne number of a1 + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Mx" + urls: + - "https://mathworld.wolfram.com/MersenneNumber.html" + - "https://www.encyclopediaofmath.org/index.php/Mersenne_number" + + - concept: mersenne-prime + arity: 1 + arguments: [a1] + speech: + en: mersenne prime of a1 + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Mx" + urls: + - "https://mathworld.wolfram.com/MersennePrime.html" + - "https://en.wikipedia.org/wiki/Mersenne_number" + - "https://en.wikipedia.org/wiki/Mersenne_prime" + + - concept: merten-function + arity: 1 + arguments: [a1] + speech: + en: merten function of a1 + property: function + subject-area: "number theory" + mathml: + - "M(x)" + urls: + - "https://mathworld.wolfram.com/MertensFunction.html" + - "https://en.wikipedia.org/wiki/Mertens_function" + + - concept: meson + arity: 1 + arguments: [a1] + speech: + en: meson of a1 + property: + urls: + - "https://en.wikipedia.org/wiki/Meson" + - "https://en.wikipedia.org/wiki/List_of_mesons" + - "https://ncatlab.org/nlab/show/meson" + + - concept: metaplectic-group + arity: 1 + arguments: [a1] + speech: en: metaplectic group - property: symbol - area: "group theory" - mathml: - - "Mp2n(R)" - urls: - - "https://mathworld.wolfram.com/MetaplecticGroup.html" - - "https://en.wikipedia.org/wiki/Metaplectic_group" - - "https://ncatlab.org/nlab/show/metaplectic+group" - - - concept: mills-constant - arity: 0 + property: symbol + subject-area: "group theory" + mathml: + - "Mp2n(R)" + urls: + - "https://mathworld.wolfram.com/MetaplecticGroup.html" + - "https://en.wikipedia.org/wiki/Metaplectic_group" + - "https://ncatlab.org/nlab/show/metaplectic+group" + + - concept: mills-constant + arity: 0 + arguments: [] + speech: en: mills constant - property: symbol - area: "number theory" - mathml: - - "A" - urls: - - "https://mathworld.wolfram.com/MillsConstant.html" - - "https://en.wikipedia.org/wiki/Mills%27_constant" - - "https://en.wikipedia.org/wiki/Mills_prime" - - - concept: mills-ratio - arity: 1 - en: mills ratio of $1 - property: function - area: "probability theory" - mathml: - - "mX" - - "MX" - urls: - - "https://mathworld.wolfram.com/MillsRatio.html" - - "https://en.wikipedia.org/wiki/Mills_ratio" - - "https://dlmf.nist.gov/7.8#E1" - - - concept: minimum-degree - arity: 1 - en: minimum degree of $1 - property: function - area: "graph theory" - mathml: - - "δ(x)" - urls: - - "https://mathworld.wolfram.com/MinimumDegree.html" - - "https://en.wikipedia.org/wiki/Degree_(graph_theory)" - - "https://en.wikipedia.org/wiki/Degree_sequence" - - - concept: minkowski-difference - arity: 2 - en: $1 minkowski difference $2 - property: infix - area: "geometry" - mathml: - - "X-Y" - urls: - - "https://en.wikipedia.org/wiki/Minkowski_addition" - alias: - - geometric-difference - - - concept: minkowski-sum - arity: 2 - en: $1 minkowski sum $2 - property: infix - area: "geometry" - mathml: - - "X+Y" - urls: - - "https://mathworld.wolfram.com/MinkowskiSum.html" - - "https://en.wikipedia.org/wiki/Minkowski_addition" - alias: - - dilation - - - concept: mittag-leffler-function - arity: 1 - en: mittag leffler function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "Ex" - urls: - - "https://mathworld.wolfram.com/Mittag-LefflerFunction.html" - - "https://en.wikipedia.org/wiki/Mittag-Leffler_function" - - "https://dlmf.nist.gov/10.46#E3" - - "https://www.encyclopediaofmath.org/index.php/Mittag-Leffler_function" - - - concept: mobius-function - arity: 1 - en: mobius function of $1 - property: function - area: "number theory" - mathml: - - "μ(x)" - urls: - - "https://mathworld.wolfram.com/MoebiusFunction.html" - - "https://en.wikipedia.org/wiki/%CE%9C(n)" - - "https://en.wikipedia.org/wiki/M%C3%B6bius_function" - - "https://dlmf.nist.gov/27.2#E12" - - "https://www.encyclopediaofmath.org/index.php/Möbius_function" - - - concept: modified-bessel-function-of-first-kind - arity: 1 - en: modified bessel function of first kind of $1 - property: function - area: "special functions" - mathml: - - "Ix" - urls: - - "https://dlmf.nist.gov/10#PT3" - - "https://dlmf.nist.gov/10.25#E2" - - "https://dlmf.nist.gov/10.25#E3" - - - concept: modified-bessel-function-of-second-kind - arity: 1 - en: modified bessel function of second kind of $1 - property: function - area: "special functions" - mathml: - - "Kx" - urls: - - "https://dlmf.nist.gov/10#PT3" - - "https://dlmf.nist.gov/10.25#E2" - - "https://dlmf.nist.gov/10.25#E3" - - - concept: modified-mathieu-function - arity: 1 - en: modified mathieu function of $1 - property: function - area: "special functions" - mathml: - - "Cex" - - "Sex" - - "Mex" - - "Fex" - - "Gex" - urls: - - "https://dlmf.nist.gov/28#PT4" - - "https://dlmf.nist.gov/28.20#E3" - - "https://dlmf.nist.gov/28.20#E6" - - "https://dlmf.nist.gov/28.20#E7" - - "https://dlmf.nist.gov/28.20#E17" - - "https://dlmf.nist.gov/28.20#E18" - - "https://dlmf.nist.gov/28.20#E19" - - "https://dlmf.nist.gov/28.20#E20" - - "https://dlmf.nist.gov/28.20#SS3.p1" - - "https://dlmf.nist.gov/28.20#E5" - - "https://dlmf.nist.gov/28.20#E4" - - - concept: modified-spherical-bessel-function - arity: 1 - en: modified spherical bessel function of $1 - property: function - area: "special functions" - mathml: - - "in(1)(z)" - - "in(2)(z)" - - "kn(z)" - urls: - - "https://mathworld.wolfram.com/ModifiedSphericalBesselFunction.html" - - "https://dlmf.nist.gov/10.47#E7" - - "https://dlmf.nist.gov/10.47#E8" - - "https://dlmf.nist.gov/10.47#E9" - - - concept: modified-struve-function - arity: 1 - en: modified struve function of $1 - property: function - area: "special functions" - mathml: - - "Lx" - urls: - - "https://mathworld.wolfram.com/ModifiedStruveFunction.html" - - "https://dlmf.nist.gov/11.2#E2" - - "https://dlmf.nist.gov/11.2#E6" - - - concept: modular-discriminant - arity: 1 - en: modular discriminant of $1 - property: operator - area: "special functions" - mathml: - - "Δ(x)" - urls: - - "https://mathworld.wolfram.com/ModularDiscriminant.html" - - "https://en.wikipedia.org/wiki/Modular_form#The_modular_discriminant" - - - concept: modulo - arity: 2 - en: $1 modulo $2 - property: infix, mixfix - area: "modular arithmetic" - mathml: - - "x(modp)" - urls: - - "https://mathworld.wolfram.com/Modulo.html" - - "https://en.wikipedia.org/wiki/Modulo_(jargon)" - - "https://en.wikipedia.org/wiki/Modulo_operation" - - "https://dlmf.nist.gov/front/introduction#Sx4.p2.t1.r10" - alias: - - mod - - - concept: moebius-function - arity: 1 - en: moebius function of $1 - property: function - area: "number theory" - mathml: - - "μ(x)" - urls: - - "https://www.encyclopediaofmath.org/index.php/Moebius_function" - - "https://en.wikipedia.org/wiki/M%C3%B6bius_function" - - - concept: moment-of-function - arity: - en: $1th moment - property: "msub, mixfix" - area: "mathematics" - mathml: - - "μn" - notationa: "mrow E [ msup $1 $2 ]" - urls: - - "https://en.wikipedia.org/wiki/Moment_(mathematics)" - alias: - - moment - - - concept: moment - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "A" + urls: + - "https://mathworld.wolfram.com/MillsConstant.html" + - "https://en.wikipedia.org/wiki/Mills%27_constant" + - "https://en.wikipedia.org/wiki/Mills_prime" + + - concept: mills-ratio + arity: 1 + arguments: [a1] + speech: + en: mills ratio of a1 + property: function + subject-area: "probability theory" + mathml: + - "mX" + - "MX" + urls: + - "https://mathworld.wolfram.com/MillsRatio.html" + - "https://en.wikipedia.org/wiki/Mills_ratio" + - "https://dlmf.nist.gov/7.8#E1" + + - concept: minimum-degree + arity: 1 + arguments: [a1] + speech: + en: minimum degree of a1 + property: function + subject-area: "graph theory" + mathml: + - "δ(x)" + urls: + - "https://mathworld.wolfram.com/MinimumDegree.html" + - "https://en.wikipedia.org/wiki/Degree_(graph_theory)" + - "https://en.wikipedia.org/wiki/Degree_sequence" + + - concept: minkowski-difference + arity: 2 + arguments: [a1, a2] + speech: + en: a1 minkowski difference a2 + property: infix + subject-area: "geometry" + mathml: + - "X-Y" + urls: + - "https://en.wikipedia.org/wiki/Minkowski_addition" + alias: + - geometric-difference + + - concept: minkowski-sum + arity: 2 + arguments: [a1, a2] + speech: + en: a1 minkowski sum a2 + property: infix + subject-area: "geometry" + mathml: + - "X+Y" + urls: + - "https://mathworld.wolfram.com/MinkowskiSum.html" + - "https://en.wikipedia.org/wiki/Minkowski_addition" + alias: + - dilation + + - concept: mittag-leffler-function + arity: 1 + arguments: [a1] + speech: + en: mittag leffler function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Ex" + urls: + - "https://mathworld.wolfram.com/Mittag-LefflerFunction.html" + - "https://en.wikipedia.org/wiki/Mittag-Leffler_function" + - "https://dlmf.nist.gov/10.46#E3" + - "https://www.encyclopediaofmath.org/index.php/Mittag-Leffler_function" + + - concept: mobius-function + arity: 1 + arguments: [a1] + speech: + en: mobius function of a1 + property: function + subject-area: "number theory" + mathml: + - "μ(x)" + urls: + - "https://mathworld.wolfram.com/MoebiusFunction.html" + - "https://en.wikipedia.org/wiki/%CE%9C(n)" + - "https://en.wikipedia.org/wiki/M%C3%B6bius_function" + - "https://dlmf.nist.gov/27.2#E12" + - "https://www.encyclopediaofmath.org/index.php/Möbius_function" + + - concept: modified-bessel-function-of-first-kind + arity: 1 + arguments: [a1] + speech: + en: modified bessel function of first kind of a1 + property: function + subject-area: "special functions" + mathml: + - "Ix" + urls: + - "https://dlmf.nist.gov/10#PT3" + - "https://dlmf.nist.gov/10.25#E2" + - "https://dlmf.nist.gov/10.25#E3" + + - concept: modified-bessel-function-of-second-kind + arity: 1 + arguments: [a1] + speech: + en: modified bessel function of second kind of a1 + property: function + subject-area: "special functions" + mathml: + - "Kx" + urls: + - "https://dlmf.nist.gov/10#PT3" + - "https://dlmf.nist.gov/10.25#E2" + - "https://dlmf.nist.gov/10.25#E3" + + - concept: modified-mathieu-function + arity: 1 + arguments: [a1] + speech: + en: modified mathieu function of a1 + property: function + subject-area: "special functions" + mathml: + - "Cex" + - "Sex" + - "Mex" + - "Fex" + - "Gex" + urls: + - "https://dlmf.nist.gov/28#PT4" + - "https://dlmf.nist.gov/28.20#E3" + - "https://dlmf.nist.gov/28.20#E6" + - "https://dlmf.nist.gov/28.20#E7" + - "https://dlmf.nist.gov/28.20#E17" + - "https://dlmf.nist.gov/28.20#E18" + - "https://dlmf.nist.gov/28.20#E19" + - "https://dlmf.nist.gov/28.20#E20" + - "https://dlmf.nist.gov/28.20#SS3.p1" + - "https://dlmf.nist.gov/28.20#E5" + - "https://dlmf.nist.gov/28.20#E4" + + - concept: modified-spherical-bessel-function + arity: 1 + arguments: [a1] + speech: + en: modified spherical bessel function of a1 + property: function + subject-area: "special functions" + mathml: + - "in(1)(z)" + - "in(2)(z)" + - "kn(z)" + urls: + - "https://mathworld.wolfram.com/ModifiedSphericalBesselFunction.html" + - "https://dlmf.nist.gov/10.47#E7" + - "https://dlmf.nist.gov/10.47#E8" + - "https://dlmf.nist.gov/10.47#E9" + + - concept: modified-struve-function + arity: 1 + arguments: [a1] + speech: + en: modified struve function of a1 + property: function + subject-area: "special functions" + mathml: + - "Lx" + urls: + - "https://mathworld.wolfram.com/ModifiedStruveFunction.html" + - "https://dlmf.nist.gov/11.2#E2" + - "https://dlmf.nist.gov/11.2#E6" + + - concept: modular-discriminant + arity: 1 + arguments: [a1] + speech: + en: modular discriminant of a1 + property: operator + subject-area: "special functions" + mathml: + - "Δ(x)" + urls: + - "https://mathworld.wolfram.com/ModularDiscriminant.html" + - "https://en.wikipedia.org/wiki/Modular_form#The_modular_discriminant" + + - concept: modulo + arity: 2 + arguments: [a1, a2] + speech: + en: a1 modulo a2 + property: infix, mixfix + subject-area: "modular arithmetic" + mathml: + - "x(modp)" + urls: + - "https://mathworld.wolfram.com/Modulo.html" + - "https://en.wikipedia.org/wiki/Modulo_(jargon)" + - "https://en.wikipedia.org/wiki/Modulo_operation" + - "https://dlmf.nist.gov/front/introduction#Sx4.p2.t1.r10" + alias: + - mod + + - concept: moebius-function + arity: 1 + arguments: [a1] + speech: + en: moebius function of a1 + property: function + subject-area: "number theory" + mathml: + - "μ(x)" + urls: + - "https://www.encyclopediaofmath.org/index.php/Moebius_function" + - "https://en.wikipedia.org/wiki/M%C3%B6bius_function" + + - concept: moment-of-function + arity: 2 + arguments: [a1, a2] + speech: + en: a1th moment + property: "msub, mixfix" + subject-area: "mathematics" + mathml: + - "μn" + notationa: "mrow E [ msup a1 a2 ]" + urls: + - "https://en.wikipedia.org/wiki/Moment_(mathematics)" + alias: + - moment + + - concept: moment + arity: 0 + arguments: [] + speech: en: moment - property: symbol - area: "mechanics" - mathml: - - "M" - urls: - - "https://mathworld.wolfram.com/Moment.html" - - "https://en.wikipedia.org/wiki/Moment_(mathematics)" - - "https://en.wikipedia.org/wiki/Torque" - - "https://ncatlab.org/nlab/show/moment" - - "https://www.encyclopediaofmath.org/index.php/Moment" - - - concept: moment-of-inertia - arity: 0 + property: symbol + subject-area: "mechanics" + mathml: + - "M" + urls: + - "https://mathworld.wolfram.com/Moment.html" + - "https://en.wikipedia.org/wiki/Moment_(mathematics)" + - "https://en.wikipedia.org/wiki/Torque" + - "https://ncatlab.org/nlab/show/moment" + - "https://www.encyclopediaofmath.org/index.php/Moment" + + - concept: moment-of-inertia + arity: 0 + arguments: [] + speech: en: moment of inertia - property: symbol - area: "physics" - mathml: - - "I" - urls: - - "https://mathworld.wolfram.com/MomentofInertia.html" - - "https://en.wikipedia.org/wiki/Moment_of_inertia" - - "https://ncatlab.org/nlab/show/moment+of+inertia" - alias: - - mass-moment-of-inertia - - angular-mass - - rotational-inertia - - - concept: momentum - arity: 0 + property: symbol + subject-area: "physics" + mathml: + - "I" + urls: + - "https://mathworld.wolfram.com/MomentofInertia.html" + - "https://en.wikipedia.org/wiki/Moment_of_inertia" + - "https://ncatlab.org/nlab/show/moment+of+inertia" + alias: + - mass-moment-of-inertia + - angular-mass + - rotational-inertia + + - concept: momentum + arity: 0 + arguments: [] + speech: en: momentum - property: symbol - area: "mechanics" - mathml: - - "p" - - "mip" - urls: - - "https://en.wikipedia.org/wiki/Momentum" - - "https://ncatlab.org/nlab/show/momentum" - alias: - - linear-momentum - - translational-momentum - - - concept: monster-group - arity: 0 + property: symbol + subject-area: "mechanics" + mathml: + - "p" + - "mip" + urls: + - "https://en.wikipedia.org/wiki/Momentum" + - "https://ncatlab.org/nlab/show/momentum" + alias: + - linear-momentum + - translational-momentum + + - concept: monster-group + arity: 0 + arguments: [] + speech: en: monster group - property: symbol - area: "group theory" - mathml: - - "M" - urls: - - "https://mathworld.wolfram.com/MonsterGroup.html" - - "https://en.wikipedia.org/wiki/Monster_group" - - "https://ncatlab.org/nlab/show/Monster+group" - alias: - - friendly-giant - - - concept: moore-penrose-inverse - arity: 1 - en: moore penrose inverse of $1 - property: msup - area: "linear algebra" - mathml: - - "X+" - urls: - - "https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse" - alias: - - moore-penrose-pseudoinverse - - - concept: moore-smith-sequence - arity: 1 - en: moore smith sequence of $1 - property: fenced - area: "topology" - mathml: - - "(xa)a∈A" - urls: - - "https://en.wikipedia.org/wiki/Moore%E2%80%93Smith_limit" - - "https://en.wikipedia.org/wiki/Net_(mathematics)" - alias: - - net - - - concept: motzkin-number - arity: 1 - en: motzkin number of $1 - property: "indexed symbol" - area: "combinatorial analysis" - mathml: - - "Mx" - - "M(x)" - urls: - - "https://mathworld.wolfram.com/MotzkinNumber.html" - - "https://en.wikipedia.org/wiki/Motzkin_number" - - "https://en.wikipedia.org/wiki/Motzkin_prime" - - "https://dlmf.nist.gov/26.6#E2" - - - concept: multiple-integral - arity: 1 - en: multiple integral of $1 - property: indexed - area: "multivariable calculus" - mathml: - - "∫⋯∫f" - urls: - - "https://mathworld.wolfram.com/MultipleIntegral.html" - - "https://en.wikipedia.org/wiki/%E2%88%AB%E2%88%ABf(x,y)dxdy" - - "https://en.wikipedia.org/wiki/Multiple_integral" - - "https://www.encyclopediaofmath.org/index.php/Multiple_integral" - - - concept: multiplicative-inverse - arity: 1 - en: multiplicative inverse of $1 - property: msup, mixfix - area: "abstract algebra" - mathml: - - "x-1" - - "1/x" - urls: - - "https://mathworld.wolfram.com/Inverse.html" - - "https://en.wikipedia.org/wiki/Inverse_function" - - "https://en.wikipedia.org/wiki/Inverse_functions_and_differentiation" - - "https://ncatlab.org/nlab/show/inverse" - - "https://mathworld.wolfram.com/MultiplicativeInverse.html" - - "https://en.wikipedia.org/wiki/Multiplicative_inverse" - alias: - - inverse - - - concept: multiplicative-order - arity: 1 - en: multiplicative order of $1 - property: "indexed function" - area: "modular arithmetic" - mathml: - - "Ox" - - "ordx" - urls: - - "https://mathworld.wolfram.com/MultiplicativeOrder.html" - - "https://en.wikipedia.org/wiki/Multiplicative_order" - - - concept: multiplier-algebra - arity: 1 - en: multiplier algebra of $1 - property: function - area: "functional analysis" - mathml: - - "M(A)" - urls: - - "https://mathworld.wolfram.com/MultiplierAlgebra.html" - - "https://en.wikipedia.org/wiki/Multiplier_algebra" - - "https://ncatlab.org/nlab/show/multiplier+algebra" - - - concept: multichoose - arity: 2 + property: symbol + subject-area: "group theory" + mathml: + - "M" + urls: + - "https://mathworld.wolfram.com/MonsterGroup.html" + - "https://en.wikipedia.org/wiki/Monster_group" + - "https://ncatlab.org/nlab/show/Monster+group" + alias: + - friendly-giant + + - concept: moore-penrose-inverse + arity: 1 + arguments: [a1] + speech: + en: moore penrose inverse of a1 + property: msup + subject-area: "linear algebra" + mathml: + - "X+" + urls: + - "https://en.wikipedia.org/wiki/Moore%E2%80%93Penrose_inverse" + alias: + - moore-penrose-pseudoinverse + + - concept: moore-smith-sequence + arity: 1 + arguments: [a1] + speech: + en: moore smith sequence of a1 + property: fenced + subject-area: "topology" + mathml: + - "(xa)a∈A" + urls: + - "https://en.wikipedia.org/wiki/Moore%E2%80%93Smith_limit" + - "https://en.wikipedia.org/wiki/Net_(mathematics)" + alias: + - net + + - concept: motzkin-number + arity: 1 + arguments: [a1] + speech: + en: motzkin number of a1 + property: "indexed symbol" + subject-area: "combinatorial analysis" + mathml: + - "Mx" + - "M(x)" + urls: + - "https://mathworld.wolfram.com/MotzkinNumber.html" + - "https://en.wikipedia.org/wiki/Motzkin_number" + - "https://en.wikipedia.org/wiki/Motzkin_prime" + - "https://dlmf.nist.gov/26.6#E2" + + - concept: multiple-integral + arity: 1 + arguments: [a1] + speech: + en: multiple integral of a1 + property: indexed + subject-area: "multivariable calculus" + mathml: + - "∫⋯∫f" + urls: + - "https://mathworld.wolfram.com/MultipleIntegral.html" + - "https://en.wikipedia.org/wiki/%E2%88%AB%E2%88%ABf(x,y)dxdy" + - "https://en.wikipedia.org/wiki/Multiple_integral" + - "https://www.encyclopediaofmath.org/index.php/Multiple_integral" + + - concept: multiplicative-inverse + arity: 1 + arguments: [a1] + speech: + en: multiplicative inverse of a1 + property: msup, mixfix + subject-area: "abstract algebra" + mathml: + - "x-1" + - "1/x" + urls: + - "https://mathworld.wolfram.com/Inverse.html" + - "https://en.wikipedia.org/wiki/Inverse_function" + - "https://en.wikipedia.org/wiki/Inverse_functions_and_differentiation" + - "https://ncatlab.org/nlab/show/inverse" + - "https://mathworld.wolfram.com/MultiplicativeInverse.html" + - "https://en.wikipedia.org/wiki/Multiplicative_inverse" + alias: + - inverse + + - concept: multiplicative-order + arity: 1 + arguments: [a1] + speech: + en: multiplicative order of a1 + property: "indexed function" + subject-area: "modular arithmetic" + mathml: + - "Ox" + - "ordx" + urls: + - "https://mathworld.wolfram.com/MultiplicativeOrder.html" + - "https://en.wikipedia.org/wiki/Multiplicative_order" + + - concept: multiplier-algebra + arity: 1 + arguments: [a1] + speech: + en: multiplier algebra of a1 + property: function + subject-area: "functional analysis" + mathml: + - "M(A)" + urls: + - "https://mathworld.wolfram.com/MultiplierAlgebra.html" + - "https://en.wikipedia.org/wiki/Multiplier_algebra" + - "https://ncatlab.org/nlab/show/multiplier+algebra" + + - concept: multichoose + arity: 2 + arguments: [a1, a2] + speech: en: multichoose - property: fenced-stacked - area: "combinatorics" - mathml: - - "(mn)" - urls: - - "https://mathworld.wolfram.com/Multiset.html" - - - concept: multiset-coefficient - arity: 2 + property: fenced-stacked + subject-area: "combinatorics" + mathml: + - "(mn)" + urls: + - "https://mathworld.wolfram.com/Multiset.html" + + - concept: multiset-coefficient + arity: 2 + arguments: [a1, a2] + speech: en: multiset coefficient - property: fenced-stacked - area: "combinatorics" - mathml: - - "⦅nn⦆" - urls: - - "https://en.wikipedia.org/wiki/Multiset" - alias: - - multiset-number - - - concept: multivariate-gaussian-distribution - arity: 1 + property: fenced-stacked + subject-area: "combinatorics" + mathml: + - "⦅nn⦆" + urls: + - "https://en.wikipedia.org/wiki/Multiset" + alias: + - multiset-number + + - concept: multivariate-gaussian-distribution + arity: 1 + arguments: [a1] + speech: en: multivariate gaussian distribution - property: symbol - area: "probability theory" - mathml: - - "𝒩x" - urls: - - "https://en.wikipedia.org/wiki/Multivariate_normal_distribution" - alias: - - multivariate-normal-distribution - - joint-normal-distribution - - - concept: mutation - arity: 2 + property: symbol + subject-area: "probability theory" + mathml: + - "𝒩x" + urls: + - "https://en.wikipedia.org/wiki/Multivariate_normal_distribution" + alias: + - multivariate-normal-distribution + - joint-normal-distribution + + - concept: mutation + arity: 2 + arguments: [a1, a2] + speech: en: mutation - property: msup - area: "abstract algebra" - mathml: - - "Ay" - notation: "msup $1 $2" - urls: - - "https://mathworld.wolfram.com/Mutation.html" - - "https://en.wikipedia.org/wiki/Mutation_(knot_theory)" - - "https://en.wikipedia.org/wiki/Mutation_(Jordan_algebra)" - - "https://en.wikipedia.org/wiki/Hua%27s_identity_(Jordan_algebra)" - - "https://en.wikipedia.org/wiki/Mutation_(algebra)" - - "https://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)" - alias: - - homotope - - - concept: mutual-information - arity: 1 - en: mutual information of $1 - property: function - area: "information theory" - mathml: - - "I(x)" - urls: - - "https://mathworld.wolfram.com/MutualInformation.html" - - "https://en.wikipedia.org/wiki/Mutual_information" - - - concept: narayana-number - arity: 2 + property: msup + subject-area: "abstract algebra" + mathml: + - "Ay" + notation: "msup a1 a2" + urls: + - "https://mathworld.wolfram.com/Mutation.html" + - "https://en.wikipedia.org/wiki/Mutation_(knot_theory)" + - "https://en.wikipedia.org/wiki/Mutation_(Jordan_algebra)" + - "https://en.wikipedia.org/wiki/Hua%27s_identity_(Jordan_algebra)" + - "https://en.wikipedia.org/wiki/Mutation_(algebra)" + - "https://en.wikipedia.org/wiki/Mutation_(genetic_algorithm)" + alias: + - homotope + + - concept: mutual-information + arity: 1 + arguments: [a1] + speech: + en: mutual information of a1 + property: function + subject-area: "information theory" + mathml: + - "I(x)" + urls: + - "https://mathworld.wolfram.com/MutualInformation.html" + - "https://en.wikipedia.org/wiki/Mutual_information" + + - concept: narayana-number + arity: 2 + arguments: [a1, a2] + speech: en: narayana number - property: function - area: "combinatorial analysis" - mathml: - - "N(n,k)" - urls: - - "https://mathworld.wolfram.com/NarayanaNumber.html" - - "https://en.wikipedia.org/wiki/Narayana_number" - - "https://dlmf.nist.gov/26.6#E3" - - - concept: narrow-denjoy-integral - arity: 1 - en: narrow denjoy integral of $1 - property: indexed - area: "calculus" - mathml: - - "∫f" - urls: - - "https://mathworld.wolfram.com/DenjoyIntegral.html" - - "https://en.wikipedia.org/wiki/Henstock%E2%80%93Kurzweil_integral" - - "https://www.encyclopediaofmath.org/index.php/Denjoy_integral" - alias: - - henstock-kurzweil-integral - - luzin-integral - - perron-integral - - - concept: negative-binomial-distribution - arity: 0 + property: function + subject-area: "combinatorial analysis" + mathml: + - "N(n,k)" + urls: + - "https://mathworld.wolfram.com/NarayanaNumber.html" + - "https://en.wikipedia.org/wiki/Narayana_number" + - "https://dlmf.nist.gov/26.6#E3" + + - concept: narrow-denjoy-integral + arity: 1 + arguments: [a1] + speech: + en: narrow denjoy integral of a1 + property: indexed + subject-area: "calculus" + mathml: + - "∫f" + urls: + - "https://mathworld.wolfram.com/DenjoyIntegral.html" + - "https://en.wikipedia.org/wiki/Henstock%E2%80%93Kurzweil_integral" + - "https://www.encyclopediaofmath.org/index.php/Denjoy_integral" + alias: + - henstock-kurzweil-integral + - luzin-integral + - perron-integral + + - concept: negative-binomial-distribution + arity: 0 + arguments: [] + speech: en: negative binomial distribution - property: symbol - area: "probability theory" - mathml: - - "NB" - urls: - - "https://mathworld.wolfram.com/NegativeBinomialDistribution.html" - - "https://en.wikipedia.org/wiki/Negative_binomial_distribution" - - "https://www.encyclopediaofmath.org/index.php/Negative_binomial_distribution" - - - concept: negative-hypergeometric-distribution - arity: 1 - en: negative hypergeometric distribution of $1 - property: "indexed symbol" - area: "probability theory" - mathml: - - "NHG(x)" - urls: - - "https://en.wikipedia.org/wiki/Negative_hypergeometric_distribution" - - "https://www.encyclopediaofmath.org/index.php/Negative_hypergeometric_distribution" - - - concept: neighbourhood - arity: 2 - en: neighbourhood of $2 in $1 - property: "indexed function, function" - area: "graph theory" - mathml: - - "Nv(G)" - notation: "msub N $1 ( $2 )" - notationa: "mrow N ( $1" - urls: - - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)" - alias: - - open-neighbourhood - - - concept: neighbourhood-filter - arity: 1 - en: neighbourhood filter of $1 - property: function - area: "topology" - mathml: - - "𝒩(x)" - urls: - - "https://en.wikipedia.org/wiki/Neighbourhood_system" - alias: - - neighbourhood-system - - complete-system-of-neighbourhoods - - - concept: neron-severi-group - arity: 1 - en: neron severi group of $1 - property: function - area: "group theory" - mathml: - - "NS(x)" - urls: - - "https://mathworld.wolfram.com/Neron-SeveriGroup.html" - - "https://encyclopediaofmath.org/wiki/N%C3%A9ron-Severi_group" - - - concept: neron-tate-height - arity: 0 + property: symbol + subject-area: "probability theory" + mathml: + - "NB" + urls: + - "https://mathworld.wolfram.com/NegativeBinomialDistribution.html" + - "https://en.wikipedia.org/wiki/Negative_binomial_distribution" + - "https://www.encyclopediaofmath.org/index.php/Negative_binomial_distribution" + + - concept: negative-hypergeometric-distribution + arity: 1 + arguments: [a1] + speech: + en: negative hypergeometric distribution of a1 + property: "indexed symbol" + subject-area: "probability theory" + mathml: + - "NHG(x)" + urls: + - "https://en.wikipedia.org/wiki/Negative_hypergeometric_distribution" + - "https://www.encyclopediaofmath.org/index.php/Negative_hypergeometric_distribution" + + - concept: neighbourhood + arity: 2 + arguments: [a1, a2] + speech: + en: neighbourhood of a2 in a1 + property: "indexed function, function" + subject-area: "graph theory" + mathml: + - "Nv(G)" + notation: "msub N a1 ( a2 )" + notationa: "mrow N ( a1" + urls: + - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)" + alias: + - open-neighbourhood + + - concept: neighbourhood-filter + arity: 1 + arguments: [a1] + speech: + en: neighbourhood filter of a1 + property: function + subject-area: "topology" + mathml: + - "𝒩(x)" + urls: + - "https://en.wikipedia.org/wiki/Neighbourhood_system" + alias: + - neighbourhood-system + - complete-system-of-neighbourhoods + + - concept: neron-severi-group + arity: 1 + arguments: [a1] + speech: + en: neron severi group of a1 + property: function + subject-area: "group theory" + mathml: + - "NS(x)" + urls: + - "https://mathworld.wolfram.com/Neron-SeveriGroup.html" + - "https://encyclopediaofmath.org/wiki/N%C3%A9ron-Severi_group" + + - concept: neron-tate-height + arity: 0 + arguments: [] + speech: en: neron tate height - property: symbol - area: "number theory" - mathml: - - "h^" - urls: - - "https://en.wikipedia.org/wiki/N%C3%A9ron%E2%80%93Tate_height" - alias: - - canonical-height - - - concept: nerve - arity: 1 - en: nerve of $1 - property: function - area: "category theory" - mathml: - - "N(x)" - urls: - - "https://mathworld.wolfram.com/Nerve.html" - - "https://en.wikipedia.org/wiki/Nerve_(category_theory)" - - "https://ncatlab.org/nlab/show/nerve" - - - concept: nome - arity: 1 - en: nome of $1 - property: function - area: "special functions" - mathml: - - "q(x)" - urls: - - "https://mathworld.wolfram.com/Nome.html" - - "https://en.wikipedia.org/wiki/Nome_(mathematics)" - - - concept: non-oriented-angle - arity: 1 - en: non oriented angle of $1 - property: prefix - area: "geometry" - mathml: - - "∠x" - urls: - - "https://en.wikipedia.org/wiki/Orientation_(vector_space)" - - "https://en.wikipedia.org/wiki/Euclidean_space#Angle" - alias: - - angle - - - concept: nor - arity: 2 - en: $1 nor $2 - property: infix - area: "logic" - mathml: - - "X↓Y" - urls: - - "https://mathworld.wolfram.com/Nor.html" - - "https://mathworld.wolfram.com/NOR.html" - alias: - - joint-denial - - - concept: norm - arity: 1 - en: norm of $1 - property: fenced - area: "linear algebra" - mathml: - - "‖x‖" - notationa: "mrow | $1" - urls: - - "https://mathworld.wolfram.com/Norm.html" - - "https://en.wikipedia.org/wiki/Norm_(mathematics)" - - "https://en.wikipedia.org/wiki/Norm_(abelian_group)" - - "https://ncatlab.org/nlab/show/norm" - - "https://www.encyclopediaofmath.org/index.php/Norm" - - - concept: normalizer - arity: 1 - en: normalizer of $1 - property: function - area: "group theory" - mathml: - - "Nx" - urls: - - "https://mathworld.wolfram.com/Normalizer.html" - - "https://en.wikipedia.org/wiki/Centralizer_and_normalizer" - - "https://ncatlab.org/nlab/show/normalizer" - - - concept: not-divisible-by - arity: 2 - en: $1 not divisible by $2 - property: infix - area: "number theory" - mathml: - - "X∤Y" - urls: - - "https://en.wikipedia.org/wiki/Divisor" - - - concept: null-graph - arity: 1 - en: null graph of order $1 - property: symbol - area: "graph theory" - mathml: - - "K¯n" - urls: - - "https://mathworld.wolfram.com/NullGraph.html" - - "https://en.wikipedia.org/wiki/Null_graph" - - "https://en.wikipedia.org/wiki/Order-zero_graph" - alias: - - edgeless-graph - - - concept: numerical-part - arity: 1 - en: numerical part of $1 - property: fenced - area: "SI units" - mathml: - - "{x}" - urls: - - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values" - - - concept: object - arity: 1 - en: object of $1 - property: prefix - area: "category theory" - mathml: - - "Obj(x)" - urls: - - "https://mathworld.wolfram.com/Object.html" - - "https://en.wikipedia.org/wiki/Lattice-based_access_control" - - "https://ncatlab.org/nlab/show/object" - - - concept: octant - arity: 3 - en: octant of $1, $2 and $3 - property: fenced - area: "euclidean solid geometry" - mathml: - - "(±,±,±)" - urls: - - "https://mathworld.wolfram.com/Octant.html" - - "https://en.wikipedia.org/wiki/Octant_(plane_geometry)" - - "https://en.wikipedia.org/wiki/Octant_(solid_geometry)" - - "https://www.encyclopediaofmath.org/index.php/Octant" - - - concept: octonions - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "h^" + urls: + - "https://en.wikipedia.org/wiki/N%C3%A9ron%E2%80%93Tate_height" + alias: + - canonical-height + + - concept: nerve + arity: 1 + arguments: [a1] + speech: + en: nerve of a1 + property: function + subject-area: "category theory" + mathml: + - "N(x)" + urls: + - "https://mathworld.wolfram.com/Nerve.html" + - "https://en.wikipedia.org/wiki/Nerve_(category_theory)" + - "https://ncatlab.org/nlab/show/nerve" + + - concept: nome + arity: 1 + arguments: [a1] + speech: + en: nome of a1 + property: function + subject-area: "special functions" + mathml: + - "q(x)" + urls: + - "https://mathworld.wolfram.com/Nome.html" + - "https://en.wikipedia.org/wiki/Nome_(mathematics)" + + - concept: non-oriented-angle + arity: 1 + arguments: [a1] + speech: + en: non oriented angle of a1 + property: prefix + subject-area: "geometry" + mathml: + - "∠x" + urls: + - "https://en.wikipedia.org/wiki/Orientation_(vector_space)" + - "https://en.wikipedia.org/wiki/Euclidean_space#Angle" + alias: + - angle + + - concept: nor + arity: 2 + arguments: [a1, a2] + speech: + en: a1 nor a2 + property: infix + subject-area: "logic" + mathml: + - "X↓Y" + urls: + - "https://mathworld.wolfram.com/Nor.html" + - "https://mathworld.wolfram.com/NOR.html" + alias: + - joint-denial + + - concept: norm + arity: 1 + arguments: [a1] + speech: + en: norm of a1 + property: fenced + subject-area: "linear algebra" + mathml: + - "‖x‖" + notationa: "mrow | a1" + urls: + - "https://mathworld.wolfram.com/Norm.html" + - "https://en.wikipedia.org/wiki/Norm_(mathematics)" + - "https://en.wikipedia.org/wiki/Norm_(abelian_group)" + - "https://ncatlab.org/nlab/show/norm" + - "https://www.encyclopediaofmath.org/index.php/Norm" + + - concept: normalizer + arity: 1 + arguments: [a1] + speech: + en: normalizer of a1 + property: function + subject-area: "group theory" + mathml: + - "Nx" + urls: + - "https://mathworld.wolfram.com/Normalizer.html" + - "https://en.wikipedia.org/wiki/Centralizer_and_normalizer" + - "https://ncatlab.org/nlab/show/normalizer" + + - concept: not-divisible-by + arity: 2 + arguments: [a1, a2] + speech: + en: a1 not divisible by a2 + property: infix + subject-area: "number theory" + mathml: + - "X∤Y" + urls: + - "https://en.wikipedia.org/wiki/Divisor" + + - concept: null-graph + arity: 1 + arguments: [a1] + speech: + en: null graph of order a1 + property: symbol + subject-area: "graph theory" + mathml: + - "K¯n" + urls: + - "https://mathworld.wolfram.com/NullGraph.html" + - "https://en.wikipedia.org/wiki/Null_graph" + - "https://en.wikipedia.org/wiki/Order-zero_graph" + alias: + - edgeless-graph + + - concept: numerical-part + arity: 1 + arguments: [a1] + speech: + en: numerical part of a1 + property: fenced + subject-area: "SI units" + mathml: + - "{x}" + urls: + - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values" + + - concept: object + arity: 1 + arguments: [a1] + speech: + en: object of a1 + property: prefix + subject-area: "category theory" + mathml: + - "Obj(x)" + urls: + - "https://mathworld.wolfram.com/Object.html" + - "https://en.wikipedia.org/wiki/Lattice-based_access_control" + - "https://ncatlab.org/nlab/show/object" + + - concept: octant + arity: 3 + arguments: [a1, a2, a3] + speech: + en: octant of a1, a2 and a3 + property: fenced + subject-area: "euclidean solid geometry" + mathml: + - "(±,±,±)" + urls: + - "https://mathworld.wolfram.com/Octant.html" + - "https://en.wikipedia.org/wiki/Octant_(plane_geometry)" + - "https://en.wikipedia.org/wiki/Octant_(solid_geometry)" + - "https://www.encyclopediaofmath.org/index.php/Octant" + + - concept: octonions + arity: 0 + arguments: [] + speech: en: octonions - property: symbol - area: "compositional algebra" - mathml: - - "𝕆" - - "O" - urls: - - "https://mathworld.wolfram.com/Octonion.html" - - "https://en.wikipedia.org/wiki/Octonion" - - "https://ncatlab.org/nlab/show/octonion" - - "https://www.encyclopediaofmath.org/index.php/Octonion" - alias: - - cayley-numbers - - - concept: odds-ratio - arity: 0 + property: symbol + subject-area: "compositional algebra" + mathml: + - "𝕆" + - "O" + urls: + - "https://mathworld.wolfram.com/Octonion.html" + - "https://en.wikipedia.org/wiki/Octonion" + - "https://ncatlab.org/nlab/show/octonion" + - "https://www.encyclopediaofmath.org/index.php/Octonion" + alias: + - cayley-numbers + + - concept: odds-ratio + arity: 0 + arguments: [] + speech: en: odds ratio - property: symbol - area: "statistics" - mathml: - - "OR" - urls: - - "https://en.wikipedia.org/wiki/Odds_ratio" - - - concept: onsager-machlup-function - arity: 1 - en: onsager machlup function of $1 - property: function - area: "functional analysis" - mathml: - - "L(x)" - urls: - - "https://en.wikipedia.org/wiki/Onsager%E2%80%93Machlup_function" - - "https://www.encyclopediaofmath.org/index.php/Onsager-Machlup_function" - - - - concept: open-ball - arity: 2 - en: open ball $1 $2 - property: mixfix - area: "topology" - mathml: - - "Br(p)" - urls: - - "https://mathworld.wolfram.com/OpenBall.html" - - "https://en.wikipedia.org/wiki/Ball_(mathematics)" - alias: - - open-metric-ball - - - concept: open-interval - arity: 2 + property: symbol + subject-area: "statistics" + mathml: + - "OR" + urls: + - "https://en.wikipedia.org/wiki/Odds_ratio" + + - concept: onsager-machlup-function + arity: 1 + arguments: [a1] + speech: + en: onsager machlup function of a1 + property: function + subject-area: "functional analysis" + mathml: + - "L(x)" + urls: + - "https://en.wikipedia.org/wiki/Onsager%E2%80%93Machlup_function" + - "https://www.encyclopediaofmath.org/index.php/Onsager-Machlup_function" + + + - concept: open-ball + arity: 2 + arguments: [a1, a2] + speech: + en: open ball a1 a2 + property: mixfix + subject-area: "topology" + mathml: + - "Br(p)" + urls: + - "https://mathworld.wolfram.com/OpenBall.html" + - "https://en.wikipedia.org/wiki/Ball_(mathematics)" + alias: + - open-metric-ball + + - concept: open-interval + arity: 2 + arguments: [a1, a2] + speech: en: open interval - property: fenced - area: "algebra" - mathml: - - "(x,y)" - - "]x,y[" - urls: - - "https://mathworld.wolfram.com/OpenInterval.html" - - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r28" - - - concept: open-real-interval - arity: 2 - en: open real interval $1 to $2 - property: fenced - area: "algebra" - mathml: - - "(x,y)" - urls: - - "https://proofwiki.org/wiki/Definition: Real_Interval/Open" - - - concept: opposite - arity: 1 - en: opposite of $1 - property: msup - area: "category theory,, group theory" - mathml: - - "Xop" - urls: - - "https://en.wikipedia.org/wiki/Opposite_category" - - "https://ncatlab.org/nlab/show/opposite+category" - - "https://en.wikipedia.org/wiki/Opposite_group" - - "https://en.wikipedia.org/wiki/Opposite_ring" - alias: - - dual - - - concept: opposite-charge - arity: 2 - en: $1 opposite charge $2 - property: infix - area: "physics" - mathml: - - "X⇅Y" - urls: - - "https://youtu.be/HZ7a9YkF204?t=4657" - - - concept: or-product - arity: 2 - en: $1 or product $2 - property: infix - area: "graph theory" - mathml: - - "X*Y" - urls: - - "https://en.wikipedia.org/wiki/Graph_product" - alias: - - disjunctive-product - - co-normal-product - - - concept: order-of-group - arity: 1 - en: order of group of $1 - property: "function, fenced" - area: "group theory" - mathml: - - "ordX" - - "|x|" - urls: - - "https://en.wikipedia.org/wiki/Order_(group_theory))" - - - concept: orthocomplement - arity: 1 - en: orthocomplement of $1 - property: msup - area: "lattice theory" - mathml: - - "X⊥" - urls: - - "https://en.wikipedia.org/wiki/Complemented_lattice" - - - concept: orthogonal - arity: 2 - en: $1 orthogonal $2 - property: infix - area: "geometry,, algebra" - mathml: - - "X⊥Y" - urls: - - "https://mathworld.wolfram.com/Orthogonal.html" - - "https://en.1wikipedia.org/wiki/Orthogonal_functions" - - "https://en.wikipedia.org/wiki/Orthogonality_(term_rewriting)" - - "https://en.wikipedia.org/wiki/Orthogonality" - - "https://ncatlab.org/nlab/show/orthogonality" - - "https://www.encyclopediaofmath.org/index.php/Orthogonality" - alias: - - perpendicular - - - concept: orthogonal-group - arity: 1 - en: orthogonal group of $1 - property: function - area: "group theory" - mathml: - - "O(x)" - urls: - - "https://mathworld.wolfram.com/OrthogonalGroup.html" - - "https://en.wikipedia.org/wiki/Orthogonal_group" - - "https://en.wikipedia.org/wiki/Special_orthogonal_Lie_algebra" - - "https://ncatlab.org/nlab/show/orthogonal+group" - - "https://www.encyclopediaofmath.org/index.php/Orthogonal_group" - - - concept: outer-automorphism-group - arity: 1 - en: outer automorphism group of $1 - property: function - area: "abstract algebra" - mathml: - - "Out(x)" - urls: - - "https://mathworld.wolfram.com/OuterAutomorphismGroup.html" - - "https://en.wikipedia.org/wiki/Outer_automorphism_group" - alias: - - outer-automorphism - - - concept: outer-jordan-measure - arity: 1 - en: outer jordan measure of $1 - property: function - area: "measure theory" - mathml: - - "m*(N)" - urls: - - "https://mathworld.wolfram.com/JordanMeasure.html" - - "https://en.wikipedia.org/wiki/Jordan_measure" - - "https://www.encyclopediaofmath.org/index.php/Jordan_measure" - - - concept: outer-product - arity: 2 - en: $1 outer product $2 - property: infix - area: "linear algebra" - mathml: - - "X⊗Y" - urls: - - "https://mathworld.wolfram.com/OuterProduct.html" - - "https://en.wikipedia.org/wiki/Outer_product" - - "https://en.wikipedia.org/wiki/Tensor_product" - - - concept: p-core - arity: 1 - en: p core of $1 - property: function - area: "group theory" - mathml: - - "Op(G)" - urls: - - "https://en.wikipedia.org/wiki/Core_(group)" - - "https://en.wikipedia.org/wiki/P-soluble_group" - - "https://en.wikipedia.org/wiki/P-core" - - "https://en.wikipedia.org/wiki/Upper_p-series" - - - concept: pade-approximant - arity: 3 - en: pade approximant of $1, $2 and $3 - property: mixfix - area: "numerical analysis" - mathml: - - "[X/Y]f" - urls: - - "https://dlmf.nist.gov/3.11#SS4.p1" - - "https://mathworld.wolfram.com/PadeApproximant.html" - - "https://en.wikipedia.org/wiki/Pad%C3%A9_approximant" - - - concept: padovan-sequence - arity: 1 - en: padovan sequence of $1 - property: function - area: "number theory" - mathml: - - "P(x)" - urls: - - "https://mathworld.wolfram.com/PadovanSequence.html" - - "https://en.wikipedia.org/wiki/Padovan_sequence" - - - concept: paraboloidal-coordinate - arity: 3 - en: paraboloidal coordinate of $1, $2 and $3 - property: fenced - area: "geometry" - mathml: - - "(a,b,c)" - urls: - - "https://mathworld.wolfram.com/ParaboloidalCoordinates.html" - - "https://en.wikipedia.org/wiki/Paraboloidal_coordinates" - - "https://www.encyclopediaofmath.org/index.php/Paraboloidal_coordinates" - - - concept: parallel - arity: 2 - en: $1 parallel $2 - property: infix - area: "geometry" - mathml: - - "X∥Y" - urls: - - "https://mathworld.wolfram.com/Parallel.html" - - "https://en.wikipedia.org/wiki/Parallel_(geometry)" - - "https://en.wikipedia.org/wiki/Parallel_curve" - - - concept: parallel-morphism - arity: 2 + property: fenced + subject-area: "algebra" + mathml: + - "(x,y)" + - "]x,y[" + urls: + - "https://mathworld.wolfram.com/OpenInterval.html" + - "https://dlmf.nist.gov/front/introduction#Sx4.p1.t1.r28" + + - concept: open-real-interval + arity: 2 + arguments: [a1, a2] + speech: + en: open real interval a1 to a2 + property: fenced + subject-area: "algebra" + mathml: + - "(x,y)" + urls: + - "https://proofwiki.org/wiki/Definition: Real_Interval/Open" + + - concept: opposite + arity: 1 + arguments: [a1] + speech: + en: opposite of a1 + property: msup + subject-area: "category theory,, group theory" + mathml: + - "Xop" + urls: + - "https://en.wikipedia.org/wiki/Opposite_category" + - "https://ncatlab.org/nlab/show/opposite+category" + - "https://en.wikipedia.org/wiki/Opposite_group" + - "https://en.wikipedia.org/wiki/Opposite_ring" + alias: + - dual + + - concept: opposite-charge + arity: 2 + arguments: [a1, a2] + speech: + en: a1 opposite charge a2 + property: infix + subject-area: "physics" + mathml: + - "X⇅Y" + urls: + - "https://youtu.be/HZ7a9YkF204?t=4657" + + - concept: or-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 or product a2 + property: infix + subject-area: "graph theory" + mathml: + - "X*Y" + urls: + - "https://en.wikipedia.org/wiki/Graph_product" + alias: + - disjunctive-product + - co-normal-product + + - concept: order-of-group + arity: 1 + arguments: [a1] + speech: + en: order of group of a1 + property: "function, fenced" + subject-area: "group theory" + mathml: + - "ordX" + - "|x|" + urls: + - "https://en.wikipedia.org/wiki/Order_(group_theory))" + + - concept: orthocomplement + arity: 1 + arguments: [a1] + speech: + en: orthocomplement of a1 + property: msup + subject-area: "lattice theory" + mathml: + - "X⊥" + urls: + - "https://en.wikipedia.org/wiki/Complemented_lattice" + + - concept: orthogonal + arity: 2 + arguments: [a1, a2] + speech: + en: a1 orthogonal a2 + property: infix + subject-area: "geometry,, algebra" + mathml: + - "X⊥Y" + urls: + - "https://mathworld.wolfram.com/Orthogonal.html" + - "https://en.1wikipedia.org/wiki/Orthogonal_functions" + - "https://en.wikipedia.org/wiki/Orthogonality_(term_rewriting)" + - "https://en.wikipedia.org/wiki/Orthogonality" + - "https://ncatlab.org/nlab/show/orthogonality" + - "https://www.encyclopediaofmath.org/index.php/Orthogonality" + alias: + - perpendicular + + - concept: orthogonal-group + arity: 1 + arguments: [a1] + speech: + en: orthogonal group of a1 + property: function + subject-area: "group theory" + mathml: + - "O(x)" + urls: + - "https://mathworld.wolfram.com/OrthogonalGroup.html" + - "https://en.wikipedia.org/wiki/Orthogonal_group" + - "https://en.wikipedia.org/wiki/Special_orthogonal_Lie_algebra" + - "https://ncatlab.org/nlab/show/orthogonal+group" + - "https://www.encyclopediaofmath.org/index.php/Orthogonal_group" + + - concept: outer-automorphism-group + arity: 1 + arguments: [a1] + speech: + en: outer automorphism group of a1 + property: function + subject-area: "abstract algebra" + mathml: + - "Out(x)" + urls: + - "https://mathworld.wolfram.com/OuterAutomorphismGroup.html" + - "https://en.wikipedia.org/wiki/Outer_automorphism_group" + alias: + - outer-automorphism + + - concept: outer-jordan-measure + arity: 1 + arguments: [a1] + speech: + en: outer jordan measure of a1 + property: function + subject-area: "measure theory" + mathml: + - "m*(N)" + urls: + - "https://mathworld.wolfram.com/JordanMeasure.html" + - "https://en.wikipedia.org/wiki/Jordan_measure" + - "https://www.encyclopediaofmath.org/index.php/Jordan_measure" + + - concept: outer-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 outer product a2 + property: infix + subject-area: "linear algebra" + mathml: + - "X⊗Y" + urls: + - "https://mathworld.wolfram.com/OuterProduct.html" + - "https://en.wikipedia.org/wiki/Outer_product" + - "https://en.wikipedia.org/wiki/Tensor_product" + + - concept: p-core + arity: 1 + arguments: [a1] + speech: + en: p core of a1 + property: function + subject-area: "group theory" + mathml: + - "Op(G)" + urls: + - "https://en.wikipedia.org/wiki/Core_(group)" + - "https://en.wikipedia.org/wiki/P-soluble_group" + - "https://en.wikipedia.org/wiki/P-core" + - "https://en.wikipedia.org/wiki/Upper_p-series" + + - concept: pade-approximant + arity: 3 + arguments: [a1, a2, a3] + speech: + en: pade approximant of a1, a2 and a3 + property: mixfix + subject-area: "numerical analysis" + mathml: + - "[X/Y]f" + urls: + - "https://dlmf.nist.gov/3.11#SS4.p1" + - "https://mathworld.wolfram.com/PadeApproximant.html" + - "https://en.wikipedia.org/wiki/Pad%C3%A9_approximant" + + - concept: padovan-sequence + arity: 1 + arguments: [a1] + speech: + en: padovan sequence of a1 + property: function + subject-area: "number theory" + mathml: + - "P(x)" + urls: + - "https://mathworld.wolfram.com/PadovanSequence.html" + - "https://en.wikipedia.org/wiki/Padovan_sequence" + + - concept: paraboloidal-coordinate + arity: 3 + arguments: [a1, a2, a3] + speech: + en: paraboloidal coordinate of a1, a2 and a3 + property: fenced + subject-area: "geometry" + mathml: + - "(a,b,c)" + urls: + - "https://mathworld.wolfram.com/ParaboloidalCoordinates.html" + - "https://en.wikipedia.org/wiki/Paraboloidal_coordinates" + - "https://www.encyclopediaofmath.org/index.php/Paraboloidal_coordinates" + + - concept: parallel + arity: 2 + arguments: [a1, a2] + speech: + en: a1 parallel a2 + property: infix + subject-area: "geometry" + mathml: + - "X∥Y" + urls: + - "https://mathworld.wolfram.com/Parallel.html" + - "https://en.wikipedia.org/wiki/Parallel_(geometry)" + - "https://en.wikipedia.org/wiki/Parallel_curve" + + - concept: parallel-morphism + arity: 2 + arguments: [a1, a2] + speech: en: parallel morphism - property: embellished infix - area: "category theory" - mathml: - - "x⇉y" - urls: - - "https://ncatlab.org/nlab/show/parallel+morphisms" - - - concept: partial-charge - arity: 1 + property: embellished infix + subject-area: "category theory" + mathml: + - "x⇉y" + urls: + - "https://ncatlab.org/nlab/show/parallel+morphisms" + + - concept: partial-charge + arity: 1 + arguments: [a1] + speech: en: partial charge - property: symbol - area: "chemistry" - mathml: - - "δ+" - - "δ+" - urls: - - "https://en.wikipedia.org/wiki/Partial_charge" - - "https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/08._Basic_Concepts_of_Chemical_Bonding/8.S%3A_Basic_Concepts_of_Chemical_Bonding_(Summary)" - alias: - - delta-sign - - - concept: partition - arity: 2 - en: $1 partition $2 - property: infix - area: "number theory" - mathml: - - "X⊢Y" - urls: - - "https://mathworld.wolfram.com/Partition.html" - - "https://mathworld.wolfram.com/FrequencyRepresentation.html" - - "https://en.wikipedia.org/wiki/Partition_(number_theory)" - - "https://en.wikipedia.org/wiki/List_of_partition_topics" - - - concept: partition-frequency-representation - arity: ">=0" - en: "partition $1 sup $2, $2 sup $3, ..." - property: mixfix - area: "number theory" - mathml: - - "(1a2b3c)" - urls: - - "https://mathworld.wolfram.com/FrequencyRepresentation.html" - - - concept: partition-function - arity: 1 - en: partition function of $1 - property: function - area: "number theory" - mathml: - - "p(x)" - urls: - - "https://en.wikipedia.org/wiki/Partition_(number_theory)" - - - concept: pauli-matrix - arity: 1 - en: pauli matrix of $1 - property: "indexed symbol" - area: "mathematical physics" - mathml: - - "σG" - urls: - - "https://mathworld.wolfram.com/PauliMatrices.html" - - "https://mathworld.wolfram.com/PauliMatrix.html" - - "https://en.wikipedia.org/wiki/Pauli_matrices" - - "https://www.encyclopediaofmath.org/index.php/Pauli_matrices" - - - concept: peclet-number - arity: 1 - en: peclet number of $1 - property: "indexed symbol" - area: "fluid dynamics" - mathml: - - "Pex" - urls: - - "https://en.wikipedia.org/wiki/P%C3%A9clet_number" - - "https://www.encyclopediaofmath.org/index.php/Peclet_number" - - "https://www.encyclopediaofmath.org/index.php/Péclet_number" - - - concept: peirce-arrow - arity: 2 - en: $1 peirce arrow $2 - property: infix - area: "logic" - mathml: - - "X↓Y" - urls: - - "https://www.encyclopediaofmath.org/index.php/Peirce_arrow" - - - concept: pell-number - arity: 1 + property: symbol + subject-area: "chemistry" + mathml: + - "δ+" + - "δ+" + urls: + - "https://en.wikipedia.org/wiki/Partial_charge" + - "https://chem.libretexts.org/Bookshelves/General_Chemistry/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)/08._Basic_Concepts_of_Chemical_Bonding/8.S%3A_Basic_Concepts_of_Chemical_Bonding_(Summary)" + alias: + - delta-sign + + - concept: partition + arity: 2 + arguments: [a1, a2] + speech: + en: a1 partition a2 + property: infix + subject-area: "number theory" + mathml: + - "X⊢Y" + urls: + - "https://mathworld.wolfram.com/Partition.html" + - "https://mathworld.wolfram.com/FrequencyRepresentation.html" + - "https://en.wikipedia.org/wiki/Partition_(number_theory)" + - "https://en.wikipedia.org/wiki/List_of_partition_topics" + + - concept: partition-frequency-representation + arity: ">=0" + speech: + en: "partition a1 sup a2, a2 sup a3, ..." + property: mixfix + subject-area: "number theory" + mathml: + - "(1a2b3c)" + urls: + - "https://mathworld.wolfram.com/FrequencyRepresentation.html" + + - concept: partition-function + arity: 1 + arguments: [a1] + speech: + en: partition function of a1 + property: function + subject-area: "number theory" + mathml: + - "p(x)" + urls: + - "https://en.wikipedia.org/wiki/Partition_(number_theory)" + + - concept: pauli-matrix + arity: 1 + arguments: [a1] + speech: + en: pauli matrix of a1 + property: "indexed symbol" + subject-area: "mathematical physics" + mathml: + - "σG" + urls: + - "https://mathworld.wolfram.com/PauliMatrices.html" + - "https://mathworld.wolfram.com/PauliMatrix.html" + - "https://en.wikipedia.org/wiki/Pauli_matrices" + - "https://www.encyclopediaofmath.org/index.php/Pauli_matrices" + + - concept: peclet-number + arity: 1 + arguments: [a1] + speech: + en: peclet number of a1 + property: "indexed symbol" + subject-area: "fluid dynamics" + mathml: + - "Pex" + urls: + - "https://en.wikipedia.org/wiki/P%C3%A9clet_number" + - "https://www.encyclopediaofmath.org/index.php/Peclet_number" + - "https://www.encyclopediaofmath.org/index.php/Péclet_number" + + - concept: peirce-arrow + arity: 2 + arguments: [a1, a2] + speech: + en: a1 peirce arrow a2 + property: infix + subject-area: "logic" + mathml: + - "X↓Y" + urls: + - "https://www.encyclopediaofmath.org/index.php/Peirce_arrow" + + - concept: pell-number + arity: 1 + arguments: [a1] + speech: en: pell number - property: symbol - area: "number theory" - mathml: - - "Px" - urls: - - "https://mathworld.wolfram.com/PellNumber.html" - - "https://en.wikipedia.org/wiki/Pell_number" - - - concept: pell-luca-number - arity: 1 + property: symbol + subject-area: "number theory" + mathml: + - "Px" + urls: + - "https://mathworld.wolfram.com/PellNumber.html" + - "https://en.wikipedia.org/wiki/Pell_number" + + - concept: pell-luca-number + arity: 1 + arguments: [a1] + speech: en: pell luca number - property: symbol - area: "number theory" - mathml: - - "Qx" - urls: - - "https://mathworld.wolfram.com/Pell-LucasNumber.html" - - "https://en.wikipedia.org/wiki/Pell_number" - - - concept: periodic-continued-fraction - arity: 1 - en: periodic continued fraction $1 - property: mfrac - area: "mathematical analysis" - mathml: - - "a0+1a1+⋱" - urls: - - "https://mathworld.wolfram.com/PeriodicContinuedFraction.html" - - "https://en.wikipedia.org/wiki/Periodic_continued_fraction" - - - concept: permanent - arity: 1 - en: permanent of $1 - property: function - area: "linear algebra" - mathml: - - "perm(x)" - urls: - - "https://mathworld.wolfram.com/Permanent.html" - - "https://en.wikipedia.org/wiki/Permanent" - - "https://www.encyclopediaofmath.org/index.php/Permanent" - - - concept: permutation - arity: 1 - en: permutation $1 - property: fenced, mtable, mixfix - area: "combinatorics" - mathml: - - "1234524513" - - "(124)(35)" - urls: - - "https://mathworld.wolfram.com/Permutation.html" - - "https://en.wikipedia.org/wiki/Permutation" - - "https://en.wikipedia.org/wiki/Permutation_(music)" - - "https://ncatlab.org/nlab/show/permutation" - - "https://www.encyclopediaofmath.org/index.php/Permutation" - - - concept: perpendicular - arity: 2 - en: $1 perpendicular $2 - property: infix - area: "geometry" - mathml: - - "X⟂Y" - urls: - - "https://en.wikipedia.org/wiki/Perpendicular" - - "https://www.encyclopediaofmath.org/index.php/Perpendicular" - - - concept: perrin-sequence - arity: 1 - en: perrin sequence of $1 - property: function - area: "number theory" - mathml: - - "P(x)" - urls: - - "https://mathworld.wolfram.com/PerrinNumber.html" - - "https://en.wikipedia.org/wiki/Perrin_number" - - - concept: pfaffian - arity: 1 - en: pfaffian of $1 - property: function - area: "multilinear algebra" - mathml: - - "PfX" - - "pfX" - urls: - - "https://mathworld.wolfram.com/Pfaffian.html" - - "https://en.wikipedia.org/wiki/Pfaffian" - - "https://ncatlab.org/nlab/show/Pfaffian" - - "https://ncatlab.org/nlab/show/Pfaffian" - - "https://www.encyclopediaofmath.org/index.php/Pfaffian" - - - concept: ph - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "Qx" + urls: + - "https://mathworld.wolfram.com/Pell-LucasNumber.html" + - "https://en.wikipedia.org/wiki/Pell_number" + + - concept: periodic-continued-fraction + arity: 1 + arguments: [a1] + speech: + en: periodic continued fraction a1 + property: mfrac + subject-area: "mathematical analysis" + mathml: + - "a0+1a1+⋱" + urls: + - "https://mathworld.wolfram.com/PeriodicContinuedFraction.html" + - "https://en.wikipedia.org/wiki/Periodic_continued_fraction" + + - concept: permanent + arity: 1 + arguments: [a1] + speech: + en: permanent of a1 + property: function + subject-area: "linear algebra" + mathml: + - "perm(x)" + urls: + - "https://mathworld.wolfram.com/Permanent.html" + - "https://en.wikipedia.org/wiki/Permanent" + - "https://www.encyclopediaofmath.org/index.php/Permanent" + + - concept: permutation + arity: 1 + arguments: [a1] + speech: + en: permutation a1 + property: fenced, mtable, mixfix + subject-area: "combinatorics" + mathml: + - "1234524513" + - "(124)(35)" + urls: + - "https://mathworld.wolfram.com/Permutation.html" + - "https://en.wikipedia.org/wiki/Permutation" + - "https://en.wikipedia.org/wiki/Permutation_(music)" + - "https://ncatlab.org/nlab/show/permutation" + - "https://www.encyclopediaofmath.org/index.php/Permutation" + + - concept: perpendicular + arity: 2 + arguments: [a1, a2] + speech: + en: a1 perpendicular a2 + property: infix + subject-area: "geometry" + mathml: + - "X⟂Y" + urls: + - "https://en.wikipedia.org/wiki/Perpendicular" + - "https://www.encyclopediaofmath.org/index.php/Perpendicular" + + - concept: perrin-sequence + arity: 1 + arguments: [a1] + speech: + en: perrin sequence of a1 + property: function + subject-area: "number theory" + mathml: + - "P(x)" + urls: + - "https://mathworld.wolfram.com/PerrinNumber.html" + - "https://en.wikipedia.org/wiki/Perrin_number" + + - concept: pfaffian + arity: 1 + arguments: [a1] + speech: + en: pfaffian of a1 + property: function + subject-area: "multilinear algebra" + mathml: + - "PfX" + - "pfX" + urls: + - "https://mathworld.wolfram.com/Pfaffian.html" + - "https://en.wikipedia.org/wiki/Pfaffian" + - "https://ncatlab.org/nlab/show/Pfaffian" + - "https://ncatlab.org/nlab/show/Pfaffian" + - "https://www.encyclopediaofmath.org/index.php/Pfaffian" + + - concept: ph + arity: 0 + arguments: [] + speech: en: p h - property: symbol - area: "chemistry" - mathml: - - "pH" - urls: - - "https://en.wikipedia.org/wiki/PH" - alias: - - potential-of-hydrogen - - power-of-hydrogen - - - concept: phase - arity: 1 - en: phase of $1 - property: function - area: "physics" - mathml: - - "ϕX" - - "phX" - urls: - - "https://mathworld.wolfram.com/Phase.html" - - "https://en.wikipedia.org/wiki/Phase_(waves)" - - "https://dlmf.nist.gov/1.9#E7" - - "https://ncatlab.org/nlab/show/phase" - - - concept: phi-coefficient - arity: 0 + property: symbol + subject-area: "chemistry" + mathml: + - "pH" + urls: + - "https://en.wikipedia.org/wiki/PH" + alias: + - potential-of-hydrogen + - power-of-hydrogen + + - concept: phase + arity: 1 + arguments: [a1] + speech: + en: phase of a1 + property: function + subject-area: "physics" + mathml: + - "ϕX" + - "phX" + urls: + - "https://mathworld.wolfram.com/Phase.html" + - "https://en.wikipedia.org/wiki/Phase_(waves)" + - "https://dlmf.nist.gov/1.9#E7" + - "https://ncatlab.org/nlab/show/phase" + + - concept: phi-coefficient + arity: 0 + arguments: [] + speech: en: phi coefficient - property: symbol - area: "statistics" - mathml: - - "φ" - notationa: "msub r φ" - urls: - - "https://en.wikipedia.org/wiki/Phi_coefficient" - alias: - - mean-square-contingency-coefficient - - - concept: picard-group - arity: 1 - en: picard group of $1 - property: function - area: "group theory" - mathml: - - "Pic(x)" - urls: - - "https://mathworld.wolfram.com/PicardGroup.html" - - "https://en.wikipedia.org/wiki/Picard_group" - - "https://ncatlab.org/nlab/show/Picard+group" - - "https://www.encyclopediaofmath.org/index.php/Picard_group" - - - concept: planck-constant - arity: 0 + property: symbol + subject-area: "statistics" + mathml: + - "φ" + notationa: "msub r φ" + urls: + - "https://en.wikipedia.org/wiki/Phi_coefficient" + alias: + - mean-square-contingency-coefficient + + - concept: picard-group + arity: 1 + arguments: [a1] + speech: + en: picard group of a1 + property: function + subject-area: "group theory" + mathml: + - "Pic(x)" + urls: + - "https://mathworld.wolfram.com/PicardGroup.html" + - "https://en.wikipedia.org/wiki/Picard_group" + - "https://ncatlab.org/nlab/show/Picard+group" + - "https://www.encyclopediaofmath.org/index.php/Picard_group" + + - concept: planck-constant + arity: 0 + arguments: [] + speech: en: planck constant - property: constant - area: "physics" - mathml: - - "h" - - "ℎ" - urls: - - "https://en.wikipedia.org/wiki/Planck_constant" - - "https://ncatlab.org/nlab/show/Planck's+constant" - - "https://www.encyclopediaofmath.org/index.php/Planck_constant" - - - concept: plastic-constant - arity: 0 + property: constant + subject-area: "physics" + mathml: + - "h" + - "ℎ" + urls: + - "https://en.wikipedia.org/wiki/Planck_constant" + - "https://ncatlab.org/nlab/show/Planck's+constant" + - "https://www.encyclopediaofmath.org/index.php/Planck_constant" + + - concept: plastic-constant + arity: 0 + arguments: [] + speech: en: plastic constant - property: constant - area: "geometry" - mathml: - - "P" - - "p" - urls: - - "https://mathworld.wolfram.com/PlasticConstant.html" - - "https://en.wikipedia.org/wiki/Plastic_number" - alias: - - plastic-number - - platin-number - - minimal-pisot-number - - plastic-ratio - - siegel-number - - le-nombre-radiant - - - concept: playing-card-suit - arity: 1 + property: constant + subject-area: "geometry" + mathml: + - "P" + - "p" + urls: + - "https://mathworld.wolfram.com/PlasticConstant.html" + - "https://en.wikipedia.org/wiki/Plastic_number" + alias: + - plastic-number + - platin-number + - minimal-pisot-number + - plastic-ratio + - siegel-number + - le-nombre-radiant + + - concept: playing-card-suit + arity: 1 + arguments: [a1] + speech: en: playing card suit - property: unit - area: "game theory" - mathml: - - "♣" - - "♠" - - "♦" - - "♥" - urls: - - "https://en.wikipedia.org/wiki/Playing_card_suit" - - "https://en.wikipedia.org/wiki/Poker_probability" - - - - concept: plethysm - arity: 2 - en: plethysm $1 $2 - property: mixfix - area: "algebra" - mathml: - - "{λ}⊗{μ}" - urls: - - "https://mathworld.wolfram.com/Plethysm.html" - - "https://en.wikipedia.org/wiki/Plethysm" - - "https://ncatlab.org/nlab/show/plethysm" - - - concept: plucker-coordinate - arity: 2 + property: unit + subject-area: "game theory" + mathml: + - "♣" + - "♠" + - "♦" + - "♥" + urls: + - "https://en.wikipedia.org/wiki/Playing_card_suit" + - "https://en.wikipedia.org/wiki/Poker_probability" + + + - concept: plethysm + arity: 2 + arguments: [a1, a2] + speech: + en: plethysm a1 a2 + property: mixfix + subject-area: "algebra" + mathml: + - "{λ}⊗{μ}" + urls: + - "https://mathworld.wolfram.com/Plethysm.html" + - "https://en.wikipedia.org/wiki/Plethysm" + - "https://ncatlab.org/nlab/show/plethysm" + + - concept: plucker-coordinate + arity: 2 + arguments: [a1, a2] + speech: en: plucker coordinate - property: fenced - area: "geometry" - mathml: - - "(𝐝:𝐦)" - urls: - - "https://mathworld.wolfram.com/PlueckerCoordinates.html" - - "https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates" - - "https://www.encyclopediaofmath.org/index.php/Plücker_coordinates" - - - concept: pointwise-convergent - arity: 1 - en: $1 converges pointwise - property: postfix - area: "convergence" - mathml: - - "fpointwise" - urls: - - "https://mathworld.wolfram.com/PointwiseConvergence.html" - - "https://en.wikipedia.org/wiki/Pointwise_convergence" - - "https://www.encyclopediaofmath.org/index.php/Pointwise_convergence" - - - concept: poisson-bracket - arity: 2 + property: fenced + subject-area: "geometry" + mathml: + - "(𝐝:𝐦)" + urls: + - "https://mathworld.wolfram.com/PlueckerCoordinates.html" + - "https://en.wikipedia.org/wiki/Pl%C3%BCcker_coordinates" + - "https://www.encyclopediaofmath.org/index.php/Plücker_coordinates" + + - concept: pointwise-convergent + arity: 1 + arguments: [a1] + speech: + en: a1 converges pointwise + property: postfix + subject-area: "convergence" + mathml: + - "fpointwise" + urls: + - "https://mathworld.wolfram.com/PointwiseConvergence.html" + - "https://en.wikipedia.org/wiki/Pointwise_convergence" + - "https://www.encyclopediaofmath.org/index.php/Pointwise_convergence" + + - concept: poisson-bracket + arity: 2 + arguments: [a1, a2] + speech: en: poisson bracket - property: fenced - area: "classical mechanics" - mathml: - - "{x,y}" - urls: - - "https://mathworld.wolfram.com/PoissonBracket.html" - - "https://en.wikipedia.org/wiki/Poisson_bracket" - - "https://www.encyclopediaofmath.org/index.php/Poisson_brackets" - - - concept: poisson-distribution - arity: 0 + property: fenced + subject-area: "classical mechanics" + mathml: + - "{x,y}" + urls: + - "https://mathworld.wolfram.com/PoissonBracket.html" + - "https://en.wikipedia.org/wiki/Poisson_bracket" + - "https://www.encyclopediaofmath.org/index.php/Poisson_brackets" + + - concept: poisson-distribution + arity: 0 + arguments: [] + speech: en: poisson distribution - property: symbol - area: "probability theory" - mathml: - - "Pois" - urls: - - "https://mathworld.wolfram.com/PoissonDistribution.html" - - "https://en.wikipedia.org/wiki/Poisson_distribution" - - "https://en.wikipedia.org/wiki/Poisson_random_numbers" - - "https://www.encyclopediaofmath.org/index.php/Poisson_distribution" - - - concept: polar-set - arity: 1 - en: polar set of $1 - property: msup - area: "functional analysis" - mathml: - - "X°" - urls: - - "https://en.wikipedia.org/wiki/Polar_set" - - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" - - "https://www.encyclopediaofmath.org/index.php/Polar_set" - - - concept: pollaczek-polynomial - arity: 1 - en: $1th pollaczek polynomial - property: "indexed function" - area: "orthogonal polynomials" - mathml: - - "Pn(λ)" - urls: - - "https://mathworld.wolfram.com/PollaczekPolynomial.html" - - "https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek_polynomials" - - "https://dlmf.nist.gov/18.35#E4" - - - concept: polygamma-function - arity: 1 - en: polygamma function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "ψ(x)" - urls: - - "https://mathworld.wolfram.com/PolygammaFunction.html" - - "https://en.wikipedia.org/wiki/Polygamma_function" - - "https://dlmf.nist.gov/5.15" - - "https://dlmf.nist.gov/5.15" - - - concept: polynomial-ring - arity: 2 - en: polynomial ring $1 $2 - property: mixfix - area: "ring theory" - mathml: - - "R[x]" - urls: - - "https://en.wikipedia.org/wiki/Polynomial_ring#Definition_(univariate_case)" - alias: - - polynomial-algebra - - - concept: polylogarithm - arity: 1 - en: polylogarithm of $1 - property: "indexed function" - area: "special functions" - mathml: - - "Lix" - urls: - - "https://mathworld.wolfram.com/Polylogarithm.html" - - "https://en.wikipedia.org/wiki/Polylogarithm" - - "https://dlmf.nist.gov/25.12#ii" - - "https://dlmf.nist.gov/25.12#E10" - - "https://ncatlab.org/nlab/show/polylogarithm" - - - concept: pontrjagin-dual - arity: 1 - en: pontrjagin dual of $1 - property: mover - area: "harmonic analysis" - mathml: - - "G^" - urls: - - "https://ncatlab.org/nlab/show/Pontrjagin+dual" - - "https://en.wikipedia.org/wiki/Pontryagin_duality#Definition" - - - concept: pontryagin-class - arity: 1 - en: pontryagin class of $1 - property: "indexed symbol" - area: "differential topology" - mathml: - - "px" - urls: - - "https://mathworld.wolfram.com/PontryaginClass.html" - - "https://en.wikipedia.org/wiki/Pontryagin_class" - - "https://ncatlab.org/nlab/show/Pontryagin+class" - - "https://www.encyclopediaofmath.org/index.php/Pontryagin_class" - - - concept: positive-part - arity: 1 - en: positive part of $1 - property: msup, msub - area: "elementary mathematics" - mathml: - - "X+" - notationa: "msub $1 +" - urls: - - "https://mathworld.wolfram.com/PositiveElement.html" - - "https://en.wikipedia.org/wiki/Positive_and_negative_parts" - - "https://www.encyclopediaofmath.org/index.php/Positive_element" - - - concept: positivitiy-predicate - arity: 1 - en: positivitiy predicate of $1 - property: prefix - area: "predicative mathematics" - mathml: - - "◊x" - urls: - - "https://ncatlab.org/nlab/show/positive+element" - - - concept: post-canonical-system - arity: 3 - en: post canonical system $1 $2 $3 - property: fenced - area: "formal languages" - mathml: - - "(A,I,R)" - urls: - - "https://en.wikipedia.org/wiki/Post_canonical_system" - - "https://en.wikipedia.org/wiki/Tag_system" - - "https://www.encyclopediaofmath.org/index.php/Post_canonical_system" - - - concept: power-set - arity: 1 - en: power set of $1 - property: "function, msup" - area: "set theory" - mathml: - - "PX" - - "𝒫X" - - "ℙX" - - "℘X" - - "2X" - notationa: "msup 2 $1" - urls: - - "https://mathworld.wolfram.com/PowerSet.html" - - "https://en.wikipedia.org/wiki/Power_set" - - "https://ncatlab.org/nlab/show/power+set" - - - concept: preregular-space - arity: 0 + property: symbol + subject-area: "probability theory" + mathml: + - "Pois" + urls: + - "https://mathworld.wolfram.com/PoissonDistribution.html" + - "https://en.wikipedia.org/wiki/Poisson_distribution" + - "https://en.wikipedia.org/wiki/Poisson_random_numbers" + - "https://www.encyclopediaofmath.org/index.php/Poisson_distribution" + + - concept: polar-set + arity: 1 + arguments: [a1] + speech: + en: polar set of a1 + property: msup + subject-area: "functional analysis" + mathml: + - "X°" + urls: + - "https://en.wikipedia.org/wiki/Polar_set" + - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" + - "https://www.encyclopediaofmath.org/index.php/Polar_set" + + - concept: pollaczek-polynomial + arity: 1 + arguments: [a1] + speech: + en: a1th pollaczek polynomial + property: "indexed function" + subject-area: "orthogonal polynomials" + mathml: + - "Pn(λ)" + urls: + - "https://mathworld.wolfram.com/PollaczekPolynomial.html" + - "https://en.wikipedia.org/wiki/Meixner%E2%80%93Pollaczek_polynomials" + - "https://dlmf.nist.gov/18.35#E4" + + - concept: polygamma-function + arity: 1 + arguments: [a1] + speech: + en: polygamma function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "ψ(x)" + urls: + - "https://mathworld.wolfram.com/PolygammaFunction.html" + - "https://en.wikipedia.org/wiki/Polygamma_function" + - "https://dlmf.nist.gov/5.15" + - "https://dlmf.nist.gov/5.15" + + - concept: polynomial-ring + arity: 2 + arguments: [a1, a2] + speech: + en: polynomial ring a1 a2 + property: mixfix + subject-area: "ring theory" + mathml: + - "R[x]" + urls: + - "https://en.wikipedia.org/wiki/Polynomial_ring#Definition_(univariate_case)" + alias: + - polynomial-algebra + + - concept: polylogarithm + arity: 1 + arguments: [a1] + speech: + en: polylogarithm of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Lix" + urls: + - "https://mathworld.wolfram.com/Polylogarithm.html" + - "https://en.wikipedia.org/wiki/Polylogarithm" + - "https://dlmf.nist.gov/25.12#ii" + - "https://dlmf.nist.gov/25.12#E10" + - "https://ncatlab.org/nlab/show/polylogarithm" + + - concept: pontrjagin-dual + arity: 1 + arguments: [a1] + speech: + en: pontrjagin dual of a1 + property: mover + subject-area: "harmonic analysis" + mathml: + - "G^" + urls: + - "https://ncatlab.org/nlab/show/Pontrjagin+dual" + - "https://en.wikipedia.org/wiki/Pontryagin_duality#Definition" + + - concept: pontryagin-class + arity: 1 + arguments: [a1] + speech: + en: pontryagin class of a1 + property: "indexed symbol" + subject-area: "differential topology" + mathml: + - "px" + urls: + - "https://mathworld.wolfram.com/PontryaginClass.html" + - "https://en.wikipedia.org/wiki/Pontryagin_class" + - "https://ncatlab.org/nlab/show/Pontryagin+class" + - "https://www.encyclopediaofmath.org/index.php/Pontryagin_class" + + - concept: positive-part + arity: 1 + arguments: [a1] + speech: + en: positive part of a1 + property: msup, msub + subject-area: "elementary mathematics" + mathml: + - "X+" + notationa: "msub a1 +" + urls: + - "https://mathworld.wolfram.com/PositiveElement.html" + - "https://en.wikipedia.org/wiki/Positive_and_negative_parts" + - "https://www.encyclopediaofmath.org/index.php/Positive_element" + + - concept: positivitiy-predicate + arity: 1 + arguments: [a1] + speech: + en: positivitiy predicate of a1 + property: prefix + subject-area: "predicative mathematics" + mathml: + - "◊x" + urls: + - "https://ncatlab.org/nlab/show/positive+element" + + - concept: post-canonical-system + arity: 3 + arguments: [a1, a2, a3] + speech: + en: post canonical system a1 a2 a3 + property: fenced + subject-area: "formal languages" + mathml: + - "(A,I,R)" + urls: + - "https://en.wikipedia.org/wiki/Post_canonical_system" + - "https://en.wikipedia.org/wiki/Tag_system" + - "https://www.encyclopediaofmath.org/index.php/Post_canonical_system" + + - concept: power-set + arity: 1 + arguments: [a1] + speech: + en: power set of a1 + property: "function, msup" + subject-area: "set theory" + mathml: + - "PX" + - "𝒫X" + - "ℙX" + - "℘X" + - "2X" + notationa: "msup 2 a1" + urls: + - "https://mathworld.wolfram.com/PowerSet.html" + - "https://en.wikipedia.org/wiki/Power_set" + - "https://ncatlab.org/nlab/show/power+set" + + - concept: preregular-space + arity: 0 + arguments: [] + speech: en: preregular space - property: constant - area: "topology" - mathml: - - "R1" - urls: - - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions)s" - - - concept: present-value - arity: 0 + property: constant + subject-area: "topology" + mathml: + - "R1" + urls: + - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions)s" + + - concept: present-value + arity: 0 + arguments: [] + speech: en: present value - property: symbol - area: "economics" - mathml: - - "PV" - - "v" - urls: - - "https://mathworld.wolfram.com/PresentValue.html" - - "https://en.wikipedia.org/wiki/Present_value" - - - concept: prime-constant - arity: 0 + property: symbol + subject-area: "economics" + mathml: + - "PV" + - "v" + urls: + - "https://mathworld.wolfram.com/PresentValue.html" + - "https://en.wikipedia.org/wiki/Present_value" + + - concept: prime-constant + arity: 0 + arguments: [] + speech: en: prime constant - property: symbol - area: "number theory" - mathml: - - "P" - - "ρ" - urls: - - "https://mathworld.wolfram.com/PrimeConstant.html" - - "https://en.wikipedia.org/wiki/Prime_constant" - - - - - concept: prime-counting-function - arity: 1 - en: prime counting function of $1 - property: function - area: "number theory" - mathml: - - "π(x)" - urls: - - "https://mathworld.wolfram.com/PrimeCountingFunction.html" - - - concept: prime-difference-function - arity: 1 - en: prime difference function of $1 - property: "indexed function" - area: "number theory" - mathml: - - "d(x)" - urls: - - "https://mathworld.wolfram.com/PrimeDifferenceFunction.html" - - - concept: prime-gap - arity: 1 - en: prime gap of $1 - property: "indexed function" - area: "number theory" - mathml: - - "GX" - - "gX" - urls: - - "https://mathworld.wolfram.com/PrimeGaps.html" - - "https://en.wikipedia.org/wiki/Prime_gap" - - - concept: primorial - arity: 1 - en: primorial of $1 - property: postfix - area: "number theory" - mathml: - - "x#" - urls: - - "https://mathworld.wolfram.com/Primorial.html" - - "https://en.wikipedia.org/wiki/Primorial" - - - concept: principal-value - arity: 1 - en: principal value of $1 - property: function - area: "complex analysis" - mathml: - - "Log(x)" - urls: - - "https://en.wikipedia.org/wiki/Complex_logarithm#Principal_value" - - - concept: probability-limit - arity: 1 - en: probability limit of $1 - property: "indexed function" - area: "probability theory" - mathml: - - "plim(x)" - urls: - - "https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_probability" - alias: - - convergence-in-probability - - - concept: product-integral - arity: 1 - en: product integral of $1 - property: indexed - area: "calculus" - mathml: - - "∏f" - urls: - - "https://en.wikipedia.org/wiki/Continuous_product" - - "https://en.wikipedia.org/wiki/Product_integral" - - "https://www.encyclopediaofmath.org/index.php/Product_integral" - - - concept: product-measure - arity: 2 + property: symbol + subject-area: "number theory" + mathml: + - "P" + - "ρ" + urls: + - "https://mathworld.wolfram.com/PrimeConstant.html" + - "https://en.wikipedia.org/wiki/Prime_constant" + + + + - concept: prime-counting-function + arity: 1 + arguments: [a1] + speech: + en: prime counting function of a1 + property: function + subject-area: "number theory" + mathml: + - "π(x)" + urls: + - "https://mathworld.wolfram.com/PrimeCountingFunction.html" + + - concept: prime-difference-function + arity: 1 + arguments: [a1] + speech: + en: prime difference function of a1 + property: "indexed function" + subject-area: "number theory" + mathml: + - "d(x)" + urls: + - "https://mathworld.wolfram.com/PrimeDifferenceFunction.html" + + - concept: prime-gap + arity: 1 + arguments: [a1] + speech: + en: prime gap of a1 + property: "indexed function" + subject-area: "number theory" + mathml: + - "GX" + - "gX" + urls: + - "https://mathworld.wolfram.com/PrimeGaps.html" + - "https://en.wikipedia.org/wiki/Prime_gap" + + - concept: primorial + arity: 1 + arguments: [a1] + speech: + en: primorial of a1 + property: postfix + subject-area: "number theory" + mathml: + - "x#" + urls: + - "https://mathworld.wolfram.com/Primorial.html" + - "https://en.wikipedia.org/wiki/Primorial" + + - concept: principal-value + arity: 1 + arguments: [a1] + speech: + en: principal value of a1 + property: function + subject-area: "complex analysis" + mathml: + - "Log(x)" + urls: + - "https://en.wikipedia.org/wiki/Complex_logarithm#Principal_value" + + - concept: probability-limit + arity: 1 + arguments: [a1] + speech: + en: probability limit of a1 + property: "indexed function" + subject-area: "probability theory" + mathml: + - "plim(x)" + urls: + - "https://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_probability" + alias: + - convergence-in-probability + + - concept: product-integral + arity: 1 + arguments: [a1] + speech: + en: product integral of a1 + property: indexed + subject-area: "calculus" + mathml: + - "∏f" + urls: + - "https://en.wikipedia.org/wiki/Continuous_product" + - "https://en.wikipedia.org/wiki/Product_integral" + - "https://www.encyclopediaofmath.org/index.php/Product_integral" + + - concept: product-measure + arity: 2 + arguments: [a1, a2] + speech: en: product measure - property: function - area: "measure theory" - mathml: - - "x×y" - urls: - - "https://mathworld.wolfram.com/ProductMeasure.html" - - "https://en.wikipedia.org/wiki/Product_measure" - - - concept: projective-line - arity: 1 - en: projective line of $1 - property: function - area: "projective geometry" - mathml: - - "P(x)" - urls: - - "https://en.wikipedia.org/wiki/Projective_line" - - "https://ncatlab.org/nlab/show/projective+line" - - - concept: projective-space - arity: 0 + property: function + subject-area: "measure theory" + mathml: + - "x×y" + urls: + - "https://mathworld.wolfram.com/ProductMeasure.html" + - "https://en.wikipedia.org/wiki/Product_measure" + + - concept: projective-line + arity: 1 + arguments: [a1] + speech: + en: projective line of a1 + property: function + subject-area: "projective geometry" + mathml: + - "P(x)" + urls: + - "https://en.wikipedia.org/wiki/Projective_line" + - "https://ncatlab.org/nlab/show/projective+line" + + - concept: projective-space + arity: 0 + arguments: [] + speech: en: projective space - property: symbol - area: "projective geometry" - mathml: - - "ℙ" - notationa: "mi ℝ⁢ ℙ" - urls: - - "https://mathworld.wolfram.com/ProjectiveSpace.html" - - "https://en.wikipedia.org/wiki/Algebraic_geometry_of_projective_spaces" - - "https://en.wikipedia.org/wiki/Projective_space" - - "https://ncatlab.org/nlab/show/projective+space" - - "https://www.encyclopediaofmath.org/index.php/Projective_space" - alias: - - real-projective-space - - - concept: proper-subgroup - arity: 2 - en: $1 proper subgroup $2 - property: infix - area: "group theory" - mathml: - - "X<Y" - urls: - - "https://en.wikipedia.org/wiki/Subgroup" - - - concept: proportional - arity: 2 - en: $1 proportional $2 - property: infix - area: "arithmetic" - mathml: - - "X∝Y" - - "X~Y" - urls: - - "https://mathworld.wolfram.com/Proportional.html" - - "https://en.wikipedia.org/wiki/Proportionality_(mathematics)" - - "https://en.wikipedia.org/wiki/Proportional_(fair_division)" - alias: - - directly-proportional - - - concept: prouhet-thue-morse-constant - arity: 0 + property: symbol + subject-area: "projective geometry" + mathml: + - "ℙ" + notationa: "mi ℝ⁢ ℙ" + urls: + - "https://mathworld.wolfram.com/ProjectiveSpace.html" + - "https://en.wikipedia.org/wiki/Algebraic_geometry_of_projective_spaces" + - "https://en.wikipedia.org/wiki/Projective_space" + - "https://ncatlab.org/nlab/show/projective+space" + - "https://www.encyclopediaofmath.org/index.php/Projective_space" + alias: + - real-projective-space + + - concept: proper-subgroup + arity: 2 + arguments: [a1, a2] + speech: + en: a1 proper subgroup a2 + property: infix + subject-area: "group theory" + mathml: + - "X<Y" + urls: + - "https://en.wikipedia.org/wiki/Subgroup" + + - concept: proportional + arity: 2 + arguments: [a1, a2] + speech: + en: a1 proportional a2 + property: infix + subject-area: "arithmetic" + mathml: + - "X∝Y" + - "X~Y" + urls: + - "https://mathworld.wolfram.com/Proportional.html" + - "https://en.wikipedia.org/wiki/Proportionality_(mathematics)" + - "https://en.wikipedia.org/wiki/Proportional_(fair_division)" + alias: + - directly-proportional + + - concept: prouhet-thue-morse-constant + arity: 0 + arguments: [] + speech: en: prouhet thue morse constant - property: constant - area: "number theory" - mathml: - - "τ" - urls: - - "https://en.wikipedia.org/wiki/Prouhet%E2%80%93Thue%E2%80%93Morse_constant" - - - concept: prufer-group - arity: 1 - en: prufer group of $1 - property: mixfix - area: "group theory" - mathml: - - "𝐙(p∞)" - notation: "mrow Z ( msup $1 ∞ /msup" - urls: - - "https://en.wikipedia.org/wiki/Pr%C3%BCfer_group" - alias: - - quasicyclic-group - - - concept: pseudovector - arity: 1 - en: pseudovector $1 - property: mixfix - area: "vector calculus" - mathml: - - "v" - urls: - - "https://mathworld.wolfram.com/Pseudovector.html" - - "https://en.wikipedia.org/wiki/Pseudovector" - alias: - - axial-vector - - - concept: pseudo-inner-product - arity: 2 + property: constant + subject-area: "number theory" + mathml: + - "τ" + urls: + - "https://en.wikipedia.org/wiki/Prouhet%E2%80%93Thue%E2%80%93Morse_constant" + + - concept: prufer-group + arity: 1 + arguments: [a1] + speech: + en: prufer group of a1 + property: mixfix + subject-area: "group theory" + mathml: + - "𝐙(p∞)" + notation: "mrow Z ( msup a1 ∞ /msup" + urls: + - "https://en.wikipedia.org/wiki/Pr%C3%BCfer_group" + alias: + - quasicyclic-group + + - concept: pseudovector + arity: 1 + arguments: [a1] + speech: + en: pseudovector a1 + property: mixfix + subject-area: "vector calculus" + mathml: + - "v" + urls: + - "https://mathworld.wolfram.com/Pseudovector.html" + - "https://en.wikipedia.org/wiki/Pseudovector" + alias: + - axial-vector + + - concept: pseudo-inner-product + arity: 2 + arguments: [a1, a2] + speech: en: pseudo inner product - property: fenced - area: "lie algebra" - mathml: - - "(x,y)" - urls: - - "https://youtu.be/mJ8ZDdA10GY?t=870" - - - concept: pullback - arity: 0 + property: fenced + subject-area: "lie algebra" + mathml: + - "(x,y)" + urls: + - "https://youtu.be/mJ8ZDdA10GY?t=870" + + - concept: pullback + arity: 0 + arguments: [] + speech: en: pullback - property: symbol - area: "differential geometry" - mathml: - - "φ*" - urls: - - "https://en.wikipedia.org/wiki/Pullback_(differential_geometry)" - - - concept: pushforward - arity: 2 - en: $1 pushforward $2 - property: infix - area: "differential geometry" - mathml: - - "X*Y" - urls: - - "https://youtu.be/mJ8ZDdA10GY?t=2555" - - "https://en.wikipedia.org/wiki/Pushforward_(differential)" - - - concept: pythagoras-constant - arity: 0 + property: symbol + subject-area: "differential geometry" + mathml: + - "φ*" + urls: + - "https://en.wikipedia.org/wiki/Pullback_(differential_geometry)" + + - concept: pushforward + arity: 2 + arguments: [a1, a2] + speech: + en: a1 pushforward a2 + property: infix + subject-area: "differential geometry" + mathml: + - "X*Y" + urls: + - "https://youtu.be/mJ8ZDdA10GY?t=2555" + - "https://en.wikipedia.org/wiki/Pushforward_(differential)" + + - concept: pythagoras-constant + arity: 0 + arguments: [] + speech: en: pythagoras constant - property: constant - area: "geometry" - mathml: - - "2" - urls: - - "https://mathworld.wolfram.com/PythagorassConstant.html" - - "https://en.wikipedia.org/wiki/Sqrt(2)" - - "https://en.wikipedia.org/wiki/%E2%88%9A2" - - "https://en.wikipedia.org/wiki/Square_root_of_2" - alias: - - pythagoras-number - - - concept: pythagorean-triple - arity: 3 - en: pythagorean triple $1, $2 and $3 - property: fenced - area: "geometry" - mathml: - - "(a,b,c)" - urls: - - "https://mathworld.wolfram.com/PythagoreanTriple.html" - - "https://en.wikipedia.org/wiki/Pythagorean_triple" - - - concept: q-binomial-coefficient - arity: 3 - en: $3 q binomial coefficient of $1, $2 - property: fenced-stacked - area: "combinatorics" - mathml: - - "[nm]q" - urls: - - "https://mathworld.wolfram.com/q-BinomialCoefficient.html" - - - concept: qed - arity: 0 + property: constant + subject-area: "geometry" + mathml: + - "2" + urls: + - "https://mathworld.wolfram.com/PythagorassConstant.html" + - "https://en.wikipedia.org/wiki/Sqrt(2)" + - "https://en.wikipedia.org/wiki/%E2%88%9A2" + - "https://en.wikipedia.org/wiki/Square_root_of_2" + alias: + - pythagoras-number + + - concept: pythagorean-triple + arity: 3 + arguments: [a1, a2, a3] + speech: + en: pythagorean triple a1, a2 and a3 + property: fenced + subject-area: "geometry" + mathml: + - "(a,b,c)" + urls: + - "https://mathworld.wolfram.com/PythagoreanTriple.html" + - "https://en.wikipedia.org/wiki/Pythagorean_triple" + + - concept: q-binomial-coefficient + arity: 3 + arguments: [a1, a2, a3] + speech: + en: a3 q binomial coefficient of a1, a2 + property: fenced-stacked + subject-area: "combinatorics" + mathml: + - "[nm]q" + urls: + - "https://mathworld.wolfram.com/q-BinomialCoefficient.html" + + - concept: qed + arity: 0 + arguments: [] + speech: en: qed - property: symbol - area: "mathematical symbols" - mathml: - - "□" - - "∎" - urls: - - "https://en.wikipedia.org/wiki/Tombstone_(typography)" - alias: - - end-of-proof - - quod-erat-demonstrandum - - - concept: quadratic-differential - arity: 1 - en: quadratic differential of $1 - property: mixfix - area: "complex manifolds" - mathml: - - "f(z)dz⊗dz" - notation: "mrow d $1 d $1" - urls: - - "https://en.wikipedia.org/wiki/Quadratic_differential" - - "https://ncatlab.org/nlab/show/quadratic+differential" - - "https://www.encyclopediaofmath.org/index.php/Quadratic_differential" - - - concept: quadratic-variation - arity: 2 - en: quadratic variation $1 $2 - property: indexed fenced - area: "stochastic processes" - mathml: - - "[X]t" - notation: "msub mrow [ $1 ] /mrow $2" - urls: - - "https://en.wikipedia.org/wiki/Quadratic_variation" - - - concept: quadrilateral - arity: 1 - en: quadrilateral of $1 - property: prefix - area: "geometry" - mathml: - - "◻x" - urls: - - "https://mathworld.wolfram.com/Quadrangle.html" - - "https://en.wikipedia.org/wiki/Quadrilateral" - - "https://www.encyclopediaofmath.org/index.php/Quadrangle" - alias: - - quadrangle - - - concept: quotient-group - arity: 2 - en: $1 quotient group $2 - property: infix - area: "group theory" - mathml: - - "X/Y" - urls: - - "https://mathworld.wolfram.com/QuotientGroup.html" - - "https://ncatlab.org/nlab/show/quotient+group" - - "https://www.encyclopediaofmath.org/index.php/Quotient_group" - - - concept: quotient-space - arity: 2 - en: $1 quotient space $2 - property: infix - area: "topology" - mathml: - - "X/Y" - urls: - - "https://mathworld.wolfram.com/QuotientSpace.html" - - "https://en.wikipedia.org/wiki/Quotient_space_(topology)" - - "https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)" - - "https://ncatlab.org/nlab/show/quotient+space" - - "https://www.encyclopediaofmath.org/index.php/Quotient_space" - alias: - - quotient-set - - - concept: r-complexity-class - arity: 0 + property: symbol + subject-area: "mathematical symbols" + mathml: + - "□" + - "∎" + urls: + - "https://en.wikipedia.org/wiki/Tombstone_(typography)" + alias: + - end-of-proof + - quod-erat-demonstrandum + + - concept: quadratic-differential + arity: 1 + arguments: [a1] + speech: + en: quadratic differential of a1 + property: mixfix + subject-area: "complex manifolds" + mathml: + - "f(z)dz⊗dz" + notation: "mrow d a1 d a1" + urls: + - "https://en.wikipedia.org/wiki/Quadratic_differential" + - "https://ncatlab.org/nlab/show/quadratic+differential" + - "https://www.encyclopediaofmath.org/index.php/Quadratic_differential" + + - concept: quadratic-variation + arity: 2 + arguments: [a1, a2] + speech: + en: quadratic variation a1 a2 + property: indexed fenced + subject-area: "stochastic processes" + mathml: + - "[X]t" + notation: "msub mrow [ a1 ] /mrow a2" + urls: + - "https://en.wikipedia.org/wiki/Quadratic_variation" + + - concept: quadrilateral + arity: 1 + arguments: [a1] + speech: + en: quadrilateral of a1 + property: prefix + subject-area: "geometry" + mathml: + - "◻x" + urls: + - "https://mathworld.wolfram.com/Quadrangle.html" + - "https://en.wikipedia.org/wiki/Quadrilateral" + - "https://www.encyclopediaofmath.org/index.php/Quadrangle" + alias: + - quadrangle + + - concept: quotient-group + arity: 2 + arguments: [a1, a2] + speech: + en: a1 quotient group a2 + property: infix + subject-area: "group theory" + mathml: + - "X/Y" + urls: + - "https://mathworld.wolfram.com/QuotientGroup.html" + - "https://ncatlab.org/nlab/show/quotient+group" + - "https://www.encyclopediaofmath.org/index.php/Quotient_group" + + - concept: quotient-space + arity: 2 + arguments: [a1, a2] + speech: + en: a1 quotient space a2 + property: infix + subject-area: "topology" + mathml: + - "X/Y" + urls: + - "https://mathworld.wolfram.com/QuotientSpace.html" + - "https://en.wikipedia.org/wiki/Quotient_space_(topology)" + - "https://en.wikipedia.org/wiki/Quotient_space_(linear_algebra)" + - "https://ncatlab.org/nlab/show/quotient+space" + - "https://www.encyclopediaofmath.org/index.php/Quotient_space" + alias: + - quotient-set + + - concept: r-complexity-class + arity: 0 + arguments: [] + speech: en: r complexity class - property: symbol - area: "complexity theory" - mathml: - - "R" - urls: - - "https://mathworld.wolfram.com/R.html" - - "https://en.wikipedia.org/wiki/R_(complexity)" - - "https://en.wikipedia.org/wiki/R_(cross_section_ratio)" - - - concept: racah-polynomial - arity: 1 - en: racah polynomial of $1 - property: "indexed function" - area: "special functions" - mathml: - - "Rx" - urls: - - "https://mathworld.wolfram.com/RacahPolynomial.html" - - "https://en.wikipedia.org/wiki/Racah_polynomials" - - "https://dlmf.nist.gov/18.25#T1.t1.r4" - - - concept: radial-mathieu-function - arity: 1 - en: radial mathieu function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "McX" - - "MsX" - urls: - - "https://dlmf.nist.gov/28.20#iv" - - "https://dlmf.nist.gov/28.20#E15" - - "https://dlmf.nist.gov/28.20#E16" - - - concept: radical - arity: 1 - en: radical of $1 - property: function - area: "number theory" - mathml: - - "rad(x)" - urls: - - "https://mathworld.wolfram.com/Radical.html" - - "https://en.wikipedia.org/wiki/Radical_of_a_Lie_algebra" - - "https://en.wikipedia.org/wiki/Radical_of_an_integer" - - "https://en.wikipedia.org/wiki/Radical_of_a_module" - - "https://ncatlab.org/nlab/show/radical" - - "https://www.encyclopediaofmath.org/index.php/Radical" - - - concept: radius-vector - arity: 0 + property: symbol + subject-area: "complexity theory" + mathml: + - "R" + urls: + - "https://mathworld.wolfram.com/R.html" + - "https://en.wikipedia.org/wiki/R_(complexity)" + - "https://en.wikipedia.org/wiki/R_(cross_section_ratio)" + + - concept: racah-polynomial + arity: 1 + arguments: [a1] + speech: + en: racah polynomial of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Rx" + urls: + - "https://mathworld.wolfram.com/RacahPolynomial.html" + - "https://en.wikipedia.org/wiki/Racah_polynomials" + - "https://dlmf.nist.gov/18.25#T1.t1.r4" + + - concept: radial-mathieu-function + arity: 1 + arguments: [a1] + speech: + en: radial mathieu function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "McX" + - "MsX" + urls: + - "https://dlmf.nist.gov/28.20#iv" + - "https://dlmf.nist.gov/28.20#E15" + - "https://dlmf.nist.gov/28.20#E16" + + - concept: radical + arity: 1 + arguments: [a1] + speech: + en: radical of a1 + property: function + subject-area: "number theory" + mathml: + - "rad(x)" + urls: + - "https://mathworld.wolfram.com/Radical.html" + - "https://en.wikipedia.org/wiki/Radical_of_a_Lie_algebra" + - "https://en.wikipedia.org/wiki/Radical_of_an_integer" + - "https://en.wikipedia.org/wiki/Radical_of_a_module" + - "https://ncatlab.org/nlab/show/radical" + - "https://www.encyclopediaofmath.org/index.php/Radical" + + - concept: radius-vector + arity: 0 + arguments: [] + speech: en: radius vector - property: symbol - area: "geometry" - mathml: - - "x" - - "r" - - "s" - urls: - - "https://mathworld.wolfram.com/RadiusVector.html" - - "https://en.wikipedia.org/wiki/Position_(vector)" - - "https://www.encyclopediaofmath.org/index.php/Radius_vector" - alias: - - location-vector - - position-vector - - position - - - concept: ramanujan-sum - arity: 1 - en: ramanujan sum of $1 - property: "indexed function" - area: "number theory" - mathml: - - "cx" - urls: - - "https://mathworld.wolfram.com/RamanujansSum.html" - - "https://dlmf.nist.gov/27.10#E4" - - "https://www.encyclopediaofmath.org/index.php/Ramanujan_sums" - - - concept: ramanujan-tau-function - arity: 1 - en: ramanujan tau function of $1 - property: function - area: "number theory" - mathml: - - "τ(x)" - urls: - - "https://mathworld.wolfram.com/RamanujansTauFunction.html" - - "https://en.wikipedia.org/wiki/Ramanujan_tau_function" - - "https://dlmf.nist.gov/27.14#E18" - - - concept: ramanujan-soldner-constant - arity: 0 + property: symbol + subject-area: "geometry" + mathml: + - "x" + - "r" + - "s" + urls: + - "https://mathworld.wolfram.com/RadiusVector.html" + - "https://en.wikipedia.org/wiki/Position_(vector)" + - "https://www.encyclopediaofmath.org/index.php/Radius_vector" + alias: + - location-vector + - position-vector + - position + + - concept: ramanujan-sum + arity: 1 + arguments: [a1] + speech: + en: ramanujan sum of a1 + property: "indexed function" + subject-area: "number theory" + mathml: + - "cx" + urls: + - "https://mathworld.wolfram.com/RamanujansSum.html" + - "https://dlmf.nist.gov/27.10#E4" + - "https://www.encyclopediaofmath.org/index.php/Ramanujan_sums" + + - concept: ramanujan-tau-function + arity: 1 + arguments: [a1] + speech: + en: ramanujan tau function of a1 + property: function + subject-area: "number theory" + mathml: + - "τ(x)" + urls: + - "https://mathworld.wolfram.com/RamanujansTauFunction.html" + - "https://en.wikipedia.org/wiki/Ramanujan_tau_function" + - "https://dlmf.nist.gov/27.14#E18" + + - concept: ramanujan-soldner-constant + arity: 0 + arguments: [] + speech: en: ramanujan soldner constant - property: constant - area: "special functions" - mathml: - - "μ" - urls: - - "https://mathworld.wolfram.com/Ramanujan-SoldnerConstant.html" - - "https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constant" - - "https://mathworld.wolfram.com/SoldnersConstant.html" - alias: - - soldner-constant - - - concept: ramification-index - arity: 1 - en: ramification index of $1 - property: msub - area: "algebraic number theory" - mathml: - - "ex" - urls: - - "https://mathworld.wolfram.com/RamificationIndex.html" - - "https://en.wikipedia.org/wiki/Ramification_(mathematics)#In_algebraic_number_theory" - - - concept: ramsey-number - arity: 1 - en: ramsey number of $1 - property: function - area: "graph theory" - mathml: - - "R(x)" - urls: - - "https://mathworld.wolfram.com/RamseyNumber.html" - - "https://www.encyclopediaofmath.org/index.php/Ramsey_number" - - - concept: rank - arity: 1 - en: rank of $1 - property: function - area: "graph theory, linear algebra, " - mathml: - - "rX" - - "rankX" - - "rkX" - urls: - - "https://mathworld.wolfram.com/Rank.html" - - "https://en.wikipedia.org/wiki/Rank_(graph_theory)" - - "https://en.wikipedia.org/wiki/Rank_(linear_algebra)" - - "https://en.wikipedia.org/wiki/Rank_(differential_topology)" - - "https://ncatlab.org/nlab/show/rank" - - "https://www.encyclopediaofmath.org/index.php/Rank" - - - concept: real-bipolar - arity: 1 - en: real bipolar of $1 - property: msup - area: "functional analysis" - mathml: - - "A∘" - urls: - - "https://en.wikipedia.org/wiki/Polar_set" - - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" - - "https://www.encyclopediaofmath.org/index.php/Polar_set" - - - concept: real-part - arity: 1 - en: real part of $1 - property: function - area: "complex analysis" - mathml: - - "ℜX" - - "ReX" - - "ℛℯX" - urls: - - "https://mathworld.wolfram.com/RealPart.html" - - "https://dlmf.nist.gov/1.9#E2" - - "https://en.wikipedia.org/wiki/Complex_number#Notation" - - - concept: real-prepolar - arity: 1 - en: real prepolar of $1 - property: prescript - area: "functional analysis" - mathml: - - "B∘" - urls: - - "https://en.wikipedia.org/wiki/Polar_set" - - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" - - "https://www.encyclopediaofmath.org/index.php/Polar_set" - - - concept: real-polar - arity: 1 - en: real polar of $1 - property: msup - area: "functional analysis" - mathml: - - "Xr" - urls: - - "https://en.wikipedia.org/wiki/Polar_set" - - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" - - "https://www.encyclopediaofmath.org/index.php/Polar_set" - - - concept: recession-cone - arity: 1 - en: recession cone of $1 - property: function - area: "convex analysis" - mathml: - - "recc(x)" - urls: - - "https://en.wikipedia.org/wiki/Recession_cone" - - - concept: reciprocal-polynomial - arity: 1 - en: reciprocal polynomial of $1 - property: msup - area: "algebra" - mathml: - - "X*" - - "XR" - urls: - - "https://mathworld.wolfram.com/ReciprocalPolynomial.html" - - "https://en.wikipedia.org/wiki/Reciprocal_polynomial" - alias: - - reflected-polynomial - - - concept: rectification - arity: 1 - en: rectification of $1 - property: function - area: "euclidean geometry" - mathml: - - "r(x)" - urls: - - "https://mathworld.wolfram.com/Rectification.html" - - "https://en.wikipedia.org/wiki/Rectification_(geometry)" - - "https://ncatlab.org/nlab/show/rectification" - - - concept: reduced-suspension - arity: 1 - en: reduced suspension of $1 - property: function - area: "topology" - mathml: - - "Σ(x)" - urls: - - "https://en.wikipedia.org/wiki/Suspension_(topology)" - - - concept: relative-homology - arity: 1 - en: relative homology of $1 - property: "indexed function" - area: "algebraic topology" - mathml: - - "H(x)" - urls: - - "https://en.wikipedia.org/wiki/Relative_homology" - - "https://ncatlab.org/nlab/show/relative+homology" - - "https://www.encyclopediaofmath.org/index.php/Relative_homology" - - - concept: repunit - arity: 1 - en: repunit of $1 - property: "indexed symbol" - area: "number theory" - mathml: - - "R(x)" - urls: - - "https://mathworld.wolfram.com/Repunit.html" - - "https://en.wikipedia.org/wiki/Repunit" - - "https://en.wikipedia.org/wiki/Repunit_prime" - - - concept: residue - arity: 1 - en: residue of $1 - property: function - area: "complex analysis" - mathml: - - "ResX" - - "resX" - urls: - - "https://mathworld.wolfram.com/Residue.html" - - "https://en.wikipedia.org/wiki/Residue_(complex_analysis)" - - "https://dlmf.nist.gov/1.10#SS3.p5" - - - concept: resolvent - arity: 1 + property: constant + subject-area: "special functions" + mathml: + - "μ" + urls: + - "https://mathworld.wolfram.com/Ramanujan-SoldnerConstant.html" + - "https://en.wikipedia.org/wiki/Ramanujan%E2%80%93Soldner_constant" + - "https://mathworld.wolfram.com/SoldnersConstant.html" + alias: + - soldner-constant + + - concept: ramification-index + arity: 1 + arguments: [a1] + speech: + en: ramification index of a1 + property: msub + subject-area: "algebraic number theory" + mathml: + - "ex" + urls: + - "https://mathworld.wolfram.com/RamificationIndex.html" + - "https://en.wikipedia.org/wiki/Ramification_(mathematics)#In_algebraic_number_theory" + + - concept: ramsey-number + arity: 1 + arguments: [a1] + speech: + en: ramsey number of a1 + property: function + subject-area: "graph theory" + mathml: + - "R(x)" + urls: + - "https://mathworld.wolfram.com/RamseyNumber.html" + - "https://www.encyclopediaofmath.org/index.php/Ramsey_number" + + - concept: rank + arity: 1 + arguments: [a1] + speech: + en: rank of a1 + property: function + subject-area: "graph theory, linear algebra, " + mathml: + - "rX" + - "rankX" + - "rkX" + urls: + - "https://mathworld.wolfram.com/Rank.html" + - "https://en.wikipedia.org/wiki/Rank_(graph_theory)" + - "https://en.wikipedia.org/wiki/Rank_(linear_algebra)" + - "https://en.wikipedia.org/wiki/Rank_(differential_topology)" + - "https://ncatlab.org/nlab/show/rank" + - "https://www.encyclopediaofmath.org/index.php/Rank" + + - concept: real-bipolar + arity: 1 + arguments: [a1] + speech: + en: real bipolar of a1 + property: msup + subject-area: "functional analysis" + mathml: + - "A∘" + urls: + - "https://en.wikipedia.org/wiki/Polar_set" + - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" + - "https://www.encyclopediaofmath.org/index.php/Polar_set" + + - concept: real-part + arity: 1 + arguments: [a1] + speech: + en: real part of a1 + property: function + subject-area: "complex analysis" + mathml: + - "ℜX" + - "ReX" + - "ℛℯX" + urls: + - "https://mathworld.wolfram.com/RealPart.html" + - "https://dlmf.nist.gov/1.9#E2" + - "https://en.wikipedia.org/wiki/Complex_number#Notation" + + - concept: real-prepolar + arity: 1 + arguments: [a1] + speech: + en: real prepolar of a1 + property: prescript + subject-area: "functional analysis" + mathml: + - "B∘" + urls: + - "https://en.wikipedia.org/wiki/Polar_set" + - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" + - "https://www.encyclopediaofmath.org/index.php/Polar_set" + + - concept: real-polar + arity: 1 + arguments: [a1] + speech: + en: real polar of a1 + property: msup + subject-area: "functional analysis" + mathml: + - "Xr" + urls: + - "https://en.wikipedia.org/wiki/Polar_set" + - "https://en.wikipedia.org/wiki/Polar_set_(potential_theory)" + - "https://www.encyclopediaofmath.org/index.php/Polar_set" + + - concept: recession-cone + arity: 1 + arguments: [a1] + speech: + en: recession cone of a1 + property: function + subject-area: "convex analysis" + mathml: + - "recc(x)" + urls: + - "https://en.wikipedia.org/wiki/Recession_cone" + + - concept: reciprocal-polynomial + arity: 1 + arguments: [a1] + speech: + en: reciprocal polynomial of a1 + property: msup + subject-area: "algebra" + mathml: + - "X*" + - "XR" + urls: + - "https://mathworld.wolfram.com/ReciprocalPolynomial.html" + - "https://en.wikipedia.org/wiki/Reciprocal_polynomial" + alias: + - reflected-polynomial + + - concept: rectification + arity: 1 + arguments: [a1] + speech: + en: rectification of a1 + property: function + subject-area: "euclidean geometry" + mathml: + - "r(x)" + urls: + - "https://mathworld.wolfram.com/Rectification.html" + - "https://en.wikipedia.org/wiki/Rectification_(geometry)" + - "https://ncatlab.org/nlab/show/rectification" + + - concept: reduced-suspension + arity: 1 + arguments: [a1] + speech: + en: reduced suspension of a1 + property: function + subject-area: "topology" + mathml: + - "Σ(x)" + urls: + - "https://en.wikipedia.org/wiki/Suspension_(topology)" + + - concept: relative-homology + arity: 1 + arguments: [a1] + speech: + en: relative homology of a1 + property: "indexed function" + subject-area: "algebraic topology" + mathml: + - "H(x)" + urls: + - "https://en.wikipedia.org/wiki/Relative_homology" + - "https://ncatlab.org/nlab/show/relative+homology" + - "https://www.encyclopediaofmath.org/index.php/Relative_homology" + + - concept: repunit + arity: 1 + arguments: [a1] + speech: + en: repunit of a1 + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "R(x)" + urls: + - "https://mathworld.wolfram.com/Repunit.html" + - "https://en.wikipedia.org/wiki/Repunit" + - "https://en.wikipedia.org/wiki/Repunit_prime" + + - concept: residue + arity: 1 + arguments: [a1] + speech: + en: residue of a1 + property: function + subject-area: "complex analysis" + mathml: + - "ResX" + - "resX" + urls: + - "https://mathworld.wolfram.com/Residue.html" + - "https://en.wikipedia.org/wiki/Residue_(complex_analysis)" + - "https://dlmf.nist.gov/1.10#SS3.p5" + + - concept: resolvent + arity: 1 + arguments: [a1] + speech: en: resolvent - property: "indexed function" - area: "galois theory" - mathml: - - "RG" - urls: - - "https://mathworld.wolfram.com/Resolvent.html" - - "https://en.wikipedia.org/wiki/Resolvent_(Galois_theory)" - - "https://www.encyclopediaofmath.org/index.php/Resolvent" - - - concept: resolvent-set - arity: 1 - en: resolvent set of $1 - property: function - area: "set theory" - mathml: - - "ρ(x)" - urls: - - "https://en.wikipedia.org/wiki/Resolvent_set" - - "https://www.encyclopediaofmath.org/index.php/Resolvent_set" - - - concept: restricted-quantifier - arity: 2 - en: restricted quantifier $1 $2 - property: mixfix - area: "formal logic" - mathml: - - "(∀x)R(x)" - - "(∃x)R(x)" - urls: - - "https://www.encyclopediaofmath.org/index.php/Restricted_quantifier" - - "https://human.libretexts.org/Bookshelves/Philosophy/Book%3A_A_Modern_Formal_Logic_Primer_(Teller)/Volume_II%3A_Predicate_Logic/4%3A_Transcription/4.1%3A_Restricted_Quantifiers" - - - concept: restricted-wreath-product - arity: 2 - en: $1 restricted wreath product $2 - property: infix - area: "group theory" - mathml: - - "XwrY" - - "XwrΩY" - urls: - - "https://mathworld.wolfram.com/WreathProduct.html" - - "https://en.wikipedia.org/wiki/Wreath_product" - - "https://ncatlab.org/nlab/show/wreath+product" - - "https://www.encyclopediaofmath.org/index.php/Wreath_product" - - - concept: restriction - arity: 2 + property: "indexed function" + subject-area: "galois theory" + mathml: + - "RG" + urls: + - "https://mathworld.wolfram.com/Resolvent.html" + - "https://en.wikipedia.org/wiki/Resolvent_(Galois_theory)" + - "https://www.encyclopediaofmath.org/index.php/Resolvent" + + - concept: resolvent-set + arity: 1 + arguments: [a1] + speech: + en: resolvent set of a1 + property: function + subject-area: "set theory" + mathml: + - "ρ(x)" + urls: + - "https://en.wikipedia.org/wiki/Resolvent_set" + - "https://www.encyclopediaofmath.org/index.php/Resolvent_set" + + - concept: restricted-quantifier + arity: 2 + arguments: [a1, a2] + speech: + en: restricted quantifier a1 a2 + property: mixfix + subject-area: "formal logic" + mathml: + - "(∀x)R(x)" + - "(∃x)R(x)" + urls: + - "https://www.encyclopediaofmath.org/index.php/Restricted_quantifier" + - "https://human.libretexts.org/Bookshelves/Philosophy/Book%3A_A_Modern_Formal_Logic_Primer_(Teller)/Volume_II%3A_Predicate_Logic/4%3A_Transcription/4.1%3A_Restricted_Quantifiers" + + - concept: restricted-wreath-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 restricted wreath product a2 + property: infix + subject-area: "group theory" + mathml: + - "XwrY" + - "XwrΩY" + urls: + - "https://mathworld.wolfram.com/WreathProduct.html" + - "https://en.wikipedia.org/wiki/Wreath_product" + - "https://ncatlab.org/nlab/show/wreath+product" + - "https://www.encyclopediaofmath.org/index.php/Wreath_product" + + - concept: restriction + arity: 2 + arguments: [a1, a2] + speech: en: restriction - property: indexed postfix - area: "elementary mathematics" - mathml: - - "f↾A" - - "f|A" - urls: - - "https://en.wikipedia.org/wiki/Restricted_representation" - - "https://en.wikipedia.org/wiki/Restriction_(mathematics)" - - "https://en.wikipedia.org/wiki/Selection_(relational_algebra)" - - "https://ncatlab.org/nlab/show/restriction" - - - concept: resultant - arity: 1 - en: resultant of $1 - property: function - area: "polynomials" - mathml: - - "resX" - - "ResX" - urls: - - "https://mathworld.wolfram.com/Resultant.html" - - "https://en.wikipedia.org/wiki/Resultant" - - "https://ncatlab.org/nlab/show/resultant" - - "https://www.encyclopediaofmath.org/index.php/Resultant" - alias: - - eliminant - - - concept: rewrite-rule - arity: 2 - en: $1 rewrite rule $2 - property: infix - area: "logic" - mathml: - - "X→Y" - urls: - - "https://en.wikipedia.org/wiki/Semi-Thue_system" - alias: - - rewrite-relation - - - concept: reynolds-number - arity: 0 + property: indexed postfix + subject-area: "elementary mathematics" + mathml: + - "f↾A" + - "f|A" + urls: + - "https://en.wikipedia.org/wiki/Restricted_representation" + - "https://en.wikipedia.org/wiki/Restriction_(mathematics)" + - "https://en.wikipedia.org/wiki/Selection_(relational_algebra)" + - "https://ncatlab.org/nlab/show/restriction" + + - concept: resultant + arity: 1 + arguments: [a1] + speech: + en: resultant of a1 + property: function + subject-area: "polynomials" + mathml: + - "resX" + - "ResX" + urls: + - "https://mathworld.wolfram.com/Resultant.html" + - "https://en.wikipedia.org/wiki/Resultant" + - "https://ncatlab.org/nlab/show/resultant" + - "https://www.encyclopediaofmath.org/index.php/Resultant" + alias: + - eliminant + + - concept: rewrite-rule + arity: 2 + arguments: [a1, a2] + speech: + en: a1 rewrite rule a2 + property: infix + subject-area: "logic" + mathml: + - "X→Y" + urls: + - "https://en.wikipedia.org/wiki/Semi-Thue_system" + alias: + - rewrite-relation + + - concept: reynolds-number + arity: 0 + arguments: [] + speech: en: reynolds number - property: symbol - area: "fluid dynamics" - mathml: - - "Re" - urls: - - "https://en.wikipedia.org/wiki/Reynolds_number" - - - concept: ricci-scalar - arity: 0 + property: symbol + subject-area: "fluid dynamics" + mathml: + - "Re" + urls: + - "https://en.wikipedia.org/wiki/Reynolds_number" + + - concept: ricci-scalar + arity: 0 + arguments: [] + speech: en: ricci scalar - property: symbol - area: "riemannian geometry" - mathml: - - "S" - - "R" - - "Sc" - urls: - - "https://mathworld.wolfram.com/RicciScalar.html" - - "https://en.wikipedia.org/wiki/Scalar_curvature" - alias: - - scalar-curvature - - - concept: ricci-tensor - arity: 1 - en: ricci tensor of $1 - property: "indexed symbol" - area: "riemannian geometry" - mathml: - - "R(x)" - urls: - - "https://mathworld.wolfram.com/RicciTensor.html" - - "https://www.encyclopediaofmath.org/index.php/Ricci_tensor" - - - concept: riemann-integral - arity: 1 - en: riemann integral of $1 - property: indexed - area: "calculus" - mathml: - - "∫f" - urls: - - "https://mathworld.wolfram.com/RiemannIntegral.html" - - "https://en.wikipedia.org/wiki/Lebesgue_integrability_condition" - - "https://en.wikipedia.org/wiki/Riemann_integral" - - "https://www.encyclopediaofmath.org/index.php/Riemann_integral" - - - - concept: riemann-sphere - arity: 0 + property: symbol + subject-area: "riemannian geometry" + mathml: + - "S" + - "R" + - "Sc" + urls: + - "https://mathworld.wolfram.com/RicciScalar.html" + - "https://en.wikipedia.org/wiki/Scalar_curvature" + alias: + - scalar-curvature + + - concept: ricci-tensor + arity: 1 + arguments: [a1] + speech: + en: ricci tensor of a1 + property: "indexed symbol" + subject-area: "riemannian geometry" + mathml: + - "R(x)" + urls: + - "https://mathworld.wolfram.com/RicciTensor.html" + - "https://www.encyclopediaofmath.org/index.php/Ricci_tensor" + + - concept: riemann-integral + arity: 1 + arguments: [a1] + speech: + en: riemann integral of a1 + property: indexed + subject-area: "calculus" + mathml: + - "∫f" + urls: + - "https://mathworld.wolfram.com/RiemannIntegral.html" + - "https://en.wikipedia.org/wiki/Lebesgue_integrability_condition" + - "https://en.wikipedia.org/wiki/Riemann_integral" + - "https://www.encyclopediaofmath.org/index.php/Riemann_integral" + + + - concept: riemann-sphere + arity: 0 + arguments: [] + speech: en: riemann sphere - property: scripted symbol - area: "projective geometry" - mathml: - - "ℂ^" - - "ℂ¯" - - "ℂ∞" - urls: - - "https://mathworld.wolfram.com/RiemannSphere.html" - - "https://en.wikipedia.org/wiki/Riemann_sphere" - - "https://ncatlab.org/nlab/show/Riemann+sphere" - - "https://www.encyclopediaofmath.org/index.php/Riemann_sphere" - alias: - - extended-complex-numbers - - extended-complex-plane - - - concept: riemann-theta-function - arity: 1 - en: riemann theta function of $1 - property: function - area: "special functions" - mathml: - - "θ⁡(x)" - urls: - - "https://mathworld.wolfram.com/RiemannThetaFunction.html" - - "https://dlmf.nist.gov/21.2#i" - - "https://dlmf.nist.gov/21.2#E1" - - - concept: riemann-zeta-function - arity: 1 - en: riemann zeta function of $1 - property: function - area: "special functions" - mathml: - - "ζ(x)" - urls: - - "https://mathworld.wolfram.com/RiemannZetaFunction.html" - - "https://en.wikipedia.org/wiki/%CE%96(x)" - - "https://en.wikipedia.org/wiki/Riemann_zeta_function" - - "https://dlmf.nist.gov/25.1" - - "https://dlmf.nist.gov/25.2#E1" - alias: - - euler-riemann-zeta-function - - - concept: riemann-christoffel-tensor - arity: 1 - en: riemann christoffel tensor of $1 - property: "indexed function" - area: "riemannian geometry" - mathml: - - "R(x)" - urls: - - "https://mathworld.wolfram.com/Riemann-ChristoffelTensor.html" - - "https://en.wikipedia.org/wiki/Riemann_curvature_tensor" - - "https://www.encyclopediaofmath.org/index.php/Riemann-Christoffel_tensor" - - "https://www.encyclopediaofmath.org/index.php/RiemannâXXXXChristoffel_tensor" - alias: - - riemann-curvature-tensor - - - concept: riemann-stieltje-integral - arity: 1 - en: riemann stieltje integral of $1 - property: indexed - area: "measure theory" - mathml: - - "∫f" - urls: - - "https://mathworld.wolfram.com/Riemann-StieltjesIntegral.html" - - "https://en.wikipedia.org/wiki/%E2%88%AB_f_d%CE%B1" - - "https://en.wikipedia.org/wiki/%E2%88%ABfd%CE%B1" - - "https://en.wikipedia.org/wiki/Riemann%E2%80%93Stieltjes_integral" - - "https://www.encyclopediaofmath.org/index.php/Riemann-Stieltjes_integral" - - "https://www.encyclopediaofmath.org/index.php/RiemannâXXXXStieltjes_integral" - alias: - - stieltje-integral - - - concept: right-angle - arity: 1 - en: right angle of $1 - property: prefix - area: "geometry" - mathml: - - "∟x" - - "⊾x" - - "⦜x" - - "⦝x" - urls: - - "https://mathworld.wolfram.com/RightAngle.html" - - "https://en.wikipedia.org/wiki/Right_angle" - - - concept: right-derivative - arity: 1 - en: right derivative of $1 - property: operator - area: "calculus" - mathml: - - "∂+f" - urls: - - "https://en.wikipedia.org/wiki/Left_and_right_derivative" - - - concept: right-quotient - arity: 2 - en: $1 right quotient $2 - property: infix - area: "formal languages" - mathml: - - "X\\Y" - urls: - - "https://en.wikipedia.org/wiki/Quotient_of_a_formal_language" - - - concept: ring-of-formal-power-series - arity: 2 - en: ring of formal power series $1 $2 - property: mixfix - area: "ring theory" - mathml: - - "R⟦x⟧" - urls: - - "https://en.wikipedia.org/wiki/Formal_power_series#The_ring_of_formal_power_series" - - - concept: rising-factorial - arity: 2 - en: $2th rising factorial of $1 - property: mixfix - area: "combinatorics" - mathml: - - "x(n)" - - "xn¯" - urls: - - "https://en.wikipedia.org/wiki/Falling_and_rising_factorials" - - "https://mathworld.wolfram.com/RisingFactorial.html" - - "https://dlmf.nist.gov/26.1#P1.p1" - alias: - - pochhammer-function - - pochhammer-polynomial - - ascending-factorial - - rising-sequential-product - - upper-factorial - - - concept: roman-numeral - arity: 0 + property: scripted symbol + subject-area: "projective geometry" + mathml: + - "ℂ^" + - "ℂ¯" + - "ℂ∞" + urls: + - "https://mathworld.wolfram.com/RiemannSphere.html" + - "https://en.wikipedia.org/wiki/Riemann_sphere" + - "https://ncatlab.org/nlab/show/Riemann+sphere" + - "https://www.encyclopediaofmath.org/index.php/Riemann_sphere" + alias: + - extended-complex-numbers + - extended-complex-plane + + - concept: riemann-theta-function + arity: 1 + arguments: [a1] + speech: + en: riemann theta function of a1 + property: function + subject-area: "special functions" + mathml: + - "θ⁡(x)" + urls: + - "https://mathworld.wolfram.com/RiemannThetaFunction.html" + - "https://dlmf.nist.gov/21.2#i" + - "https://dlmf.nist.gov/21.2#E1" + + - concept: riemann-zeta-function + arity: 1 + arguments: [a1] + speech: + en: riemann zeta function of a1 + property: function + subject-area: "special functions" + mathml: + - "ζ(x)" + urls: + - "https://mathworld.wolfram.com/RiemannZetaFunction.html" + - "https://en.wikipedia.org/wiki/%CE%96(x)" + - "https://en.wikipedia.org/wiki/Riemann_zeta_function" + - "https://dlmf.nist.gov/25.1" + - "https://dlmf.nist.gov/25.2#E1" + alias: + - euler-riemann-zeta-function + + - concept: riemann-christoffel-tensor + arity: 1 + arguments: [a1] + speech: + en: riemann christoffel tensor of a1 + property: "indexed function" + subject-area: "riemannian geometry" + mathml: + - "R(x)" + urls: + - "https://mathworld.wolfram.com/Riemann-ChristoffelTensor.html" + - "https://en.wikipedia.org/wiki/Riemann_curvature_tensor" + - "https://www.encyclopediaofmath.org/index.php/Riemann-Christoffel_tensor" + - "https://www.encyclopediaofmath.org/index.php/RiemannâXXXXChristoffel_tensor" + alias: + - riemann-curvature-tensor + + - concept: riemann-stieltje-integral + arity: 1 + arguments: [a1] + speech: + en: riemann stieltje integral of a1 + property: indexed + subject-area: "measure theory" + mathml: + - "∫f" + urls: + - "https://mathworld.wolfram.com/Riemann-StieltjesIntegral.html" + - "https://en.wikipedia.org/wiki/%E2%88%AB_f_d%CE%B1" + - "https://en.wikipedia.org/wiki/%E2%88%ABfd%CE%B1" + - "https://en.wikipedia.org/wiki/Riemann%E2%80%93Stieltjes_integral" + - "https://www.encyclopediaofmath.org/index.php/Riemann-Stieltjes_integral" + - "https://www.encyclopediaofmath.org/index.php/RiemannâXXXXStieltjes_integral" + alias: + - stieltje-integral + + - concept: right-angle + arity: 1 + arguments: [a1] + speech: + en: right angle of a1 + property: prefix + subject-area: "geometry" + mathml: + - "∟x" + - "⊾x" + - "⦜x" + - "⦝x" + urls: + - "https://mathworld.wolfram.com/RightAngle.html" + - "https://en.wikipedia.org/wiki/Right_angle" + + - concept: right-derivative + arity: 1 + arguments: [a1] + speech: + en: right derivative of a1 + property: operator + subject-area: "calculus" + mathml: + - "∂+f" + urls: + - "https://en.wikipedia.org/wiki/Left_and_right_derivative" + + - concept: right-quotient + arity: 2 + arguments: [a1, a2] + speech: + en: a1 right quotient a2 + property: infix + subject-area: "formal languages" + mathml: + - "X\\Y" + urls: + - "https://en.wikipedia.org/wiki/Quotient_of_a_formal_language" + + - concept: ring-of-formal-power-series + arity: 2 + arguments: [a1, a2] + speech: + en: ring of formal power series a1 a2 + property: mixfix + subject-area: "ring theory" + mathml: + - "R⟦x⟧" + urls: + - "https://en.wikipedia.org/wiki/Formal_power_series#The_ring_of_formal_power_series" + + - concept: rising-factorial + arity: 2 + arguments: [a1, a2] + speech: + en: a2th rising factorial of a1 + property: mixfix + subject-area: "combinatorics" + mathml: + - "x(n)" + - "xn¯" + urls: + - "https://en.wikipedia.org/wiki/Falling_and_rising_factorials" + - "https://mathworld.wolfram.com/RisingFactorial.html" + - "https://dlmf.nist.gov/26.1#P1.p1" + alias: + - pochhammer-function + - pochhammer-polynomial + - ascending-factorial + - rising-sequential-product + - upper-factorial + + - concept: roman-numeral + arity: 0 + arguments: [] + speech: en: roman numeral - property: symbol - area: "number theory" - mathml: - - "i" - - "ii" - - "iii" - - "iv" - - "v" - - "vi" - - "vii" - - "viii" - - "ix" - - "x" - urls: - - "https://mathworld.wolfram.com/RomanNumerals.html" - - "https://en.wikipedia.org/wiki/Roman_numerals" - - "https://www.encyclopediaofmath.org/index.php/Roman_numerals" - - - concept: roof - arity: 3 - en: roof of $1, $2 and $3 - property: mixfix - area: "category theory" - mathml: - - "X←Y→Z" - urls: - - "https://en.wikipedia.org/wiki/Span_(category_theory)" - - "https://ncatlab.org/nlab/show/span" - alias: - - span - - correspondence - - - concept: root-of-unity - arity: 0 + property: symbol + subject-area: "number theory" + mathml: + - "i" + - "ii" + - "iii" + - "iv" + - "v" + - "vi" + - "vii" + - "viii" + - "ix" + - "x" + urls: + - "https://mathworld.wolfram.com/RomanNumerals.html" + - "https://en.wikipedia.org/wiki/Roman_numerals" + - "https://www.encyclopediaofmath.org/index.php/Roman_numerals" + + - concept: roof + arity: 3 + arguments: [a1, a2, a3] + speech: + en: roof of a1, a2 and a3 + property: mixfix + subject-area: "category theory" + mathml: + - "X←Y→Z" + urls: + - "https://en.wikipedia.org/wiki/Span_(category_theory)" + - "https://ncatlab.org/nlab/show/span" + alias: + - span + - correspondence + + - concept: root-of-unity + arity: 0 + arguments: [] + speech: en: root of unity - property: symbol - area: "complex numbers" - mathml: - - "ω" - urls: - - "https://mathworld.wolfram.com/RootofUnity.html" - - "https://en.wikipedia.org/wiki/Root_of_unity" - - "https://ncatlab.org/nlab/show/root+of+unity" - - - concept: root-mean-square - arity: 1 - en: root mean square of $1 - property: msub - area: "means" - mathml: - - "GRMS" - urls: - - "https://mathworld.wolfram.com/Root-Mean-Square.html" - alias: - - rms - - quadratic-mean - - - concept: rooted-product-of-graphs - arity: 2 - en: $1 rooted product of graphs $2 - property: infix - area: "graph theory" - mathml: - - "X∘Y" - urls: - - "https://en.wikipedia.org/wiki/Rooted_product_of_graphs" - - - concept: ruark-number - arity: 0 + property: symbol + subject-area: "complex numbers" + mathml: + - "ω" + urls: + - "https://mathworld.wolfram.com/RootofUnity.html" + - "https://en.wikipedia.org/wiki/Root_of_unity" + - "https://ncatlab.org/nlab/show/root+of+unity" + + - concept: root-mean-square + arity: 1 + arguments: [a1] + speech: + en: root mean square of a1 + property: msub + subject-area: "means" + mathml: + - "GRMS" + urls: + - "https://mathworld.wolfram.com/Root-Mean-Square.html" + alias: + - rms + - quadratic-mean + + - concept: rooted-product-of-graphs + arity: 2 + arguments: [a1, a2] + speech: + en: a1 rooted product of graphs a2 + property: infix + subject-area: "graph theory" + mathml: + - "X∘Y" + urls: + - "https://en.wikipedia.org/wiki/Rooted_product_of_graphs" + + - concept: ruark-number + arity: 0 + arguments: [] + speech: en: ruark number - property: symbol - area: "physics" - mathml: - - "Ru" - urls: - - "https://en.wikipedia.org/wiki/Euler_number_(physics)" - - - concept: s-set-theory - arity: 0 + property: symbol + subject-area: "physics" + mathml: + - "Ru" + urls: + - "https://en.wikipedia.org/wiki/Euler_number_(physics)" + + - concept: s-set-theory + arity: 0 + arguments: [] + speech: en: s set theory - property: constant - area: "set theory" - mathml: - - "S" - urls: - - "https://en.wikipedia.org/wiki/S_(set_theory)" - - - concept: s5-modal-logic - arity: 0 + property: constant + subject-area: "set theory" + mathml: + - "S" + urls: + - "https://en.wikipedia.org/wiki/S_(set_theory)" + + - concept: s5-modal-logic + arity: 0 + arguments: [] + speech: en: s5 modal logic - property: constant - area: "logic" - mathml: - - "S5" - urls: - - "https://en.wikipedia.org/wiki/S5_(modal_logic)" - - - concept: sample-space - arity: 0 + property: constant + subject-area: "logic" + mathml: + - "S5" + urls: + - "https://en.wikipedia.org/wiki/S5_(modal_logic)" + + - concept: sample-space + arity: 0 + arguments: [] + speech: en: sample space - property: symbol - area: "probability theory" - mathml: - - "S" - - "Ω" - - "U" - urls: - - "https://mathworld.wolfram.com/SampleSpace.html" - - "https://en.wikipedia.org/wiki/Sample_space" - - "https://www.encyclopediaofmath.org/index.php/Sample_space" - - - concept: sample-variance - arity: 1 - en: sample variance of $1 - property: embellished symbol - area: "probability theory" - mathml: - - "Sy2" - urls: - - "https://mathworld.wolfram.com/SampleVariance.html" - - "https://www.encyclopediaofmath.org/index.php/Sample_variance" - - "https://en.wikipedia.org/wiki/Variance#Sample_variance" - - - concept: scalar-triple-product - arity: 3 - en: scalar triple product of $1, $2 and $3 - property: mixfix, fenced - area: "vector algebra" - mathml: - - "A·(B·C)" - - "[A,B,C]" - urls: - - "https://mathworld.wolfram.com/ScalarTripleProduct.html" - - "https://en.wikipedia.org/wiki/Triple_product" - - - concept: scaled-riemann-theta-function - arity: 1 - en: scaled riemann theta function of $1 - property: mover - area: "special functions" - mathml: - - "θ^(𝐳|𝛀)" - urls: - - "https://dlmf.nist.gov/21.2#i" - - "https://dlmf.nist.gov/21.2#E1" + property: symbol + subject-area: "probability theory" + mathml: + - "S" + - "Ω" + - "U" + urls: + - "https://mathworld.wolfram.com/SampleSpace.html" + - "https://en.wikipedia.org/wiki/Sample_space" + - "https://www.encyclopediaofmath.org/index.php/Sample_space" + + - concept: sample-variance + arity: 1 + arguments: [a1] + speech: + en: sample variance of a1 + property: embellished symbol + subject-area: "probability theory" + mathml: + - "Sy2" + urls: + - "https://mathworld.wolfram.com/SampleVariance.html" + - "https://www.encyclopediaofmath.org/index.php/Sample_variance" + - "https://en.wikipedia.org/wiki/Variance#Sample_variance" + + - concept: scalar-triple-product + arity: 3 + arguments: [a1, a2, a3] + speech: + en: scalar triple product of a1, a2 and a3 + property: mixfix, fenced + subject-area: "vector algebra" + mathml: + - "A·(B·C)" + - "[A,B,C]" + urls: + - "https://mathworld.wolfram.com/ScalarTripleProduct.html" + - "https://en.wikipedia.org/wiki/Triple_product" + + - concept: scaled-riemann-theta-function + arity: 1 + arguments: [a1] + speech: + en: scaled riemann theta function of a1 + property: mover + subject-area: "special functions" + mathml: + - "θ^(𝐳|𝛀)" + urls: + - "https://dlmf.nist.gov/21.2#i" + - "https://dlmf.nist.gov/21.2#E1" - - concept: schlaefli-symbol - arity: ">=0" - en: schlaefli symbol of $1, ... - property: fenced - area: "geometry" - mathml: - - "{p,q,r}" - urls: - - "https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol" - - - concept: schroder-number - arity: 1 - en: schroder number of $1 - property: "indexed symbol" - area: "combinatorics" - mathml: - - "Sx" - urls: - - "https://mathworld.wolfram.com/SchroederNumber.html" - - "https://en.wikipedia.org/wiki/Schr%C3%B6der_number" - - "https://dlmf.nist.gov/26.6#E4" - - - concept: schur-multiplier - arity: 1 - en: schur multiplier of $1 - property: function - area: "group theory" - mathml: - - "M(x)" - urls: - - "https://mathworld.wolfram.com/SchurMultiplier.html" - - "https://en.wikipedia.org/wiki/Schur_multiplier" - - "https://en.wikipedia.org/wiki/Schur_cover" - alias: - - schur-multiplicator - - - concept: schwartz-space - arity: 0 + - concept: schlaefli-symbol + arity: ">=0" + speech: + en: schlaefli symbol of a1, ... + property: fenced + subject-area: "geometry" + mathml: + - "{p,q,r}" + urls: + - "https://en.wikipedia.org/wiki/Schl%C3%A4fli_symbol" + + - concept: schroder-number + arity: 1 + arguments: [a1] + speech: + en: schroder number of a1 + property: "indexed symbol" + subject-area: "combinatorics" + mathml: + - "Sx" + urls: + - "https://mathworld.wolfram.com/SchroederNumber.html" + - "https://en.wikipedia.org/wiki/Schr%C3%B6der_number" + - "https://dlmf.nist.gov/26.6#E4" + + - concept: schur-multiplier + arity: 1 + arguments: [a1] + speech: + en: schur multiplier of a1 + property: function + subject-area: "group theory" + mathml: + - "M(x)" + urls: + - "https://mathworld.wolfram.com/SchurMultiplier.html" + - "https://en.wikipedia.org/wiki/Schur_multiplier" + - "https://en.wikipedia.org/wiki/Schur_cover" + alias: + - schur-multiplicator + + - concept: schwartz-space + arity: 0 + arguments: [] + speech: en: schwartz space - property: symbol - area: "topology" - mathml: - - "𝒮" - - "S" - urls: - - "https://mathworld.wolfram.com/SchwartzSpace.html" - - "https://en.wikipedia.org/wiki/Schwartz_space" - - "https://ncatlab.org/nlab/show/Schwartz+space" - - - concept: schwarzian-derivative - arity: 2 - en: schwarzian derivative $1 $2 - property: fenced, mixfix - area: "complex analysis" - mathml: - - "{x,y}" - notationa: "mrow ( S $1 ) ($2" - urls: - - "https://mathworld.wolfram.com/SchwarzianDerivative.html" - - "https://en.wikipedia.org/wiki/Schwarzian_derivative" - - "https://dlmf.nist.gov/1.13#E20" - - "https://www.encyclopediaofmath.org/index.php/Schwarzian_derivative" - - - concept: second-carmichael-function - arity: 1 - en: second carmichael function of $1 - property: function - area: "number theory" - mathml: - - "λ′(n)" - urls: - - "https://mathworld.wolfram.com/CarmichaelFunction.html" - - "https://en.wikipedia.org/wiki/Carmichael_function" - - - concept: sectional-curvature - arity: 1 - en: sectional curvature of $1 - property: function - area: "riemannian geometry" - mathml: - - "KX" - - "κX" - urls: - - "https://mathworld.wolfram.com/SectionalCurvature.html" - - "https://en.wikipedia.org/wiki/Sectional_curvature" - - "https://www.encyclopediaofmath.org/index.php/Sectional_curvature" - - - concept: sedenion - arity: 0 + property: symbol + subject-area: "topology" + mathml: + - "𝒮" + - "S" + urls: + - "https://mathworld.wolfram.com/SchwartzSpace.html" + - "https://en.wikipedia.org/wiki/Schwartz_space" + - "https://ncatlab.org/nlab/show/Schwartz+space" + + - concept: schwarzian-derivative + arity: 2 + arguments: [a1, a2] + speech: + en: schwarzian derivative a1 a2 + property: fenced, mixfix + subject-area: "complex analysis" + mathml: + - "{x,y}" + notationa: "mrow ( S a1 ) (a2" + urls: + - "https://mathworld.wolfram.com/SchwarzianDerivative.html" + - "https://en.wikipedia.org/wiki/Schwarzian_derivative" + - "https://dlmf.nist.gov/1.13#E20" + - "https://www.encyclopediaofmath.org/index.php/Schwarzian_derivative" + + - concept: second-carmichael-function + arity: 1 + arguments: [a1] + speech: + en: second carmichael function of a1 + property: function + subject-area: "number theory" + mathml: + - "λ′(n)" + urls: + - "https://mathworld.wolfram.com/CarmichaelFunction.html" + - "https://en.wikipedia.org/wiki/Carmichael_function" + + - concept: sectional-curvature + arity: 1 + arguments: [a1] + speech: + en: sectional curvature of a1 + property: function + subject-area: "riemannian geometry" + mathml: + - "KX" + - "κX" + urls: + - "https://mathworld.wolfram.com/SectionalCurvature.html" + - "https://en.wikipedia.org/wiki/Sectional_curvature" + - "https://www.encyclopediaofmath.org/index.php/Sectional_curvature" + + - concept: sedenion + arity: 0 + arguments: [] + speech: en: sedenion - property: symbol - area: "abstract algebra" - mathml: - - "𝕊" - urls: - - "https://en.wikipedia.org/wiki/Sedenion" - - "https://ncatlab.org/nlab/show/sedenion" - - - concept: selection - arity: 3 + property: symbol + subject-area: "abstract algebra" + mathml: + - "𝕊" + urls: + - "https://en.wikipedia.org/wiki/Sedenion" + - "https://ncatlab.org/nlab/show/sedenion" + + - concept: selection + arity: 3 + arguments: [a1, a2, a3] + speech: en: selection - property: "indexed function" - area: "relational algebra" - mathml: - - "σaθb" - urls: - - "https://en.wikipedia.org/wiki/Selection_(relational_algebra)" - - - concept: seminorm - arity: 1 - en: seminorm of $1 - property: fenced - area: "linear algebra" - mathml: - - "‖X‖" - - "|X|" - urls: - - "https://mathworld.wolfram.com/Seminorm.html" - - "https://en.wikipedia.org/wiki/Norm_(mathematics)" - alias: - - pseudonorm - - - concept: set-of-invertible-maps - arity: 1 - en: set of invertible maps of $1 - property: prefix - area: "commutative algebra" - mathml: - - "!x" - urls: - - "https://arxiv.org/abs/2009.015866" - - - concept: shannon-entropy - arity: 0 + property: "indexed function" + subject-area: "relational algebra" + mathml: + - "σaθb" + urls: + - "https://en.wikipedia.org/wiki/Selection_(relational_algebra)" + + - concept: seminorm + arity: 1 + arguments: [a1] + speech: + en: seminorm of a1 + property: fenced + subject-area: "linear algebra" + mathml: + - "‖X‖" + - "|X|" + urls: + - "https://mathworld.wolfram.com/Seminorm.html" + - "https://en.wikipedia.org/wiki/Norm_(mathematics)" + alias: + - pseudonorm + + - concept: set-of-invertible-maps + arity: 1 + arguments: [a1] + speech: + en: set of invertible maps of a1 + property: prefix + subject-area: "commutative algebra" + mathml: + - "!x" + urls: + - "https://arxiv.org/abs/2009.015866" + + - concept: shannon-entropy + arity: 0 + arguments: [] + speech: en: shannon entropy - property: symbol - area: "information theory" - mathml: - - "H" - urls: - - "https://mathworld.wolfram.com/ShannonEntropy.html" - - "https://en.wikipedia.org/wiki/Entropy_(information_theory)" - - "https://ncatlab.org/nlab/show/entropy" - - "https://www.encyclopediaofmath.org/index.php/Entropy" - alias: - - entropy - - - concept: shift-operator - arity: 1 - en: shift operator of $1 - property: operator - area: "functional analysis" - mathml: - - "Tt(f)" - urls: - - "https://mathworld.wolfram.com/ShiftOperator.html" - - "https://en.wikipedia.org/wiki/Shift_operator" - - "https://www.encyclopediaofmath.org/index.php/Shift_operator" - alias: - - translation-operator - - lag-operator - - - concept: shimura-variety - arity: 1 - en: shimura variety of $1 - property: function - area: "algebraic geometry" - mathml: - - "Sh(x)" - urls: - - "https://en.wikipedia.org/wiki/Shimura_variety" - - "https://ncatlab.org/nlab/show/Shimura+variety" - - "https://www.encyclopediaofmath.org/index.php/Shimura_variety" - - - concept: short-exact-sequence - arity: 3 - en: short exact sequence $1 $2 $3 - property: mixfix - area: "group theory" - mathml: - - "0→X→Y→Z→0" - urls: - - "https://mathworld.wolfram.com/ShortExactSequence.html" - - "https://en.wikipedia.org/wiki/Exact_sequence" - - - concept: short-rate - arity: 0 + property: symbol + subject-area: "information theory" + mathml: + - "H" + urls: + - "https://mathworld.wolfram.com/ShannonEntropy.html" + - "https://en.wikipedia.org/wiki/Entropy_(information_theory)" + - "https://ncatlab.org/nlab/show/entropy" + - "https://www.encyclopediaofmath.org/index.php/Entropy" + alias: + - entropy + + - concept: shift-operator + arity: 1 + arguments: [a1] + speech: + en: shift operator of a1 + property: operator + subject-area: "functional analysis" + mathml: + - "Tt(f)" + urls: + - "https://mathworld.wolfram.com/ShiftOperator.html" + - "https://en.wikipedia.org/wiki/Shift_operator" + - "https://www.encyclopediaofmath.org/index.php/Shift_operator" + alias: + - translation-operator + - lag-operator + + - concept: shimura-variety + arity: 1 + arguments: [a1] + speech: + en: shimura variety of a1 + property: function + subject-area: "algebraic geometry" + mathml: + - "Sh(x)" + urls: + - "https://en.wikipedia.org/wiki/Shimura_variety" + - "https://ncatlab.org/nlab/show/Shimura+variety" + - "https://www.encyclopediaofmath.org/index.php/Shimura_variety" + + - concept: short-exact-sequence + arity: 3 + arguments: [a1, a2, a3] + speech: + en: short exact sequence a1 a2 a3 + property: mixfix + subject-area: "group theory" + mathml: + - "0→X→Y→Z→0" + urls: + - "https://mathworld.wolfram.com/ShortExactSequence.html" + - "https://en.wikipedia.org/wiki/Exact_sequence" + + - concept: short-rate + arity: 0 + arguments: [] + speech: en: short rate - property: symbol - area: "mathematical finance" - mathml: - - "rt" - urls: - - "https://en.wikipedia.org/wiki/Short_rate" - - "https://en.wikipedia.org/wiki/Short-rate_model" - - "https://en.wikipedia.org/wiki/Kalotay%E2%80%93Williams%E2%80%93Fabozzi_model" - - "https://en.wikipedia.org/wiki/Longstaff%E2%80%93Schwartz_model" - - - concept: sidon-sequence - arity: 0 + property: symbol + subject-area: "mathematical finance" + mathml: + - "rt" + urls: + - "https://en.wikipedia.org/wiki/Short_rate" + - "https://en.wikipedia.org/wiki/Short-rate_model" + - "https://en.wikipedia.org/wiki/Kalotay%E2%80%93Williams%E2%80%93Fabozzi_model" + - "https://en.wikipedia.org/wiki/Longstaff%E2%80%93Schwartz_model" + + - concept: sidon-sequence + arity: 0 + arguments: [] + speech: en: sidon sequence - property: symbol - area: "combinatorics" - mathml: - - "A" - urls: - - "https://mathworld.wolfram.com/SidonSequence.html" - - "https://en.wikipedia.org/wiki/Sidon_sequence" - alias: - - sidon-set - - - concept: sign-function - arity: 1 - en: sign function of $1 - property: function - area: "special-functions" - mathml: - - "sgn(x)" - urls: - - "https://en.wikipedia.org/wiki/Sign_function" - alias: - - signum-function - - - concept: signature-of-permutation - arity: 1 - en: signature of permutation of $1 - property: function - area: "combinatorics" - mathml: - - "sign(x)" - urls: - - "https://ncatlab.org/nlab/show/signature+of+a+permutation" - alias: - - sign-of-permutation - - - concept: silver-ratio - arity: 0 + property: symbol + subject-area: "combinatorics" + mathml: + - "A" + urls: + - "https://mathworld.wolfram.com/SidonSequence.html" + - "https://en.wikipedia.org/wiki/Sidon_sequence" + alias: + - sidon-set + + - concept: sign-function + arity: 1 + arguments: [a1] + speech: + en: sign function of a1 + property: function + subject-area: "special-functions" + mathml: + - "sgn(x)" + urls: + - "https://en.wikipedia.org/wiki/Sign_function" + alias: + - signum-function + + - concept: signature-of-permutation + arity: 1 + arguments: [a1] + speech: + en: signature of permutation of a1 + property: function + subject-area: "combinatorics" + mathml: + - "sign(x)" + urls: + - "https://ncatlab.org/nlab/show/signature+of+a+permutation" + alias: + - sign-of-permutation + + - concept: silver-ratio + arity: 0 + arguments: [] + speech: en: silver ratio - property: constant - area: "number theory" - mathml: - - "δS" - urls: - - "https://mathworld.wolfram.com/SilverRatio.html" - - "https://en.wikipedia.org/wiki/Silver_ratio" - - "https://en.wikipedia.org/wiki/Silver_rectangle" - - - concept: similar - arity: 2 - en: $1 similar $2 - property: infix - area: "geometry" - mathml: - - "X~Y" - urls: - - "https://mathworld.wolfram.com/Similar.html" - - "https://en.wikipedia.org/wiki/Matrix_similarity" - - "https://en.wikipedia.org/wiki/Similarity_(geometry)" - - - concept: simplex - arity: 1 - en: $1 simplex - property: "indexed symbol" - area: "geometry" - mathml: - - "Δn" - - "Δ[n]" - urls: - - "https://mathworld.wolfram.com/Simplex.html" - - "https://en.wikipedia.org/wiki/Simplex" - - "https://ncatlab.org/nlab/show/simplex" - - "https://www.encyclopediaofmath.org/index.php/Simplex" - - - concept: sinc-function - arity: 1 - en: sinc function of $1 - property: function - area: "special functions" - mathml: - - "SX" - - "sincX" - urls: - - "https://mathworld.wolfram.com/SincFunction.html" - - "https://en.wikipedia.org/wiki/Sinc_function" - - "https://dlmf.nist.gov/3.3#SS6.p2" - - - concept: sine-integral - arity: 1 - en: sine integral of $1 - property: operator - area: "special functions" - mathml: - - "Si(x)" - urls: - - "https://mathworld.wolfram.com/SineIntegral.html" - - "https://dlmf.nist.gov/6.2#ii" - - "https://dlmf.nist.gov/6.2#E9" - - "https://dlmf.nist.gov/6.2#E10" - - - concept: size-of-test - arity: 0 + property: constant + subject-area: "number theory" + mathml: + - "δS" + urls: + - "https://mathworld.wolfram.com/SilverRatio.html" + - "https://en.wikipedia.org/wiki/Silver_ratio" + - "https://en.wikipedia.org/wiki/Silver_rectangle" + + - concept: similar + arity: 2 + arguments: [a1, a2] + speech: + en: a1 similar a2 + property: infix + subject-area: "geometry" + mathml: + - "X~Y" + urls: + - "https://mathworld.wolfram.com/Similar.html" + - "https://en.wikipedia.org/wiki/Matrix_similarity" + - "https://en.wikipedia.org/wiki/Similarity_(geometry)" + + - concept: simplex + arity: 1 + arguments: [a1] + speech: + en: a1 simplex + property: "indexed symbol" + subject-area: "geometry" + mathml: + - "Δn" + - "Δ[n]" + urls: + - "https://mathworld.wolfram.com/Simplex.html" + - "https://en.wikipedia.org/wiki/Simplex" + - "https://ncatlab.org/nlab/show/simplex" + - "https://www.encyclopediaofmath.org/index.php/Simplex" + + - concept: sinc-function + arity: 1 + arguments: [a1] + speech: + en: sinc function of a1 + property: function + subject-area: "special functions" + mathml: + - "SX" + - "sincX" + urls: + - "https://mathworld.wolfram.com/SincFunction.html" + - "https://en.wikipedia.org/wiki/Sinc_function" + - "https://dlmf.nist.gov/3.3#SS6.p2" + + - concept: sine-integral + arity: 1 + arguments: [a1] + speech: + en: sine integral of a1 + property: operator + subject-area: "special functions" + mathml: + - "Si(x)" + urls: + - "https://mathworld.wolfram.com/SineIntegral.html" + - "https://dlmf.nist.gov/6.2#ii" + - "https://dlmf.nist.gov/6.2#E9" + - "https://dlmf.nist.gov/6.2#E10" + + - concept: size-of-test + arity: 0 + arguments: [] + speech: en: size of test - property: symbol - area: "statistics" - mathml: - - "α" - urls: - - "https://en.wikipedia.org/wiki/Size_(statistics)" - - - concept: skewes-number - arity: 1 - en: skewes number of $1 - property: "indexed symbol" - area: "number theory" - mathml: - - "Skx" - urls: - - "https://mathworld.wolfram.com/SkewesNumber.html" - - "https://en.wikipedia.org/wiki/Skewes%27_number" - - - concept: small-o - arity: 1 - en: small o of $1 - property: prefix - area: "complexity" - mathml: - - "o(x)" - urls: - - "https://en.wikipedia.org/wiki/Big_O_notation" - - "https://mathworld.wolfram.com/o.html" - - - concept: smith-number - arity: 1 - en: smith number of $1 - property: "indexed symbol" - area: "number theory" - mathml: - - "S(x)" - urls: - - "https://mathworld.wolfram.com/SmithNumber.html" - - "https://en.wikipedia.org/wiki/Smith_number" - - - concept: sobolev-space - arity: 2 + property: symbol + subject-area: "statistics" + mathml: + - "α" + urls: + - "https://en.wikipedia.org/wiki/Size_(statistics)" + + - concept: skewes-number + arity: 1 + arguments: [a1] + speech: + en: skewes number of a1 + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Skx" + urls: + - "https://mathworld.wolfram.com/SkewesNumber.html" + - "https://en.wikipedia.org/wiki/Skewes%27_number" + + - concept: small-o + arity: 1 + arguments: [a1] + speech: + en: small o of a1 + property: prefix + subject-area: "complexity" + mathml: + - "o(x)" + urls: + - "https://en.wikipedia.org/wiki/Big_O_notation" + - "https://mathworld.wolfram.com/o.html" + + - concept: smith-number + arity: 1 + arguments: [a1] + speech: + en: smith number of a1 + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "S(x)" + urls: + - "https://mathworld.wolfram.com/SmithNumber.html" + - "https://en.wikipedia.org/wiki/Smith_number" + + - concept: sobolev-space + arity: 2 + arguments: [a1, a2] + speech: en: sobolev space - property: "indexed symbol" - area: "fourier analysis" - mathml: - - "Wkp" - urls: - - "https://mathworld.wolfram.com/SobolevSpace.html" - - "https://en.wikipedia.org/wiki/Sobolev_space" - - "https://ncatlab.org/nlab/show/Sobolev+space" - - "https://www.encyclopediaofmath.org/index.php/Sobolev_space" - - - concept: socle - arity: 1 - en: socle of $1 - property: function - area: "group theory" - mathml: - - "soc(x)" - urls: - - "https://mathworld.wolfram.com/Socle.html" - - "https://en.wikipedia.org/wiki/Socle_(mathematics)" - - "https://ncatlab.org/nlab/show/socle" - - "https://www.encyclopediaofmath.org/index.php/Socle" - - - concept: soft-o - arity: 0 + property: "indexed symbol" + subject-area: "fourier analysis" + mathml: + - "Wkp" + urls: + - "https://mathworld.wolfram.com/SobolevSpace.html" + - "https://en.wikipedia.org/wiki/Sobolev_space" + - "https://ncatlab.org/nlab/show/Sobolev+space" + - "https://www.encyclopediaofmath.org/index.php/Sobolev_space" + + - concept: socle + arity: 1 + arguments: [a1] + speech: + en: socle of a1 + property: function + subject-area: "group theory" + mathml: + - "soc(x)" + urls: + - "https://mathworld.wolfram.com/Socle.html" + - "https://en.wikipedia.org/wiki/Socle_(mathematics)" + - "https://ncatlab.org/nlab/show/socle" + - "https://www.encyclopediaofmath.org/index.php/Socle" + + - concept: soft-o + arity: 0 + arguments: [] + speech: en: soft o - property: symbol - area: "complexity theory" - mathml: - - "Õ" - urls: - alias: - - Extensions_to_the_Bachmann–Landau_notations - - - concept: solid-angle - arity: 0 + property: symbol + subject-area: "complexity theory" + mathml: + - "Õ" + urls: + alias: + - Extensions_to_the_Bachmann–Landau_notations + + - concept: solid-angle + arity: 0 + arguments: [] + speech: en: solid angle - property: symbol - area: "geometry" - mathml: - - "Ω" - urls: - - "https://mathworld.wolfram.com/SolidAngle.html" - - "https://en.wikipedia.org/wiki/Solid_angle" - - "https://www.encyclopediaofmath.org/index.php/Solid_angle" - - - concept: span - arity: 1 - en: $1 span - property: unit - area: "imperial units" - mathml: - - "span(x)" - urls: - - "https://en.wikipedia.org/wiki/Span_(unit)" - - - concept: special-linear-group - arity: 1 - en: special linear group of $1 - property: "indexed function" - area: "group theory" - mathml: - - "SLx" - urls: - - "https://mathworld.wolfram.com/SpecialLinearGroup.html" - - "https://en.wikipedia.org/wiki/Special_linear_group" - - "https://ncatlab.org/nlab/show/special+linear+group" - - "https://www.encyclopediaofmath.org/index.php/Special_linear_group" - - - concept: special-orthogonal-group - arity: 1 - en: special orthogonal group of $1 - property: "indexed function" - area: "group theory" - mathml: - - "SO(x)" - urls: - - "https://mathworld.wolfram.com/SpecialOrthogonalGroup.html" - - "https://ncatlab.org/nlab/show/special+orthogonal+group" - - - concept: special-unitary-group - arity: 1 - en: special unitary group of $1 - property: function - area: "lie groups" - mathml: - - "SU(x)" - urls: - - "https://mathworld.wolfram.com/SpecialUnitaryGroup.html" - - "https://en.wikipedia.org/wiki/Special_unitary_group" - - "https://ncatlab.org/nlab/show/special+unitary+group" - - - concept: spectral-radius - arity: 1 - en: spectral radius of $1 - property: function - area: "spectral theory" - mathml: - - "ρ(x)" - urls: - - "https://mathworld.wolfram.com/SpectralRadius.html" - - "https://en.wikipedia.org/wiki/Spectral_radius" - - "https://www.encyclopediaofmath.org/index.php/Spectral_radius" - - - concept: spectrum - arity: 1 - en: spectrum of $1 - property: function - area: "functional analysis" - mathml: - - "σ(x)" - urls: - - "https://en.wikipedia.org/wiki/Spectrum_(functional_analysis)" - - - concept: spectrum-category - arity: 0 + property: symbol + subject-area: "geometry" + mathml: + - "Ω" + urls: + - "https://mathworld.wolfram.com/SolidAngle.html" + - "https://en.wikipedia.org/wiki/Solid_angle" + - "https://www.encyclopediaofmath.org/index.php/Solid_angle" + + - concept: span + arity: 1 + arguments: [a1] + speech: + en: a1 span + property: unit + subject-area: "imperial units" + mathml: + - "span(x)" + urls: + - "https://en.wikipedia.org/wiki/Span_(unit)" + + - concept: special-linear-group + arity: 1 + arguments: [a1] + speech: + en: special linear group of a1 + property: "indexed function" + subject-area: "group theory" + mathml: + - "SLx" + urls: + - "https://mathworld.wolfram.com/SpecialLinearGroup.html" + - "https://en.wikipedia.org/wiki/Special_linear_group" + - "https://ncatlab.org/nlab/show/special+linear+group" + - "https://www.encyclopediaofmath.org/index.php/Special_linear_group" + + - concept: special-orthogonal-group + arity: 1 + arguments: [a1] + speech: + en: special orthogonal group of a1 + property: "indexed function" + subject-area: "group theory" + mathml: + - "SO(x)" + urls: + - "https://mathworld.wolfram.com/SpecialOrthogonalGroup.html" + - "https://ncatlab.org/nlab/show/special+orthogonal+group" + + - concept: special-unitary-group + arity: 1 + arguments: [a1] + speech: + en: special unitary group of a1 + property: function + subject-area: "lie groups" + mathml: + - "SU(x)" + urls: + - "https://mathworld.wolfram.com/SpecialUnitaryGroup.html" + - "https://en.wikipedia.org/wiki/Special_unitary_group" + - "https://ncatlab.org/nlab/show/special+unitary+group" + + - concept: spectral-radius + arity: 1 + arguments: [a1] + speech: + en: spectral radius of a1 + property: function + subject-area: "spectral theory" + mathml: + - "ρ(x)" + urls: + - "https://mathworld.wolfram.com/SpectralRadius.html" + - "https://en.wikipedia.org/wiki/Spectral_radius" + - "https://www.encyclopediaofmath.org/index.php/Spectral_radius" + + - concept: spectrum + arity: 1 + arguments: [a1] + speech: + en: spectrum of a1 + property: function + subject-area: "functional analysis" + mathml: + - "σ(x)" + urls: + - "https://en.wikipedia.org/wiki/Spectrum_(functional_analysis)" + + - concept: spectrum-category + arity: 0 + arguments: [] + speech: en: spectrum category - property: symbol - area: "category theory" - mathml: - - "Sp" - urls: - - "https://ncatlab.org/nlab/show/Spectrum" - - - concept: spectrum-of-matrix - arity: 1 - en: spectrum of matrix of $1 - property: msub - area: "linear algebra" - mathml: - - "σx" - urls: - - "https://en.wikipedia.org/wiki/Spectrum_of_a_matrix" - - - concept: spectrum-of-algebra - arity: 1 - en: spectrum of algebra of $1 - property: mover - area: "algebra" - mathml: - - "A^" - urls: - - "https://en.wikipedia.org/wiki/Spectrum_of_a_C*-algebra" - - - concept: spectrum-of-ring - arity: 1 - en: spectrum of ring of $1 - property: function - area: "group theory" - mathml: - - "Spec(x)" - urls: - - "https://en.wikipedia.org/wiki/Spectrum_of_a_ring" - - - concept: spherical-bessel-function-of-third-kind - arity: 2 + property: symbol + subject-area: "category theory" + mathml: + - "Sp" + urls: + - "https://ncatlab.org/nlab/show/Spectrum" + + - concept: spectrum-of-matrix + arity: 1 + arguments: [a1] + speech: + en: spectrum of matrix of a1 + property: msub + subject-area: "linear algebra" + mathml: + - "σx" + urls: + - "https://en.wikipedia.org/wiki/Spectrum_of_a_matrix" + + - concept: spectrum-of-algebra + arity: 1 + arguments: [a1] + speech: + en: spectrum of algebra of a1 + property: mover + subject-area: "algebra" + mathml: + - "A^" + urls: + - "https://en.wikipedia.org/wiki/Spectrum_of_a_C*-algebra" + + - concept: spectrum-of-ring + arity: 1 + arguments: [a1] + speech: + en: spectrum of ring of a1 + property: function + subject-area: "group theory" + mathml: + - "Spec(x)" + urls: + - "https://en.wikipedia.org/wiki/Spectrum_of_a_ring" + + - concept: spherical-bessel-function-of-third-kind + arity: 2 + arguments: [a1, a2] + speech: en: spherical bessel function of third kind - property: "indexed function" - area: "special functions" - mathml: - - "hn(1)(z)" - - "hn(2)(z)" - urls: - - "https://mathworld.wolfram.com/SphericalBesselFunctionoftheThirdKind.html" - - "https://dlmf.nist.gov/10.47#E5" - - "https://dlmf.nist.gov/10.47#E6" - - - concept: spherical-coordinate - arity: 3 + property: "indexed function" + subject-area: "special functions" + mathml: + - "hn(1)(z)" + - "hn(2)(z)" + urls: + - "https://mathworld.wolfram.com/SphericalBesselFunctionoftheThirdKind.html" + - "https://dlmf.nist.gov/10.47#E5" + - "https://dlmf.nist.gov/10.47#E6" + + - concept: spherical-coordinate + arity: 3 + arguments: [a1, a2, a3] + speech: en: spherical coordinate - property: fenced - area: "geometry" - mathml: - - "(a,b,c)" - urls: - - "https://mathworld.wolfram.com/SphericalCoordinates.html" - - "https://www.encyclopediaofmath.org/index.php/Spherical_coordinates" - - - concept: spin-angular-momentum - arity: 0 + property: fenced + subject-area: "geometry" + mathml: + - "(a,b,c)" + urls: + - "https://mathworld.wolfram.com/SphericalCoordinates.html" + - "https://www.encyclopediaofmath.org/index.php/Spherical_coordinates" + + - concept: spin-angular-momentum + arity: 0 + arguments: [] + speech: en: spin angular momentum - property: symbol - area: "quantum mechanics" - mathml: - - "S" - urls: - - "https://en.wikipedia.org/wiki/Spin_(physics)" - - - concept: spin-group - arity: 0 + property: symbol + subject-area: "quantum mechanics" + mathml: + - "S" + urls: + - "https://en.wikipedia.org/wiki/Spin_(physics)" + + - concept: spin-group + arity: 0 + arguments: [] + speech: en: spin group - property: symbol - area: "group theory" - mathml: - - "Spin" - urls: - - "https://mathworld.wolfram.com/SpinGroup.html" - - "https://en.wikipedia.org/wiki/Spin_group" - - "https://ncatlab.org/nlab/show/spin+group" - - "https://www.encyclopediaofmath.org/index.php/Spin_group" - - - concept: spin-quantum-number - arity: 0 + property: symbol + subject-area: "group theory" + mathml: + - "Spin" + urls: + - "https://mathworld.wolfram.com/SpinGroup.html" + - "https://en.wikipedia.org/wiki/Spin_group" + - "https://ncatlab.org/nlab/show/spin+group" + - "https://www.encyclopediaofmath.org/index.php/Spin_group" + + - concept: spin-quantum-number + arity: 0 + arguments: [] + speech: en: spin quantum number - property: symbol - area: "quantum mechanics" - mathml: - - "s" - urls: - - "https://en.wikipedia.org/wiki/Spin_(physics)" - - - concept: square - arity: 4 - en: "square $1 $2 $3 $4" - property: prefix - area: "geometry" - mathml: - - "□A B C D" - urls: - - "https://mathworld.wolfram.com/Square.html" - - "https://en.wikipedia.org/wiki/Square" - - - concept: stable-distribution - arity: 0 + property: symbol + subject-area: "quantum mechanics" + mathml: + - "s" + urls: + - "https://en.wikipedia.org/wiki/Spin_(physics)" + + - concept: square + arity: 4 + arguments: [a1, a2, a3, a4] + speech: + en: "square a1 a2 a3 a4" + property: prefix + subject-area: "geometry" + mathml: + - "□A B C D" + urls: + - "https://mathworld.wolfram.com/Square.html" + - "https://en.wikipedia.org/wiki/Square" + + - concept: stable-distribution + arity: 0 + arguments: [] + speech: en: stable distribution - property: symbol - area: "probability theory" - mathml: - - "S1" - - "S2" - urls: - - "https://mathworld.wolfram.com/StableDistribution.html" - - "https://en.wikipedia.org/wiki/Stable_distribution" - - "https://www.encyclopediaofmath.org/index.php/Stable_distribution" - - - concept: stalk - arity: 2 - en: stalk of $1 at $2 - property: msub - area: "sheaf theory" - mathml: - - "ℱx" - urls: - - "https://en.wikipedia.org/wiki/Stalk_(sheaf)" - - - concept: standard-deviation - arity: 0 + property: symbol + subject-area: "probability theory" + mathml: + - "S1" + - "S2" + urls: + - "https://mathworld.wolfram.com/StableDistribution.html" + - "https://en.wikipedia.org/wiki/Stable_distribution" + - "https://www.encyclopediaofmath.org/index.php/Stable_distribution" + + - concept: stalk + arity: 2 + arguments: [a1, a2] + speech: + en: stalk of a1 at a2 + property: msub + subject-area: "sheaf theory" + mathml: + - "ℱx" + urls: + - "https://en.wikipedia.org/wiki/Stalk_(sheaf)" + + - concept: standard-deviation + arity: 0 + arguments: [] + speech: en: standard deviation - property: symbol - area: "probability theory" - mathml: - - "σ" - urls: - - "https://mathworld.wolfram.com/StandardDeviation.html" - - "https://en.wikipedia.org/wiki/Standard_deviation" - - "https://en.wikipedia.org/wiki/Sample_standard_deviation" - - "https://www.encyclopediaofmath.org/index.php/Standard_deviation" - - - concept: standard-flattening - arity: 1 - en: standard flattening of $1 - property: "indexed symbol" - area: "multilinear algebra" - mathml: - - "𝐀[m]" - urls: - - "https://en.wikipedia.org/wiki/Matricization" - alias: - - matricization - - unfolding - - - concept: stanley-reisner-ring - arity: 2 - en: stanley reisner ring $1 $2 - property: mixfix - area: "commutative algebra" - mathml: - - "k[Δ]" - urls: - - "https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner_ring" - - "https://www.encyclopediaofmath.org/index.php/Stanley-Reisner_ring" - - "https://www.encyclopediaofmath.org/index.php/StanleyâXXXXReisner_ring" - alias: - - face-ring - - - concept: stanley-reisner-ideal - arity: 1 - en: stanley reisner ideal of $1 - property: msub - area: "commutative algebra" - mathml: - - "Ix" - urls: - - "https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner_ring" - - "https://www.encyclopediaofmath.org/index.php/Stanley-Reisner_ring" - - "https://www.encyclopediaofmath.org/index.php/StanleyâXXXXReisner_ring" - alias: - - face-ideal - - - concept: star-game - arity: 0 + property: symbol + subject-area: "probability theory" + mathml: + - "σ" + urls: + - "https://mathworld.wolfram.com/StandardDeviation.html" + - "https://en.wikipedia.org/wiki/Standard_deviation" + - "https://en.wikipedia.org/wiki/Sample_standard_deviation" + - "https://www.encyclopediaofmath.org/index.php/Standard_deviation" + + - concept: standard-flattening + arity: 1 + arguments: [a1] + speech: + en: standard flattening of a1 + property: "indexed symbol" + subject-area: "multilinear algebra" + mathml: + - "𝐀[m]" + urls: + - "https://en.wikipedia.org/wiki/Matricization" + alias: + - matricization + - unfolding + + - concept: stanley-reisner-ring + arity: 2 + arguments: [a1, a2] + speech: + en: stanley reisner ring a1 a2 + property: mixfix + subject-area: "commutative algebra" + mathml: + - "k[Δ]" + urls: + - "https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner_ring" + - "https://www.encyclopediaofmath.org/index.php/Stanley-Reisner_ring" + - "https://www.encyclopediaofmath.org/index.php/StanleyâXXXXReisner_ring" + alias: + - face-ring + + - concept: stanley-reisner-ideal + arity: 1 + arguments: [a1] + speech: + en: stanley reisner ideal of a1 + property: msub + subject-area: "commutative algebra" + mathml: + - "Ix" + urls: + - "https://en.wikipedia.org/wiki/Stanley%E2%80%93Reisner_ring" + - "https://www.encyclopediaofmath.org/index.php/Stanley-Reisner_ring" + - "https://www.encyclopediaofmath.org/index.php/StanleyâXXXXReisner_ring" + alias: + - face-ideal + + - concept: star-game + arity: 0 + arguments: [] + speech: en: star - property: constant - area: "combinatorial game theory" - mathml: - - "∗" - - "{0|0}" - urls: - - "https://en.wikipedia.org/wiki/Star_(game_theory)" - - - concept: star-height - arity: 1 - en: star height of $1 - property: function - area: "formal languages" - mathml: - - "h(x)" - urls: - - "https://en.wikipedia.org/wiki/Star_height" - - - concept: steinberg-group - arity: 1 - en: steinberg group of $1 - property: function - area: "k-theory" - mathml: - - "St(x)" - urls: - - "https://en.wikipedia.org/wiki/Group_of_Lie_type" - - "https://en.wikipedia.org/wiki/Steinberg_group_(K-theory)" - - "https://ncatlab.org/nlab/show/Steinberg+group" - - - concept: stiefel-manifold - arity: 2 - en: $1th stiefel manifold over $2 - property: mixfix - area: "differential geometry" - mathml: - - "Vk(ℝn)" - notation: "mrow msub V $1 /msub ( $2" - urls: - - "https://mathworld.wolfram.com/StiefelManifold.html" - - "https://en.wikipedia.org/wiki/Stiefel_manifold" - - "https://www.encyclopediaofmath.org/index.php/Stiefel_manifold" - - - concept: stiefel-whitney-class - arity: 1 - en: stiefel whitney class of $1 - property: function - area: "algebraic topology" - mathml: - - "w(x)" - urls: - - "https://mathworld.wolfram.com/Stiefel-WhitneyClass.html" - - "https://en.wikipedia.org/wiki/Stiefel%E2%80%93Whitney_class" - - "https://ncatlab.org/nlab/show/Stiefel-Whitney+class" - - "https://www.encyclopediaofmath.org/index.php/Stiefel-Whitney_class" - - "https://www.encyclopediaofmath.org/index.php/StiefelâXXXXWhitney_class" - - - concept: stieltjes-wigert-polynomial - arity: 1 - en: stieltjes wigert polynomial of $1 - property: "indexed function" - area: "special functions" - mathml: - - "Sx" - urls: - - "https://mathworld.wolfram.com/Stieltjes-WigertPolynomial.html" - - "https://en.wikipedia.org/wiki/Stieltjes%E2%80%93Wigert_polynomials" - - "https://dlmf.nist.gov/18.27#E18" - - - concept: stirling-number-of-first-kind - arity: 1 - en: stirling number of first kind of $1 - property: function - area: "special functions" - mathml: - - "s(x)" - urls: - - "https://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html" - - "https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind" - - "https://dlmf.nist.gov/26.8#SS1.p1" - - - concept: stirling-number-of-second-kind - arity: 1 - en: stirling number of second kind of $1 - property: function - area: "special functions" - mathml: - - "S(x)" - urls: - - "https://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html" - - "https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind" - - "https://dlmf.nist.gov/26.8#SS1.p3" - - - concept: strength-of-a-graph - arity: 1 - en: strength of a graph of $1 - property: function - area: "graph theory" - mathml: - - "σ(x)" - urls: - - "https://en.wikipedia.org/wiki/Strength_of_a_graph" - alias: - - strength - - - concept: string-concatenation - arity: 2 - en: $1 string concatenation $2 - property: infix - area: "computer science" - mathml: - - "ABC*XYZ" - - "ABC⁢XYZ" - urls: - - "https://mathworld.wolfram.com/Concatenation.html" - - "https://en.wikipedia.org/wiki/Concatenation_(mathematics)" - - - concept: strong-product - arity: 2 - en: $1 strong product $2 - property: infix - area: "graph theory" - mathml: - - "X⊠Y" - urls: - - "https://en.wikipedia.org/w/index.php?title=Graph_product" - alias: - - normal-product - - and-product - - - concept: struve-function - arity: 1 - en: struve function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "H(x)" - urls: - - "https://mathworld.wolfram.com/StruveFunction.html" - - "https://en.wikipedia.org/wiki/Struve_function" - - "https://dlmf.nist.gov/11.2#E1" - - "https://dlmf.nist.gov/11.2#E5" - - "https://www.encyclopediaofmath.org/index.php/Struve_function" - - - concept: stufe - arity: 1 - en: stufe of $1 - property: function - area: "field theory" - mathml: - - "s(x)" - urls: - - "https://en.wikipedia.org/wiki/Stufe_(algebra)" - - - concept: subfactorial - arity: 1 - en: subfactorial of $1 - property: prefix - area: "combinatorics" - mathml: - - "!x" - urls: - - "https://en.wikipedia.org/wiki/Derangement" - alias: - - derangement-number - - de-montmort-number - - - concept: subgroup - arity: 2 - en: $1 subgroup $2 - property: infix - area: "group theory" - mathml: - - "X≤Y" - urls: - - "https://mathworld.wolfram.com/Subgroup.html" - - "https://en.wikipedia.org/wiki/Subgroup" - - "https://ncatlab.org/nlab/show/subgroup" - - "https://www.encyclopediaofmath.org/index.php/Subgroup" - - - concept: succeeds - arity: 2 - en: $1 succeeds $2 - property: infix - area: "set theory" - mathml: - - "X≻Y" - urls: - - "https://mathworld.wolfram.com/Succeeds.html" - - "https://en.wikipedia.org/wiki/Ordered_set_operators" - - - concept: succeeds-or-equals - arity: 2 - en: $1 succeeds or equals $2 - property: infix - area: "set theory" - mathml: - - "X≽Y" - urls: - - "https://en.wikipedia.org/wiki/Ordered_set_operators" - - - concept: successor - arity: 1 - en: successor of $1 - property: "function, msup" - area: "number theory" - mathml: - - "X+" - - "s(x)" - - "S(x)" - urls: - - "https://en.wikipedia.org/wiki/Proclus" - - "https://en.wikipedia.org/wiki/Successor_cardinal" - - "https://en.wikipedia.org/wiki/Successor_ordinal" - - "https://ncatlab.org/nlab/show/successor" - - - concept: such-that - arity: 2 - en: $1 such that $2 - property: infix - area: "set theory" - mathml: - - "X|Y" - - "X:Y" - urls: - - "https://en.wikipedia.org/wiki/Set_(mathematics)#Set-builder_notation" - - - concept: sumset - arity: 2 - en: $1 sumset $2 - property: infix - area: "set theory" - mathml: - - "X+Y" - urls: - - "https://mathworld.wolfram.com/Sumset.html" - - "https://en.wikipedia.org/wiki/Sumset" - - - concept: superfluous-submodule - arity: 2 - en: $1 superfluous submodule $2 - property: infix - area: "abstract algebra" - mathml: - - "X⊆sY" - - "X≪Y" - urls: - - "https://en.wikipedia.org/wiki/Essential_extension" - alias: - - small-submodule - - - concept: support - arity: 1 - en: support of $1 - property: function - area: "analysis" - mathml: - - "supp(x)" - urls: - - "https://mathworld.wolfram.com/Support.html" - - "https://en.wikipedia.org/wiki/Support_(mathematics)" - - "https://en.wikipedia.org/wiki/Support_of_a_module" - - "https://en.wikipedia.org/wiki/Support_(measure_theory)" - - "https://ncatlab.org/nlab/show/support" - alias: - - spectrum - - topological-support - - - concept: supremum - arity: 1 - en: supremum of $1 - property: "function, largeop" - area: "order theory, lattice theory" - mathml: - - "supX" - - "⋁X" - urls: - - "https://mathworld.wolfram.com/Supremum.html" - alias: - - join - - least-upper-bound - - - concept: supremum-limit - arity: 1 - en: supremum limit of $1 - property: indexed - area: "limits" - mathml: - - "lim sup(X)" - - "lim¯(X)" - urls: - - "https://mathworld.wolfram.com/SupremumLimit.html" - - "https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior" - alias: - - limit-superior - - limit-supremum - - limsup - - superior-limit - - upper-limit - - outer-limit - - - concept: surface-integral - arity: 1 - en: surface integral of $1 - property: indexed - area: "calculus" - mathml: - - "∬Sf" - urls: - - "https://mathworld.wolfram.com/SurfaceIntegral.html" - - "https://en.wikipedia.org/wiki/Surface_integral" - - "https://www.encyclopediaofmath.org/index.php/Surface_integral" - - - concept: surjection - arity: 3 - en: surjection $1, from $2 to $3 - property: mixfix, infix - area: "set theory" - mathml: - - "f:X↠Y" - urls: - - "https://en.wikipedia.org/wiki/Bijection#Definition" - - "https://en.wikipedia.org/wiki/Surjective_function" - - - concept: suspension - arity: 1 - en: suspension of $1 - property: function - area: "topology" - mathml: - - "S(x)" - urls: - - "https://mathworld.wolfram.com/Suspension.html" - - "https://en.wikipedia.org/wiki/Suspension_(topology)" - - "https://ncatlab.org/nlab/show/suspension" - - "https://www.encyclopediaofmath.org/index.php/Suspension" - - - concept: symmetric-algebra - arity: 1 - en: symmetric algebra of $1 - property: function - area: "algebra" - mathml: - - "SX" - - "SymX" - urls: - - "https://en.wikipedia.org/wiki/Symmetric_algebra" - - "https://ncatlab.org/nlab/show/symmetric+algebra" - - "https://www.encyclopediaofmath.org/index.php/Symmetric_algebra" - - - concept: symmetric-difference - arity: 2 - en: $1 symmetric difference $2 - property: infix - area: "set theory" - mathml: - - "X△Y" - - "X⊕Y" - - "X⊖Y" - urls: - - "https://mathworld.wolfram.com/SymmetricDifference.html" - - "https://en.wikipedia.org/wiki/Symmetric_difference" - - "https://ncatlab.org/nlab/show/symmetric+difference" - - - concept: symmetric-group - arity: 1 - en: symmetric group of $1 - property: "msub, function, postfix" - area: "group theory" - mathml: - - "Sx" - - "𝔖x" - - "Σx" - notationd: "mrow Σ ( $1 )" - notationc: "mrow Sym ( $1 )" - notationb: "mrow $1 !" - notationa: "" - urls: - - "https://mathworld.wolfram.com/SymmetricGroup.html" - - "https://en.wikipedia.org/wiki/Symmetric_group" - - "https://www.encyclopediaofmath.org/index.php/Symmetric_group" - - - concept: symmetric-space - arity: 0 + property: constant + subject-area: "combinatorial game theory" + mathml: + - "∗" + - "{0|0}" + urls: + - "https://en.wikipedia.org/wiki/Star_(game_theory)" + + - concept: star-height + arity: 1 + arguments: [a1] + speech: + en: star height of a1 + property: function + subject-area: "formal languages" + mathml: + - "h(x)" + urls: + - "https://en.wikipedia.org/wiki/Star_height" + + - concept: steinberg-group + arity: 1 + arguments: [a1] + speech: + en: steinberg group of a1 + property: function + subject-area: "k-theory" + mathml: + - "St(x)" + urls: + - "https://en.wikipedia.org/wiki/Group_of_Lie_type" + - "https://en.wikipedia.org/wiki/Steinberg_group_(K-theory)" + - "https://ncatlab.org/nlab/show/Steinberg+group" + + - concept: stiefel-manifold + arity: 2 + arguments: [a1, a2] + speech: + en: a1th stiefel manifold over a2 + property: mixfix + subject-area: "differential geometry" + mathml: + - "Vk(ℝn)" + notation: "mrow msub V a1 /msub ( a2" + urls: + - "https://mathworld.wolfram.com/StiefelManifold.html" + - "https://en.wikipedia.org/wiki/Stiefel_manifold" + - "https://www.encyclopediaofmath.org/index.php/Stiefel_manifold" + + - concept: stiefel-whitney-class + arity: 1 + arguments: [a1] + speech: + en: stiefel whitney class of a1 + property: function + subject-area: "algebraic topology" + mathml: + - "w(x)" + urls: + - "https://mathworld.wolfram.com/Stiefel-WhitneyClass.html" + - "https://en.wikipedia.org/wiki/Stiefel%E2%80%93Whitney_class" + - "https://ncatlab.org/nlab/show/Stiefel-Whitney+class" + - "https://www.encyclopediaofmath.org/index.php/Stiefel-Whitney_class" + - "https://www.encyclopediaofmath.org/index.php/StiefelâXXXXWhitney_class" + + - concept: stieltjes-wigert-polynomial + arity: 1 + arguments: [a1] + speech: + en: stieltjes wigert polynomial of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Sx" + urls: + - "https://mathworld.wolfram.com/Stieltjes-WigertPolynomial.html" + - "https://en.wikipedia.org/wiki/Stieltjes%E2%80%93Wigert_polynomials" + - "https://dlmf.nist.gov/18.27#E18" + + - concept: stirling-number-of-first-kind + arity: 1 + arguments: [a1] + speech: + en: stirling number of first kind of a1 + property: function + subject-area: "special functions" + mathml: + - "s(x)" + urls: + - "https://mathworld.wolfram.com/StirlingNumberoftheFirstKind.html" + - "https://en.wikipedia.org/wiki/Stirling_numbers_of_the_first_kind" + - "https://dlmf.nist.gov/26.8#SS1.p1" + + - concept: stirling-number-of-second-kind + arity: 1 + arguments: [a1] + speech: + en: stirling number of second kind of a1 + property: function + subject-area: "special functions" + mathml: + - "S(x)" + urls: + - "https://mathworld.wolfram.com/StirlingNumberoftheSecondKind.html" + - "https://en.wikipedia.org/wiki/Stirling_numbers_of_the_second_kind" + - "https://dlmf.nist.gov/26.8#SS1.p3" + + - concept: strength-of-a-graph + arity: 1 + arguments: [a1] + speech: + en: strength of a graph of a1 + property: function + subject-area: "graph theory" + mathml: + - "σ(x)" + urls: + - "https://en.wikipedia.org/wiki/Strength_of_a_graph" + alias: + - strength + + - concept: string-concatenation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 string concatenation a2 + property: infix + subject-area: "computer science" + mathml: + - "ABC*XYZ" + - "ABC⁢XYZ" + urls: + - "https://mathworld.wolfram.com/Concatenation.html" + - "https://en.wikipedia.org/wiki/Concatenation_(mathematics)" + + - concept: strong-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 strong product a2 + property: infix + subject-area: "graph theory" + mathml: + - "X⊠Y" + urls: + - "https://en.wikipedia.org/w/index.php?title=Graph_product" + alias: + - normal-product + - and-product + + - concept: struve-function + arity: 1 + arguments: [a1] + speech: + en: struve function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "H(x)" + urls: + - "https://mathworld.wolfram.com/StruveFunction.html" + - "https://en.wikipedia.org/wiki/Struve_function" + - "https://dlmf.nist.gov/11.2#E1" + - "https://dlmf.nist.gov/11.2#E5" + - "https://www.encyclopediaofmath.org/index.php/Struve_function" + + - concept: stufe + arity: 1 + arguments: [a1] + speech: + en: stufe of a1 + property: function + subject-area: "field theory" + mathml: + - "s(x)" + urls: + - "https://en.wikipedia.org/wiki/Stufe_(algebra)" + + - concept: subfactorial + arity: 1 + arguments: [a1] + speech: + en: subfactorial of a1 + property: prefix + subject-area: "combinatorics" + mathml: + - "!x" + urls: + - "https://en.wikipedia.org/wiki/Derangement" + alias: + - derangement-number + - de-montmort-number + + - concept: subgroup + arity: 2 + arguments: [a1, a2] + speech: + en: a1 subgroup a2 + property: infix + subject-area: "group theory" + mathml: + - "X≤Y" + urls: + - "https://mathworld.wolfram.com/Subgroup.html" + - "https://en.wikipedia.org/wiki/Subgroup" + - "https://ncatlab.org/nlab/show/subgroup" + - "https://www.encyclopediaofmath.org/index.php/Subgroup" + + - concept: succeeds + arity: 2 + arguments: [a1, a2] + speech: + en: a1 succeeds a2 + property: infix + subject-area: "set theory" + mathml: + - "X≻Y" + urls: + - "https://mathworld.wolfram.com/Succeeds.html" + - "https://en.wikipedia.org/wiki/Ordered_set_operators" + + - concept: succeeds-or-equals + arity: 2 + arguments: [a1, a2] + speech: + en: a1 succeeds or equals a2 + property: infix + subject-area: "set theory" + mathml: + - "X≽Y" + urls: + - "https://en.wikipedia.org/wiki/Ordered_set_operators" + + - concept: successor + arity: 1 + arguments: [a1] + speech: + en: successor of a1 + property: "function, msup" + subject-area: "number theory" + mathml: + - "X+" + - "s(x)" + - "S(x)" + urls: + - "https://en.wikipedia.org/wiki/Proclus" + - "https://en.wikipedia.org/wiki/Successor_cardinal" + - "https://en.wikipedia.org/wiki/Successor_ordinal" + - "https://ncatlab.org/nlab/show/successor" + + - concept: such-that + arity: 2 + arguments: [a1, a2] + speech: + en: a1 such that a2 + property: infix + subject-area: "set theory" + mathml: + - "X|Y" + - "X:Y" + urls: + - "https://en.wikipedia.org/wiki/Set_(mathematics)#Set-builder_notation" + + - concept: sumset + arity: 2 + arguments: [a1, a2] + speech: + en: a1 sumset a2 + property: infix + subject-area: "set theory" + mathml: + - "X+Y" + urls: + - "https://mathworld.wolfram.com/Sumset.html" + - "https://en.wikipedia.org/wiki/Sumset" + + - concept: superfluous-submodule + arity: 2 + arguments: [a1, a2] + speech: + en: a1 superfluous submodule a2 + property: infix + subject-area: "abstract algebra" + mathml: + - "X⊆sY" + - "X≪Y" + urls: + - "https://en.wikipedia.org/wiki/Essential_extension" + alias: + - small-submodule + + - concept: support + arity: 1 + arguments: [a1] + speech: + en: support of a1 + property: function + subject-area: "analysis" + mathml: + - "supp(x)" + urls: + - "https://mathworld.wolfram.com/Support.html" + - "https://en.wikipedia.org/wiki/Support_(mathematics)" + - "https://en.wikipedia.org/wiki/Support_of_a_module" + - "https://en.wikipedia.org/wiki/Support_(measure_theory)" + - "https://ncatlab.org/nlab/show/support" + alias: + - spectrum + - topological-support + + - concept: supremum + arity: 1 + arguments: [a1] + speech: + en: supremum of a1 + property: "function, largeop" + subject-area: "order theory, lattice theory" + mathml: + - "supX" + - "⋁X" + urls: + - "https://mathworld.wolfram.com/Supremum.html" + alias: + - join + - least-upper-bound + + - concept: supremum-limit + arity: 1 + arguments: [a1] + speech: + en: supremum limit of a1 + property: indexed + subject-area: "limits" + mathml: + - "lim sup(X)" + - "lim¯(X)" + urls: + - "https://mathworld.wolfram.com/SupremumLimit.html" + - "https://en.wikipedia.org/wiki/Limit_superior_and_limit_inferior" + alias: + - limit-superior + - limit-supremum + - limsup + - superior-limit + - upper-limit + - outer-limit + + - concept: surface-integral + arity: 1 + arguments: [a1] + speech: + en: surface integral of a1 + property: indexed + subject-area: "calculus" + mathml: + - "∬Sf" + urls: + - "https://mathworld.wolfram.com/SurfaceIntegral.html" + - "https://en.wikipedia.org/wiki/Surface_integral" + - "https://www.encyclopediaofmath.org/index.php/Surface_integral" + + - concept: surjection + arity: 3 + arguments: [a1, a2, a3] + speech: + en: surjection a1, from a2 to a3 + property: mixfix, infix + subject-area: "set theory" + mathml: + - "f:X↠Y" + urls: + - "https://en.wikipedia.org/wiki/Bijection#Definition" + - "https://en.wikipedia.org/wiki/Surjective_function" + + - concept: suspension + arity: 1 + arguments: [a1] + speech: + en: suspension of a1 + property: function + subject-area: "topology" + mathml: + - "S(x)" + urls: + - "https://mathworld.wolfram.com/Suspension.html" + - "https://en.wikipedia.org/wiki/Suspension_(topology)" + - "https://ncatlab.org/nlab/show/suspension" + - "https://www.encyclopediaofmath.org/index.php/Suspension" + + - concept: symmetric-algebra + arity: 1 + arguments: [a1] + speech: + en: symmetric algebra of a1 + property: function + subject-area: "algebra" + mathml: + - "SX" + - "SymX" + urls: + - "https://en.wikipedia.org/wiki/Symmetric_algebra" + - "https://ncatlab.org/nlab/show/symmetric+algebra" + - "https://www.encyclopediaofmath.org/index.php/Symmetric_algebra" + + - concept: symmetric-difference + arity: 2 + arguments: [a1, a2] + speech: + en: a1 symmetric difference a2 + property: infix + subject-area: "set theory" + mathml: + - "X△Y" + - "X⊕Y" + - "X⊖Y" + urls: + - "https://mathworld.wolfram.com/SymmetricDifference.html" + - "https://en.wikipedia.org/wiki/Symmetric_difference" + - "https://ncatlab.org/nlab/show/symmetric+difference" + + - concept: symmetric-group + arity: 1 + arguments: [a1] + speech: + en: symmetric group of a1 + property: "msub, function, postfix" + subject-area: "group theory" + mathml: + - "Sx" + - "𝔖x" + - "Σx" + notationd: "mrow Σ ( a1 )" + notationc: "mrow Sym ( a1 )" + notationb: "mrow a1 !" + notationa: "" + urls: + - "https://mathworld.wolfram.com/SymmetricGroup.html" + - "https://en.wikipedia.org/wiki/Symmetric_group" + - "https://www.encyclopediaofmath.org/index.php/Symmetric_group" + + - concept: symmetric-space + arity: 0 + arguments: [] + speech: en: symmetric space - property: constant - area: "topology" - mathml: - - "R0" - urls: - - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions)s" - - - concept: symplectic-group - arity: 1 - en: symplectic group of $1 - property: function - area: "group theory" - mathml: - - "Sp(x)" - urls: - - "https://mathworld.wolfram.com/SymplecticGroup.html" - - "https://en.wikipedia.org/wiki/Symplectic_group" - - "https://en.wikipedia.org/wiki/Symplectic_Lie_algebra" - - "https://ncatlab.org/nlab/show/symplectic+group" - - "https://www.encyclopediaofmath.org/index.php/Symplectic_group" - - - concept: szego-polynomial - arity: 1 - en: szego polynomial of $1 - property: "indexed function" - area: "orthogonal polynomials" - mathml: - - "ϕx" - urls: - - "https://en.wikipedia.org/wiki/Szeg%C5%91_polynomial" - - "https://www.encyclopediaofmath.org/index.php/Szego_polynomial" - - "https://www.encyclopediaofmath.org/index.php/Szegö_polynomial" - - - concept: tangent-bundle - arity: 1 - en: tangent bundle of $1 - property: function - area: "differential geometry" - mathml: - - "T(x)" - urls: - - "https://mathworld.wolfram.com/TangentBundle.html" - - "https://en.wikipedia.org/wiki/Tangent_bundle" - - "https://ncatlab.org/nlab/show/tangent+bundle" - - "https://www.encyclopediaofmath.org/index.php/Tangent_bundle" - - - concept: tangent-space - arity: 1 - en: tangent space of $1 - property: "indexed function" - area: "topology" - mathml: - - "Tn" - urls: - - "https://mathworld.wolfram.com/TangentSpace.html" - - "https://en.wikipedia.org/wiki/Tangent_space" - - "https://www.encyclopediaofmath.org/index.php/Tangent_space" - - - concept: tate-algebra - arity: 0 + property: constant + subject-area: "topology" + mathml: + - "R0" + urls: + - "https://en.wikipedia.org/wiki/Separation_axiom#Main_definitions)s" + + - concept: symplectic-group + arity: 1 + arguments: [a1] + speech: + en: symplectic group of a1 + property: function + subject-area: "group theory" + mathml: + - "Sp(x)" + urls: + - "https://mathworld.wolfram.com/SymplecticGroup.html" + - "https://en.wikipedia.org/wiki/Symplectic_group" + - "https://en.wikipedia.org/wiki/Symplectic_Lie_algebra" + - "https://ncatlab.org/nlab/show/symplectic+group" + - "https://www.encyclopediaofmath.org/index.php/Symplectic_group" + + - concept: szego-polynomial + arity: 1 + arguments: [a1] + speech: + en: szego polynomial of a1 + property: "indexed function" + subject-area: "orthogonal polynomials" + mathml: + - "ϕx" + urls: + - "https://en.wikipedia.org/wiki/Szeg%C5%91_polynomial" + - "https://www.encyclopediaofmath.org/index.php/Szego_polynomial" + - "https://www.encyclopediaofmath.org/index.php/Szegö_polynomial" + + - concept: tangent-bundle + arity: 1 + arguments: [a1] + speech: + en: tangent bundle of a1 + property: function + subject-area: "differential geometry" + mathml: + - "T(x)" + urls: + - "https://mathworld.wolfram.com/TangentBundle.html" + - "https://en.wikipedia.org/wiki/Tangent_bundle" + - "https://ncatlab.org/nlab/show/tangent+bundle" + - "https://www.encyclopediaofmath.org/index.php/Tangent_bundle" + + - concept: tangent-space + arity: 1 + arguments: [a1] + speech: + en: tangent space of a1 + property: "indexed function" + subject-area: "topology" + mathml: + - "Tn" + urls: + - "https://mathworld.wolfram.com/TangentSpace.html" + - "https://en.wikipedia.org/wiki/Tangent_space" + - "https://www.encyclopediaofmath.org/index.php/Tangent_space" + + - concept: tate-algebra + arity: 0 + arguments: [] + speech: en: tate algebra - property: symbol - area: "analytic geometry" - mathml: - - "Tn" - urls: - - "https://en.wikipedia.org/wiki/Tate_algebra" - - "https://ncatlab.org/nlab/show/Tate+algebra" - - "https://www.encyclopediaofmath.org/index.php/Tate_algebra" - - - concept: tate-module - arity: 1 - en: tate module of $1 - property: "indexed function" - area: "group theory" - mathml: - - "Tn" - urls: - - "https://en.wikipedia.org/wiki/Tate_module" - - "https://ncatlab.org/nlab/show/Tate+module" - - "https://www.encyclopediaofmath.org/index.php/Tate_module" - - - concept: tau-particle - arity: 0 + property: symbol + subject-area: "analytic geometry" + mathml: + - "Tn" + urls: + - "https://en.wikipedia.org/wiki/Tate_algebra" + - "https://ncatlab.org/nlab/show/Tate+algebra" + - "https://www.encyclopediaofmath.org/index.php/Tate_algebra" + + - concept: tate-module + arity: 1 + arguments: [a1] + speech: + en: tate module of a1 + property: "indexed function" + subject-area: "group theory" + mathml: + - "Tn" + urls: + - "https://en.wikipedia.org/wiki/Tate_module" + - "https://ncatlab.org/nlab/show/Tate+module" + - "https://www.encyclopediaofmath.org/index.php/Tate_module" + + - concept: tau-particle + arity: 0 + arguments: [] + speech: en: tau particle - property: symbol - area: "particle physics" - mathml: - - "τ" - urls: - - "https://en.wikipedia.org/wiki/Tau_(particle)" - - - concept: taxicab-number - arity: 1 - en: taxicab number of $1 - property: function - area: "number theory" - mathml: - - "Ta(x)" - urls: - - "https://mathworld.wolfram.com/TaxicabNumber.html" - - "https://en.wikipedia.org/wiki/Taxicab_number" - - - concept: taylor-polynomial - arity: 1 - en: taylor polynomial of $1 - property: function - area: "number theory" - mathml: - - "Ta(x)" - urls: - - "https://mathworld.wolfram.com/TaylorPolynomial.html" - - "https://en.wikipedia.org/wiki/Taylor%27s_theorem" - - "https://www.encyclopediaofmath.org/index.php/Taylor_polynomial" - - - concept: teichmuller-space - arity: 1 - en: teichmuller space of $1 - property: function - area: "differential geometry" - mathml: - - "T(x)" - urls: - - "https://mathworld.wolfram.com/TeichmuellerSpace.html" - - "https://en.wikipedia.org/wiki/Teichm%C3%BCller_space" - - "https://www.encyclopediaofmath.org/index.php/Teichmüller_space" - - - concept: temperature - arity: 0 + property: symbol + subject-area: "particle physics" + mathml: + - "τ" + urls: + - "https://en.wikipedia.org/wiki/Tau_(particle)" + + - concept: taxicab-number + arity: 1 + arguments: [a1] + speech: + en: taxicab number of a1 + property: function + subject-area: "number theory" + mathml: + - "Ta(x)" + urls: + - "https://mathworld.wolfram.com/TaxicabNumber.html" + - "https://en.wikipedia.org/wiki/Taxicab_number" + + - concept: taylor-polynomial + arity: 1 + arguments: [a1] + speech: + en: taylor polynomial of a1 + property: function + subject-area: "number theory" + mathml: + - "Ta(x)" + urls: + - "https://mathworld.wolfram.com/TaylorPolynomial.html" + - "https://en.wikipedia.org/wiki/Taylor%27s_theorem" + - "https://www.encyclopediaofmath.org/index.php/Taylor_polynomial" + + - concept: teichmuller-space + arity: 1 + arguments: [a1] + speech: + en: teichmuller space of a1 + property: function + subject-area: "differential geometry" + mathml: + - "T(x)" + urls: + - "https://mathworld.wolfram.com/TeichmuellerSpace.html" + - "https://en.wikipedia.org/wiki/Teichm%C3%BCller_space" + - "https://www.encyclopediaofmath.org/index.php/Teichmüller_space" + + - concept: temperature + arity: 0 + arguments: [] + speech: en: temperature - property: symbol - area: "physics" - mathml: - - "T" - urls: - - "https://mathworld.wolfram.com/Temperature.html" - - "https://en.wikipedia.org/wiki/Temperature" - - "https://ncatlab.org/nlab/show/temperature" - - - concept: tensor-algebra - arity: 1 - en: tensor algebra of $1 - property: function - area: "multilinear algebra" - mathml: - - "TX" - - "T•X" - urls: - - "https://en.wikipedia.org/wiki/Tensor_algebra" - - - concept: tensor-product - arity: 2 - en: $1 tensor product $2 - property: infix - area: "algebra" - mathml: - - "X⊗Y" - urls: - - "https://mathworld.wolfram.com/TensorProduct.html" - - "https://en.wikipedia.org/wiki/Tensor_product" - - "https://en.wikipedia.org/wiki/Tensor_product_of_graphs" - - "https://ncatlab.org/nlab/show/tensor+product" - - "https://www.encyclopediaofmath.org/index.php/Tensor_product" - - - concept: tensor-product-of-graphs - arity: 2 - en: $1 tensor product of graphs $2 - property: infix - area: "graph theory" - mathml: - - "X×Y" - urls: - - "https://en.wikipedia.org/wiki/Tensor_product_of_graphs" - alias: - - kronecker-product-of-graphs - - categorical-product - - - concept: therefore-sign - arity: 1 - en: therefore $1 - property: prefix - area: "logic" - mathml: - - "∴x" - urls: - - "https://en.wikipedia.org/wiki/Therefore_sign" - - "https://en.wikipedia.org/wiki/.%C2%B7." - - "https://en.wikipedia.org/wiki/%E2%88%B4" - - - concept: theta-function - arity: 1 - en: theta function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "θn" - urls: - - "https://mathworld.wolfram.com/ThetaFunction.html" - - "https://en.wikipedia.org/wiki/Theta_function" - - "https://dlmf.nist.gov/20.2#i" - - "https://dlmf.nist.gov/20.2#i" - - "https://dlmf.nist.gov/20.2#i" - - "https://ncatlab.org/nlab/show/theta+function" - - - concept: thom-space - arity: 1 - en: thom space of $1 - property: function - area: "algebraic topology" - mathml: - - "T(x)" - urls: - - "https://en.wikipedia.org/wiki/Thom_space" - - "https://ncatlab.org/nlab/show/Thom+space" - - "https://www.encyclopediaofmath.org/index.php/Thom_space" - - - concept: thompson-group - arity: 0 + property: symbol + subject-area: "physics" + mathml: + - "T" + urls: + - "https://mathworld.wolfram.com/Temperature.html" + - "https://en.wikipedia.org/wiki/Temperature" + - "https://ncatlab.org/nlab/show/temperature" + + - concept: tensor-algebra + arity: 1 + arguments: [a1] + speech: + en: tensor algebra of a1 + property: function + subject-area: "multilinear algebra" + mathml: + - "TX" + - "T•X" + urls: + - "https://en.wikipedia.org/wiki/Tensor_algebra" + + - concept: tensor-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 tensor product a2 + property: infix + subject-area: "algebra" + mathml: + - "X⊗Y" + urls: + - "https://mathworld.wolfram.com/TensorProduct.html" + - "https://en.wikipedia.org/wiki/Tensor_product" + - "https://en.wikipedia.org/wiki/Tensor_product_of_graphs" + - "https://ncatlab.org/nlab/show/tensor+product" + - "https://www.encyclopediaofmath.org/index.php/Tensor_product" + + - concept: tensor-product-of-graphs + arity: 2 + arguments: [a1, a2] + speech: + en: a1 tensor product of graphs a2 + property: infix + subject-area: "graph theory" + mathml: + - "X×Y" + urls: + - "https://en.wikipedia.org/wiki/Tensor_product_of_graphs" + alias: + - kronecker-product-of-graphs + - categorical-product + + - concept: therefore-sign + arity: 1 + arguments: [a1] + speech: + en: therefore a1 + property: prefix + subject-area: "logic" + mathml: + - "∴x" + urls: + - "https://en.wikipedia.org/wiki/Therefore_sign" + - "https://en.wikipedia.org/wiki/.%C2%B7." + - "https://en.wikipedia.org/wiki/%E2%88%B4" + + - concept: theta-function + arity: 1 + arguments: [a1] + speech: + en: theta function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "θn" + urls: + - "https://mathworld.wolfram.com/ThetaFunction.html" + - "https://en.wikipedia.org/wiki/Theta_function" + - "https://dlmf.nist.gov/20.2#i" + - "https://dlmf.nist.gov/20.2#i" + - "https://dlmf.nist.gov/20.2#i" + - "https://ncatlab.org/nlab/show/theta+function" + + - concept: thom-space + arity: 1 + arguments: [a1] + speech: + en: thom space of a1 + property: function + subject-area: "algebraic topology" + mathml: + - "T(x)" + urls: + - "https://en.wikipedia.org/wiki/Thom_space" + - "https://ncatlab.org/nlab/show/Thom+space" + - "https://www.encyclopediaofmath.org/index.php/Thom_space" + + - concept: thompson-group + arity: 0 + arguments: [] + speech: en: thompson group - property: symbol - area: "group theory" - mathml: - - "Th" - urls: - - "https://mathworld.wolfram.com/ThompsonGroup.html" - - "https://en.wikipedia.org/wiki/Thompson_groups" - - "https://en.wikipedia.org/wiki/Thompson_sporadic_group" - - - concept: to - arity: 2 - en: $1 to $2 - property: infix - area: "arithmetic" - mathml: - - "X:Y" - urls: - - "https://mathworld.wolfram.com/One-to-One.html" - - - concept: todd-class - arity: 1 - en: todd class of $1 - property: function - area: "characteristic classes" - mathml: - - "tdX" - - "TdX" - urls: - - "https://en.wikipedia.org/wiki/Todd_class" - - "https://ncatlab.org/nlab/show/Todd+class" - - "https://www.encyclopediaofmath.org/index.php/Todd_class" - - - concept: topological-entropy - arity: 1 - en: topological entropy of $1 - property: function - area: "topology" - mathml: - - "h(x)" - urls: - - "https://mathworld.wolfram.com/TopologicalEntropy.html" - - "https://en.wikipedia.org/wiki/Topological_entropy" - - "https://www.encyclopediaofmath.org/index.php/Topological_entropy" - - - concept: toroidal-coordinate - arity: 3 - en: toroidal coordinates $1 $2 $3 - property: fenced - area: "geometry" - mathml: - - "(σ,τ,ϕ)" - urls: - - "https://mathworld.wolfram.com/ToroidalCoordinates.html" - - "https://en.wikipedia.org/wiki/Toroidal_coordinates" - - "https://www.encyclopediaofmath.org/index.php/Toroidal_coordinates" - - - concept: torque - arity: 0 + property: symbol + subject-area: "group theory" + mathml: + - "Th" + urls: + - "https://mathworld.wolfram.com/ThompsonGroup.html" + - "https://en.wikipedia.org/wiki/Thompson_groups" + - "https://en.wikipedia.org/wiki/Thompson_sporadic_group" + + - concept: to + arity: 2 + arguments: [a1, a2] + speech: + en: a1 to a2 + property: infix + subject-area: "arithmetic" + mathml: + - "X:Y" + urls: + - "https://mathworld.wolfram.com/One-to-One.html" + + - concept: todd-class + arity: 1 + arguments: [a1] + speech: + en: todd class of a1 + property: function + subject-area: "characteristic classes" + mathml: + - "tdX" + - "TdX" + urls: + - "https://en.wikipedia.org/wiki/Todd_class" + - "https://ncatlab.org/nlab/show/Todd+class" + - "https://www.encyclopediaofmath.org/index.php/Todd_class" + + - concept: topological-entropy + arity: 1 + arguments: [a1] + speech: + en: topological entropy of a1 + property: function + subject-area: "topology" + mathml: + - "h(x)" + urls: + - "https://mathworld.wolfram.com/TopologicalEntropy.html" + - "https://en.wikipedia.org/wiki/Topological_entropy" + - "https://www.encyclopediaofmath.org/index.php/Topological_entropy" + + - concept: toroidal-coordinate + arity: 3 + arguments: [a1, a2, a3] + speech: + en: toroidal coordinates a1 a2 a3 + property: fenced + subject-area: "geometry" + mathml: + - "(σ,τ,ϕ)" + urls: + - "https://mathworld.wolfram.com/ToroidalCoordinates.html" + - "https://en.wikipedia.org/wiki/Toroidal_coordinates" + - "https://www.encyclopediaofmath.org/index.php/Toroidal_coordinates" + + - concept: torque + arity: 0 + arguments: [] + speech: en: torque - property: symbol - area: "mechanics" - mathml: - - "τ" - urls: - - "https://en.wikipedia.org/wiki/Torque" - - - concept: torsion - arity: 0 + property: symbol + subject-area: "mechanics" + mathml: + - "τ" + urls: + - "https://en.wikipedia.org/wiki/Torque" + + - concept: torsion + arity: 0 + arguments: [] + speech: en: torsion - property: symbol - area: "differential geometry" - mathml: - - "τ" - urls: - - "https://mathworld.wolfram.com/Torsion.html" - - "https://en.wikipedia.org/wiki/Torsion_of_a_curve" - - "https://ncatlab.org/nlab/show/torsion" - - "https://www.encyclopediaofmath.org/index.php/Torsion" - - - concept: torsion-submodule - arity: 1 - en: torsion submodule of $1 - property: function - area: "abstract algebra" - mathml: - - "T(x)" - urls: - - "https://en.wikipedia.org/wiki/Torsion_(algebra)" - - - concept: torsion-subgroup - arity: 1 - en: torsion subgroup of $1 - property: msub - area: "group theory" - mathml: - - "GT" - urls: - - "https://en.wikipedia.org/wiki/Torsion_subgroup" - - "https://ncatlab.org/nlab/show/torsion+subgroup" - - - concept: torsion-tensor - arity: 1 - en: torsion tensor of $1 - property: function - area: "differential geometry" - mathml: - - "T(x)" - urls: - - "https://en.wikipedia.org/wiki/Torsion_tensor" - - - concept: total-derivative - arity: 2 - en: total derivative of $1 at $2 - property: mixfix - area: "differential calculus" - mathml: - - "Daf" - urls: - - "https://mathworld.wolfram.com/TotalDerivative.html" - - "https://en.wikipedia.org/wiki/Total_derivative" - - "https://www.encyclopediaofmath.org/index.php/Total_derivative" - alias: - - total-differential - - - concept: total-variation - arity: 1 - en: total variation of $1 - property: fenced - area: "measure theory" - mathml: - - "|x|" - urls: - - "https://mathworld.wolfram.com/TotalVariation.html" - - "https://en.wikipedia.org/wiki/Total_variation" - - "https://dlmf.nist.gov/1.4#E33" - - - concept: trace - arity: 1 - en: trace of $1 - property: function - area: "linear algebra" - mathml: - - "tr(x)" - urls: - - "https://en.wikipedia.org/wiki/Trace_(linear_algebra)" - - - concept: transitive-closure - arity: 1 - en: transitive closure of $1 - property: msup - area: "set theory" - mathml: - - "X+" - urls: - - "https://mathworld.wolfram.com/TransitiveClosure.html" - - "https://en.wikipedia.org/wiki/Transitive_closure" - - "https://ncatlab.org/nlab/show/transitive+closure" - - - concept: triangle - arity: 3 + property: symbol + subject-area: "differential geometry" + mathml: + - "τ" + urls: + - "https://mathworld.wolfram.com/Torsion.html" + - "https://en.wikipedia.org/wiki/Torsion_of_a_curve" + - "https://ncatlab.org/nlab/show/torsion" + - "https://www.encyclopediaofmath.org/index.php/Torsion" + + - concept: torsion-submodule + arity: 1 + arguments: [a1] + speech: + en: torsion submodule of a1 + property: function + subject-area: "abstract algebra" + mathml: + - "T(x)" + urls: + - "https://en.wikipedia.org/wiki/Torsion_(algebra)" + + - concept: torsion-subgroup + arity: 1 + arguments: [a1] + speech: + en: torsion subgroup of a1 + property: msub + subject-area: "group theory" + mathml: + - "GT" + urls: + - "https://en.wikipedia.org/wiki/Torsion_subgroup" + - "https://ncatlab.org/nlab/show/torsion+subgroup" + + - concept: torsion-tensor + arity: 1 + arguments: [a1] + speech: + en: torsion tensor of a1 + property: function + subject-area: "differential geometry" + mathml: + - "T(x)" + urls: + - "https://en.wikipedia.org/wiki/Torsion_tensor" + + - concept: total-derivative + arity: 2 + arguments: [a1, a2] + speech: + en: total derivative of a1 at a2 + property: mixfix + subject-area: "differential calculus" + mathml: + - "Daf" + urls: + - "https://mathworld.wolfram.com/TotalDerivative.html" + - "https://en.wikipedia.org/wiki/Total_derivative" + - "https://www.encyclopediaofmath.org/index.php/Total_derivative" + alias: + - total-differential + + - concept: total-variation + arity: 1 + arguments: [a1] + speech: + en: total variation of a1 + property: fenced + subject-area: "measure theory" + mathml: + - "|x|" + urls: + - "https://mathworld.wolfram.com/TotalVariation.html" + - "https://en.wikipedia.org/wiki/Total_variation" + - "https://dlmf.nist.gov/1.4#E33" + + - concept: trace + arity: 1 + arguments: [a1] + speech: + en: trace of a1 + property: function + subject-area: "linear algebra" + mathml: + - "tr(x)" + urls: + - "https://en.wikipedia.org/wiki/Trace_(linear_algebra)" + + - concept: transitive-closure + arity: 1 + arguments: [a1] + speech: + en: transitive closure of a1 + property: msup + subject-area: "set theory" + mathml: + - "X+" + urls: + - "https://mathworld.wolfram.com/TransitiveClosure.html" + - "https://en.wikipedia.org/wiki/Transitive_closure" + - "https://ncatlab.org/nlab/show/transitive+closure" + + - concept: triangle + arity: 3 + arguments: [a1, a2, a3] + speech: en: triangle - property: prefix - area: "geometry" - mathml: - - "△A B C" - urls: - - "https://mathworld.wolfram.com/Triangle.html" - - "https://en.wikipedia.org/wiki/Triangle" - - "https://ncatlab.org/nlab/show/triangle" - - "https://www.encyclopediaofmath.org/index.php/Triangle" - - - concept: triangle-function - arity: 1 - en: triangle function of $1 - property: function - area: "special functions" - mathml: - - "ΛX" - - "triX" - urls: - - "https://mathworld.wolfram.com/TriangleFunction.html" - - "https://en.wikipedia.org/wiki/Triangular_function" - alias: - - hat-function - - tent-function - - - concept: triangular-number - arity: 1 - en: triangular number $1 - property: "indexed symbol" - area: "number theory" - mathml: - - "Tn" - urls: - - "https://mathworld.wolfram.com/TriangularNumber.html" - - "https://en.wikipedia.org/wiki/Triangular_number" - - "https://en.wikipedia.org/wiki/Centered_triangular_number" - - "https://www.encyclopediaofmath.org/index.php/Triangular_number" - - - concept: trilinear-coordinates - arity: 3 - en: trilinear coordinates $1, $2, $3 - property: infix - area: "geometry" - mathml: - - "x:y:z" - urls: - - "https://en.wikipedia.org/wiki/Trilinear_coordinates" - - - concept: trimean - arity: 1 - en: trimean of $1 - property: function - area: "statistics" - mathml: - - "TM(x)" - urls: - - "https://en.wikipedia.org/wiki/Trimean" - alias: - - tukey-trimean - - - concept: triple-bond - arity: 2 - en: $1 triple bond $2 - property: infix - area: "chemistry" - mathml: - - "X≡Y" - urls: - - "https://en.wikipedia.org/wiki/Triple_bond" - - - concept: triple-scalar-product - arity: 3 - en: triple scalar product of $1, $2 and $3 - property: fenced - area: "algebra" - mathml: - - "[a,b,c]" - urls: - - "https://mathworld.wolfram.com/TripleScalarProduct.html" - alias: - - scalar-triple-product - - - concept: triple-torus - arity: 0 + property: prefix + subject-area: "geometry" + mathml: + - "△A B C" + urls: + - "https://mathworld.wolfram.com/Triangle.html" + - "https://en.wikipedia.org/wiki/Triangle" + - "https://ncatlab.org/nlab/show/triangle" + - "https://www.encyclopediaofmath.org/index.php/Triangle" + + - concept: triangle-function + arity: 1 + arguments: [a1] + speech: + en: triangle function of a1 + property: function + subject-area: "special functions" + mathml: + - "ΛX" + - "triX" + urls: + - "https://mathworld.wolfram.com/TriangleFunction.html" + - "https://en.wikipedia.org/wiki/Triangular_function" + alias: + - hat-function + - tent-function + + - concept: triangular-number + arity: 1 + arguments: [a1] + speech: + en: triangular number a1 + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Tn" + urls: + - "https://mathworld.wolfram.com/TriangularNumber.html" + - "https://en.wikipedia.org/wiki/Triangular_number" + - "https://en.wikipedia.org/wiki/Centered_triangular_number" + - "https://www.encyclopediaofmath.org/index.php/Triangular_number" + + - concept: trilinear-coordinates + arity: 3 + arguments: [a1, a2, a3] + speech: + en: trilinear coordinates a1, a2, a3 + property: infix + subject-area: "geometry" + mathml: + - "x:y:z" + urls: + - "https://en.wikipedia.org/wiki/Trilinear_coordinates" + + - concept: trimean + arity: 1 + arguments: [a1] + speech: + en: trimean of a1 + property: function + subject-area: "statistics" + mathml: + - "TM(x)" + urls: + - "https://en.wikipedia.org/wiki/Trimean" + alias: + - tukey-trimean + + - concept: triple-bond + arity: 2 + arguments: [a1, a2] + speech: + en: a1 triple bond a2 + property: infix + subject-area: "chemistry" + mathml: + - "X≡Y" + urls: + - "https://en.wikipedia.org/wiki/Triple_bond" + + - concept: triple-scalar-product + arity: 3 + arguments: [a1, a2, a3] + speech: + en: triple scalar product of a1, a2 and a3 + property: fenced + subject-area: "algebra" + mathml: + - "[a,b,c]" + urls: + - "https://mathworld.wolfram.com/TripleScalarProduct.html" + alias: + - scalar-triple-product + + - concept: triple-torus + arity: 0 + arguments: [] + speech: en: triple torus - property: "indexed symbol" - area: "topology" - mathml: - - "𝕋3" - urls: - - "https://mathworld.wolfram.com/TripleTorus.html" - - "https://en.wikipedia.org/wiki/Three-torus" - - "https://en.wikipedia.org/wiki/Triple_torus" - - - concept: truncation - arity: 1 - en: truncation of $1 - property: function - area: "numerical analysis" - mathml: - - "trunc(x)" - urls: - - "https://mathworld.wolfram.com/Truncation.html" - - "https://en.wikipedia.org/wiki/Truncation" - - - concept: tube-domain - arity: 1 - en: tube domain of $1 - property: msub - area: "complex analysis" - mathml: - - "Tn" - urls: - - "https://en.wikipedia.org/wiki/Tube_domain" - - "https://www.encyclopediaofmath.org/index.php/Tube_domain" - - - concept: turan-graph - arity: 2 - en: turan graph $1 $2 - property: "function, indexed function" - area: "graph theory" - mathml: - - "T(n,r)" - urls: - - "https://mathworld.wolfram.com/TuranGraph.html" - - "https://en.wikipedia.org/wiki/Tur%C3%A1n_graph" - - "https://en.wikipedia.org/wiki/Cocktail_party_graph" - - - concept: turan-number - arity: 3 - en: turan number of $1, $2 and $3 - property: function - area: "graph theory" - mathml: - - "T(a,b,c)" - urls: - - "https://en.wikipedia.org/wiki/Tur%C3%A1n_number" - - "https://www.encyclopediaofmath.org/index.php/Turan_number" - - "https://www.encyclopediaofmath.org/index.php/Turán_number" - - - concept: turn - arity: 1 - en: turn of $1 - property: unit - area: "geometry" - mathml: - - "cycX" - - "revX" - - "trX" - - "plaX" - urls: - - "https://en.wikipedia.org/wiki/Turn_(geometry)" - alias: - - cycle - - revolution - - plenus angulus - - - concept: twisted-tensor-product - arity: 2 - en: $1 twisted tensor product $2 - property: infix - area: "topology" - mathml: - - "X⊗τY" - urls: - - "https://ncatlab.org/nlab/show/twisted+tensor+product" - - - concept: tychonoff-space - arity: 0 + property: "indexed symbol" + subject-area: "topology" + mathml: + - "𝕋3" + urls: + - "https://mathworld.wolfram.com/TripleTorus.html" + - "https://en.wikipedia.org/wiki/Three-torus" + - "https://en.wikipedia.org/wiki/Triple_torus" + + - concept: truncation + arity: 1 + arguments: [a1] + speech: + en: truncation of a1 + property: function + subject-area: "numerical analysis" + mathml: + - "trunc(x)" + urls: + - "https://mathworld.wolfram.com/Truncation.html" + - "https://en.wikipedia.org/wiki/Truncation" + + - concept: tube-domain + arity: 1 + arguments: [a1] + speech: + en: tube domain of a1 + property: msub + subject-area: "complex analysis" + mathml: + - "Tn" + urls: + - "https://en.wikipedia.org/wiki/Tube_domain" + - "https://www.encyclopediaofmath.org/index.php/Tube_domain" + + - concept: turan-graph + arity: 2 + arguments: [a1, a2] + speech: + en: turan graph a1 a2 + property: "function, indexed function" + subject-area: "graph theory" + mathml: + - "T(n,r)" + urls: + - "https://mathworld.wolfram.com/TuranGraph.html" + - "https://en.wikipedia.org/wiki/Tur%C3%A1n_graph" + - "https://en.wikipedia.org/wiki/Cocktail_party_graph" + + - concept: turan-number + arity: 3 + arguments: [a1, a2, a3] + speech: + en: turan number of a1, a2 and a3 + property: function + subject-area: "graph theory" + mathml: + - "T(a,b,c)" + urls: + - "https://en.wikipedia.org/wiki/Tur%C3%A1n_number" + - "https://www.encyclopediaofmath.org/index.php/Turan_number" + - "https://www.encyclopediaofmath.org/index.php/Turán_number" + + - concept: turn + arity: 1 + arguments: [a1] + speech: + en: turn of a1 + property: unit + subject-area: "geometry" + mathml: + - "cycX" + - "revX" + - "trX" + - "plaX" + urls: + - "https://en.wikipedia.org/wiki/Turn_(geometry)" + alias: + - cycle + - revolution + - plenus angulus + + - concept: twisted-tensor-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 twisted tensor product a2 + property: infix + subject-area: "topology" + mathml: + - "X⊗τY" + urls: + - "https://ncatlab.org/nlab/show/twisted+tensor+product" + + - concept: tychonoff-space + arity: 0 + arguments: [] + speech: en: tychonoff space - property: symbol - area: "topology" - mathml: - - "T3" - - "Tπ" - - "T3½" - urls: - - "https://mathworld.wolfram.com/TychonoffSpace.html" - - "https://en.wikipedia.org/wiki/Tychonoff_space" - - "https://ncatlab.org/nlab/show/Tychonoff+space" - - - concept: typing-judgement - arity: 2 - en: $1 typing judgement $2 - property: infix - area: "type theory" - mathml: - - "X:Y" - urls: - - "https://ncatlab.org/nlab/show/judgment" - - - concept: ulam-number - arity: 1 - en: $1th ulam number - property: "indexed symbol" - area: "integer sequences" - mathml: - - "Un" - urls: - - "https://mathworld.wolfram.com/UlamNumber.html" - - "https://en.wikipedia.org/wiki/Ulam_number" - - - concept: ultrapower - arity: 2 - en: ultrapower $1 $2 - property: mixfix - area: "abstract algebra" - mathml: - - "∏x/y" - urls: - - "https://mathworld.wolfram.com/Ultrapower.html" - - "https://en.wikipedia.org/wiki/Ultraproduct" - - "https://ncatlab.org/nlab/show/ultrapower" - - - concept: ultraproduct - arity: 3 - en: ultraproduct of $1, $2 modulo $3 - property: mixfix - area: "abstract algebra" - mathml: - - "∏i∈IM/𝒰" - urls: - - "https://mathworld.wolfram.com/Ultraproduct.html" - - "https://en.wikipedia.org/wiki/Ultraproduct" - - "https://ncatlab.org/nlab/show/ultraproduct" - - - concept: uniformly-convergent - arity: 2 - en: $1 uniformly convergs to $2 - property: infix, indexed, postfix - area: "convergence" - mathml: - - "f⇉g" - - "f⟶unifg" - - "unif limf=g" - urls: - - "https://en.wikipedia.org/wiki/Uniform_convergence" - - - concept: unit-part - arity: 1 - en: unit part of $1 - property: fenced - area: "SI units" - mathml: - - "[x]" - urls: - - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values" - - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions" - - - concept: unit-vector - arity: 1 - en: unit vector of $1 - property: mover - area: "linear algebra" - mathml: - - "v^" - urls: - - "https://mathworld.wolfram.com/UnitVector.html" - - "https://en.wikipedia.org/wiki/Unit_vector" - - "https://www.encyclopediaofmath.org/index.php/Unit_vector" - - - concept: unitary-group - arity: 1 - en: $1th unitary group - property: "indexed symbol" - area: "group theory" - mathml: - - "Un" - urls: - - "https://mathworld.wolfram.com/UnitaryGroup.html" - - "https://en.wikipedia.org/wiki/Unitary_group" - - "https://ncatlab.org/nlab/show/unitary+group" - - "https://www.encyclopediaofmath.org/index.php/Unitary_group" - - - concept: universal-gas-constant - arity: 0 + property: symbol + subject-area: "topology" + mathml: + - "T3" + - "Tπ" + - "T3½" + urls: + - "https://mathworld.wolfram.com/TychonoffSpace.html" + - "https://en.wikipedia.org/wiki/Tychonoff_space" + - "https://ncatlab.org/nlab/show/Tychonoff+space" + + - concept: typing-judgement + arity: 2 + arguments: [a1, a2] + speech: + en: a1 typing judgement a2 + property: infix + subject-area: "type theory" + mathml: + - "X:Y" + urls: + - "https://ncatlab.org/nlab/show/judgment" + + - concept: ulam-number + arity: 1 + arguments: [a1] + speech: + en: a1th ulam number + property: "indexed symbol" + subject-area: "integer sequences" + mathml: + - "Un" + urls: + - "https://mathworld.wolfram.com/UlamNumber.html" + - "https://en.wikipedia.org/wiki/Ulam_number" + + - concept: ultrapower + arity: 2 + arguments: [a1, a2] + speech: + en: ultrapower a1 a2 + property: mixfix + subject-area: "abstract algebra" + mathml: + - "∏x/y" + urls: + - "https://mathworld.wolfram.com/Ultrapower.html" + - "https://en.wikipedia.org/wiki/Ultraproduct" + - "https://ncatlab.org/nlab/show/ultrapower" + + - concept: ultraproduct + arity: 3 + arguments: [a1, a2, a3] + speech: + en: ultraproduct of a1, a2 modulo a3 + property: mixfix + subject-area: "abstract algebra" + mathml: + - "∏i∈IM/𝒰" + urls: + - "https://mathworld.wolfram.com/Ultraproduct.html" + - "https://en.wikipedia.org/wiki/Ultraproduct" + - "https://ncatlab.org/nlab/show/ultraproduct" + + - concept: uniformly-convergent + arity: 2 + arguments: [a1, a2] + speech: + en: a1 uniformly convergs to a2 + property: infix, indexed, postfix + subject-area: "convergence" + mathml: + - "f⇉g" + - "f⟶unifg" + - "unif limf=g" + urls: + - "https://en.wikipedia.org/wiki/Uniform_convergence" + + - concept: unit-part + arity: 1 + arguments: [a1] + speech: + en: unit part of a1 + property: fenced + subject-area: "SI units" + mathml: + - "[x]" + urls: + - "https://www.nist.gov/pml/special-publication-811/nist-guide-si-chapter-7-rules-and-style-conventions-expressing-values" + - "https://physics.stackexchange.com/questions/77690/square-bracket-notation-for-dimensions-and-units-usage-and-conventions" + + - concept: unit-vector + arity: 1 + arguments: [a1] + speech: + en: unit vector of a1 + property: mover + subject-area: "linear algebra" + mathml: + - "v^" + urls: + - "https://mathworld.wolfram.com/UnitVector.html" + - "https://en.wikipedia.org/wiki/Unit_vector" + - "https://www.encyclopediaofmath.org/index.php/Unit_vector" + + - concept: unitary-group + arity: 1 + arguments: [a1] + speech: + en: a1th unitary group + property: "indexed symbol" + subject-area: "group theory" + mathml: + - "Un" + urls: + - "https://mathworld.wolfram.com/UnitaryGroup.html" + - "https://en.wikipedia.org/wiki/Unitary_group" + - "https://ncatlab.org/nlab/show/unitary+group" + - "https://www.encyclopediaofmath.org/index.php/Unitary_group" + + - concept: universal-gas-constant + arity: 0 + arguments: [] + speech: en: universal gas constant - property: constant - area: "physics" - mathml: - - "R" - notationa: "mover R -" - urls: - - "https://en.wikipedia.org/wiki/Gas_constant" - alias: - - gas-constant - - molar-gas-constant - - ideal-gas-constant - - - concept: universal-parabolic-constant - arity: 0 + property: constant + subject-area: "physics" + mathml: + - "R" + notationa: "mover R -" + urls: + - "https://en.wikipedia.org/wiki/Gas_constant" + alias: + - gas-constant + - molar-gas-constant + - ideal-gas-constant + + - concept: universal-parabolic-constant + arity: 0 + arguments: [] + speech: en: universal parabolic constant - property: constant - area: "geometry" - mathml: - - "P" - urls: - - "https://mathworld.wolfram.com/UniversalParabolicConstant.html" - - "https://en.wikipedia.org/wiki/Universal_parabolic_constant" - - - concept: universal-set - arity: 0 + property: constant + subject-area: "geometry" + mathml: + - "P" + urls: + - "https://mathworld.wolfram.com/UniversalParabolicConstant.html" + - "https://en.wikipedia.org/wiki/Universal_parabolic_constant" + + - concept: universal-set + arity: 0 + arguments: [] + speech: en: universal set - property: symbol - area: "set theory" - mathml: - - "V" - - "U" - - "ξ" - urls: - - "https://mathworld.wolfram.com/UniversalSet.html" - - "https://en.wikipedia.org/wiki/Universal_set" - - "https://www.encyclopediaofmath.org/index.php/Universal_set" - alias: - - universe - - - concept: unique-existential - arity: 3 - en: There exists unique $1 - property: prefix - area: "logic" - mathml: - - "∃!n" - urls: - - "https://en.wikipedia.org/wiki/Uniqueness_quantification" - - "https://arxiv.org/pdf/1902.03852.pdf" - - - concept: unnatural-isomorphism - arity: 2 - en: $1 unnatural isomorphism $2 - property: infix - area: "set theory" - mathml: - - "X≈Y" - urls: - - "https://en.wikipedia.org/wiki/Isomorphism#Relation_with_equality" - - - concept: unrestricted-wreath-product - arity: 2 - en: $1 unrestricted wreath product $2 - property: infix - area: "group theory" - mathml: - - "X≀Y" - - "XWrY" - - "XWrΩY" - urls: - - "https://mathworld.wolfram.com/WreathProduct.html" - - "https://en.wikipedia.org/wiki/Wreath_product" - - "https://ncatlab.org/nlab/show/wreath+product" - - "https://www.encyclopediaofmath.org/index.php/Wreath_product" - - - concept: upper-closure-poset - arity: 1 - en: upper closure poset of $1 - property: prefix - area: "order theory" - mathml: - - "↑x" - urls: - - "https://en.wikipedia.org/wiki/Upper_set#Upper_closure_and_lower_closure" - - - concept: upper-darboux-integral - arity: 1 - en: upper darboux integral of $1 - property: indexed - area: "real analysis" - mathml: - - "∫ab¯f" - urls: - - "https://en.wikipedia.org/wiki/Darboux_integral" - - "https://www.encyclopediaofmath.org/index.php/Darboux_integral" - - - concept: upper-dini-derivative - arity: 1 - en: upper dini derivative of $1 - property: decorated function - area: "analysis" - mathml: - - "f′+(t)" - urls: - - "https://mathworld.wolfram.com/DiniDerivative.html" - - "https://en.wikipedia.org/wiki/Dini_derivative" - - "https://www.encyclopediaofmath.org/index.php/Dini_derivative" - - - concept: upper-half-plane - arity: 0 + property: symbol + subject-area: "set theory" + mathml: + - "V" + - "U" + - "ξ" + urls: + - "https://mathworld.wolfram.com/UniversalSet.html" + - "https://en.wikipedia.org/wiki/Universal_set" + - "https://www.encyclopediaofmath.org/index.php/Universal_set" + alias: + - universe + + - concept: unique-existential + arity: 3 + arguments: [a1, a2, a3] + speech: + en: There exists unique a1 + property: prefix + subject-area: "logic" + mathml: + - "∃!n" + urls: + - "https://en.wikipedia.org/wiki/Uniqueness_quantification" + - "https://arxiv.org/pdf/1902.03852.pdf" + + - concept: unnatural-isomorphism + arity: 2 + arguments: [a1, a2] + speech: + en: a1 unnatural isomorphism a2 + property: infix + subject-area: "set theory" + mathml: + - "X≈Y" + urls: + - "https://en.wikipedia.org/wiki/Isomorphism#Relation_with_equality" + + - concept: unrestricted-wreath-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 unrestricted wreath product a2 + property: infix + subject-area: "group theory" + mathml: + - "X≀Y" + - "XWrY" + - "XWrΩY" + urls: + - "https://mathworld.wolfram.com/WreathProduct.html" + - "https://en.wikipedia.org/wiki/Wreath_product" + - "https://ncatlab.org/nlab/show/wreath+product" + - "https://www.encyclopediaofmath.org/index.php/Wreath_product" + + - concept: upper-closure-poset + arity: 1 + arguments: [a1] + speech: + en: upper closure poset of a1 + property: prefix + subject-area: "order theory" + mathml: + - "↑x" + urls: + - "https://en.wikipedia.org/wiki/Upper_set#Upper_closure_and_lower_closure" + + - concept: upper-darboux-integral + arity: 1 + arguments: [a1] + speech: + en: upper darboux integral of a1 + property: indexed + subject-area: "real analysis" + mathml: + - "∫ab¯f" + urls: + - "https://en.wikipedia.org/wiki/Darboux_integral" + - "https://www.encyclopediaofmath.org/index.php/Darboux_integral" + + - concept: upper-dini-derivative + arity: 1 + arguments: [a1] + speech: + en: upper dini derivative of a1 + property: decorated function + subject-area: "analysis" + mathml: + - "f′+(t)" + urls: + - "https://mathworld.wolfram.com/DiniDerivative.html" + - "https://en.wikipedia.org/wiki/Dini_derivative" + - "https://www.encyclopediaofmath.org/index.php/Dini_derivative" + + - concept: upper-half-plane + arity: 0 + arguments: [] + speech: en: upper half plane - property: symbol - area: "complex analysis" - mathml: - - "ℍ" - - "ℍ+" - urls: - - "https://mathworld.wolfram.com/UpperHalf-Plane.html" - - "https://en.wikipedia.org/wiki/Upper_half-plane" - - "https://ncatlab.org/nlab/show/upper+half-plane" - - - concept: upper-shadow - arity: 1 - en: upper shadow of $1 - property: function - area: "combinatorics" - mathml: - - "𝜕+A" - urls: - - "http://qk206.user.srcf.net/notes/combinatorics.pdf" - - - concept: variance - arity: 1 - en: variance of $1 - property: function - area: "statistics" - mathml: - - "Var(x)" - urls: - - "https://en.wikipedia.org/wiki/Variance" - alias: - - dispersion - - - concept: vect - arity: 1 - en: vect of $1 - property: "indexed symbol" - area: "category theory" - mathml: - - "Vectn" - urls: - - "https://ncatlab.org/nlab/show/Vect" - - - concept: vector-concatenation - arity: 2 - en: $1 vector concatenation $2 - property: infix - area: "machine learning" - mathml: - - "X◦Y" - - "X⊕Y" - urls: - - "https://arxiv.org/pdf/1903.00172v1.pdf" - - "https://arxiv.org/abs/1901.10879" - - - concept: vector-projection - arity: 1 - en: vector projection of $1 - property: function - area: "linear algebra" - mathml: - - "proj(x)" - urls: - - "https://en.wikipedia.org/wiki/Vector_projection" - alias: - - vector-component - - vector-resolution - - - concept: vectorization - arity: 1 - en: vectorization of $1 - property: function - area: "linear algebra" - mathml: - - "vec(x)" - urls: - - "https://en.wikipedia.org/wiki/Vectorization_(mathematics)" - - "https://en.wikipedia.org/wiki/Vectorization_(parallel_computing)" - - "https://en.wikipedia.org/wiki/Vectorization_(image_tracing)" - - - concept: versor - arity: 1 - en: versor of $1 - property: function - area: "quaternions" - mathml: - - "U(x)" - urls: - - "https://en.wikipedia.org/wiki/Versor_(physics)" - - "https://en.wikipedia.org/wiki/Versor" - - "https://www.encyclopediaofmath.org/index.php/Versor" - - - concept: vertical - arity: 0 + property: symbol + subject-area: "complex analysis" + mathml: + - "ℍ" + - "ℍ+" + urls: + - "https://mathworld.wolfram.com/UpperHalf-Plane.html" + - "https://en.wikipedia.org/wiki/Upper_half-plane" + - "https://ncatlab.org/nlab/show/upper+half-plane" + + - concept: upper-shadow + arity: 1 + arguments: [a1] + speech: + en: upper shadow of a1 + property: function + subject-area: "combinatorics" + mathml: + - "𝜕+A" + urls: + - "http://qk206.user.srcf.net/notes/combinatorics.pdf" + + - concept: variance + arity: 1 + arguments: [a1] + speech: + en: variance of a1 + property: function + subject-area: "statistics" + mathml: + - "Var(x)" + urls: + - "https://en.wikipedia.org/wiki/Variance" + alias: + - dispersion + + - concept: vect + arity: 1 + arguments: [a1] + speech: + en: vect of a1 + property: "indexed symbol" + subject-area: "category theory" + mathml: + - "Vectn" + urls: + - "https://ncatlab.org/nlab/show/Vect" + + - concept: vector-concatenation + arity: 2 + arguments: [a1, a2] + speech: + en: a1 vector concatenation a2 + property: infix + subject-area: "machine learning" + mathml: + - "X◦Y" + - "X⊕Y" + urls: + - "https://arxiv.org/pdf/1903.00172v1.pdf" + - "https://arxiv.org/abs/1901.10879" + + - concept: vector-projection + arity: 1 + arguments: [a1] + speech: + en: vector projection of a1 + property: function + subject-area: "linear algebra" + mathml: + - "proj(x)" + urls: + - "https://en.wikipedia.org/wiki/Vector_projection" + alias: + - vector-component + - vector-resolution + + - concept: vectorization + arity: 1 + arguments: [a1] + speech: + en: vectorization of a1 + property: function + subject-area: "linear algebra" + mathml: + - "vec(x)" + urls: + - "https://en.wikipedia.org/wiki/Vectorization_(mathematics)" + - "https://en.wikipedia.org/wiki/Vectorization_(parallel_computing)" + - "https://en.wikipedia.org/wiki/Vectorization_(image_tracing)" + + - concept: versor + arity: 1 + arguments: [a1] + speech: + en: versor of a1 + property: function + subject-area: "quaternions" + mathml: + - "U(x)" + urls: + - "https://en.wikipedia.org/wiki/Versor_(physics)" + - "https://en.wikipedia.org/wiki/Versor" + - "https://www.encyclopediaofmath.org/index.php/Versor" + + - concept: vertical + arity: 0 + arguments: [] + speech: en: vertical - property: - area: - mathml: - - "vertical" - notation: - urls: - - "https://mathworld.wolfram.com/Vertical.html" - - "https://en.wikipedia.org/wiki/Horizontal_and_vertical" - - "https://en.wikipedia.org/wiki/Vertical_direction" - - - concept: vertical-composition - arity: 2 - en: $1 vertical composition $2 - property: infix - area: "category theory" - mathml: - - "X∘Y" - urls: - - "https://ncatlab.org/nlab/show/vertical+composition" - - "https://proofwiki.org/wiki/Definition: Vertical_Composition_of_Natural_Transformations" - - - concept: volterra-integral - arity: 1 - en: volterra integral of $1 - property: indexed - area: "calculus" - mathml: - - "Πf" - urls: - - "https://en.wikipedia.org/wiki/Product_integral" - - - concept: volume - arity: 0 + property: + subject-area: + mathml: + - "vertical" + notation: + urls: + - "https://mathworld.wolfram.com/Vertical.html" + - "https://en.wikipedia.org/wiki/Horizontal_and_vertical" + - "https://en.wikipedia.org/wiki/Vertical_direction" + + - concept: vertical-composition + arity: 2 + arguments: [a1, a2] + speech: + en: a1 vertical composition a2 + property: infix + subject-area: "category theory" + mathml: + - "X∘Y" + urls: + - "https://ncatlab.org/nlab/show/vertical+composition" + - "https://proofwiki.org/wiki/Definition: Vertical_Composition_of_Natural_Transformations" + + - concept: volterra-integral + arity: 1 + arguments: [a1] + speech: + en: volterra integral of a1 + property: indexed + subject-area: "calculus" + mathml: + - "Πf" + urls: + - "https://en.wikipedia.org/wiki/Product_integral" + + - concept: volume + arity: 0 + arguments: [] + speech: en: volume - property: symbol - area: "physics" - mathml: - - "V" - urls: - - "https://mathworld.wolfram.com/Volume.html" - - "https://en.wikipedia.org/wiki/Volume_(compression)" - - "https://en.wikipedia.org/wiki/Lebesgue_measure" - - "https://en.wikipedia.org/wiki/Volume_(thermodynamics)" - - "https://en.wikipedia.org/wiki/Volume" - - "https://ncatlab.org/nlab/show/volume" - - "https://www.encyclopediaofmath.org/index.php/Volume" - - - concept: volume-element - arity: 0 + property: symbol + subject-area: "physics" + mathml: + - "V" + urls: + - "https://mathworld.wolfram.com/Volume.html" + - "https://en.wikipedia.org/wiki/Volume_(compression)" + - "https://en.wikipedia.org/wiki/Lebesgue_measure" + - "https://en.wikipedia.org/wiki/Volume_(thermodynamics)" + - "https://en.wikipedia.org/wiki/Volume" + - "https://ncatlab.org/nlab/show/volume" + - "https://www.encyclopediaofmath.org/index.php/Volume" + + - concept: volume-element + arity: 0 + arguments: [] + speech: en: volume element - property: symbol - area: "measure theory" - mathml: - - "dV" - urls: - - "https://mathworld.wolfram.com/VolumeElement.html" - - "https://en.wikipedia.org/wiki/Volume_element" - - - concept: walsh-function - arity: 1 - en: walsh function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "W(x)" - urls: - - "https://mathworld.wolfram.com/WalshFunction.html" - - "https://en.wikipedia.org/wiki/Walsh_function" - - "https://www.encyclopediaofmath.org/index.php/Walsh_functions" - - - concept: wavelet-transform - arity: 2 - en: wavelet transform $1 $2 - property: "embellished function" - area: "functional analysis" - mathml: - - "Wψy" - notation: "mrow [ msub W $1 /msub $2 ]" - urls: - - "https://mathworld.wolfram.com/WaveletTransform.html" - - "https://en.wikipedia.org/wiki/Wavelet_transform" - - "https://en.wikipedia.org/wiki/Embedded_Zerotrees_of_Wavelet_transforms" - alias: - - integral-wavelet-transform - - - concept: way-below - arity: 2 - en: $1 way below $2 - property: infix - area: "domain theory" - mathml: - - "X≪Y" - urls: - - "http://mizar.org/fm/1997-6/pdf6-1/waybel_3.pdf" - - "https://en.wikipedia.org/wiki/Domain_theory" - alias: - - way-inside - - order-of-approximation - - - concept: weak-convergence - arity: 2 - en: $1 weak convergence $2 - property: infix - area: "analysis" - mathml: - - "X→wY" - - "X⇀Y" - urls: - - "https://mathworld.wolfram.com/WeakConvergence.html" - - "https://en.wikipedia.org/wiki/Weak_convergence_(Hilbert_space)" - - - concept: weber-function - arity: 1 - en: weber function of $1 - property: "indexed function" - area: "special functions" - mathml: - - "𝐄ν(x)" - urls: - - "https://mathworld.wolfram.com/WeberFunctions.html" - - "https://dlmf.nist.gov/11.10#E2" - - "https://www.encyclopediaofmath.org/index.php/Weber_function" - - - concept: weierstrass-elliptic-function - arity: 1 - en: weierstrass elliptic function of $1 - property: function - area: "special functions" - mathml: - - "℘(x)" - urls: - - "https://mathworld.wolfram.com/WeierstrassEllipticFunction.html" - - "https://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions" - - "https://dlmf.nist.gov/23.2#ii" - - "https://ncatlab.org/nlab/show/Weierstrass+elliptic+function" - - "https://www.encyclopediaofmath.org/index.php/Weierstrass_elliptic_functions" - - - concept: weierstrass-sigma-function - arity: 1 - en: weierstrass sigma function of $1 - property: function - area: "special functions" - mathml: - - "σ(x)" - urls: - - "https://mathworld.wolfram.com/WeierstrassSigmaFunction.html" - - "https://dlmf.nist.gov/23.1" - - "https://dlmf.nist.gov/23.2#E6" - - "https://dlmf.nist.gov/23.3#SS1.p3" - - - concept: weierstrass-zeta-function - arity: 1 - en: weierstrass zeta function of $1 - property: function - area: "special functions" - mathml: - - "ζ(x)" - urls: - - "https://mathworld.wolfram.com/WeierstrassZetaFunction.html" - - "https://dlmf.nist.gov/23.1" - - "https://dlmf.nist.gov/23.2#E5" - - "https://dlmf.nist.gov/23.3#SS1.p3" - - - concept: weight - arity: 1 - en: weight of $1 - property: function - area: "group theory" - mathml: - - "wt(x)" - urls: - - "https://en.wikipedia.org/wiki/Weight_(strings)" - - "https://ncatlab.org/nlab/show/weight" - - "https://www.encyclopediaofmath.org/index.php/Weight" - - - concept: weighted-lehmer-mean - arity: ">=0" - en: weighted lehmer mean of $1 $2 ... - property: "indexed function" - area: "means" - mathml: - - "Lp(x,y,z)" - urls: - - "https://mathworld.wolfram.com/LehmerMean.html" - - "https://en.wikipedia.org/wiki/Lehmer_mean" - - - concept: weighted-mean - arity: 1 - en: weighted mean of $1 - property: fenced - area: "special functions" - mathml: - - "⟨x⟩" - urls: - - "https://mathworld.wolfram.com/WeightedMean.html" - - "https://en.wikipedia.org/wiki/Weighted_arithmetic_mean" - alias: - - weighted-arithmetic-mean - - weighted-average - - - concept: wheel-graph - arity: 1 - en: wheel graph of $1 - property: "indexed symbol" - area: "graph theory" - mathml: - - "Wn" - urls: - - "https://mathworld.wolfram.com/WheelGraph.html" - - "https://en.wikipedia.org/wiki/Wheel_graph" - - - concept: whitehead-group - arity: 1 - en: whitehead group of $1 - property: function - area: "group theory" - mathml: - - "Wh(x)" - urls: - - "https://mathworld.wolfram.com/WhiteheadGroup.html" - - "https://en.wikipedia.org/wiki/Whitehead_torsion" - - "https://www.encyclopediaofmath.org/index.php/Whitehead_group" - - - concept: whitehead-bracket - arity: 2 - en: whitehead bracket $1 $2 - property: fenced - area: "lie algebra" - mathml: - - "[x,y]" - urls: - - "https://en.wikipedia.org/wiki/Whitehead_product" - - "https://ncatlab.org/nlab/show/Whitehead+product" - - "https://www.encyclopediaofmath.org/index.php/Whitehead_product" - - - concept: whitehead-torsion - arity: 1 - en: whitehead torsion of $1 - property: function - area: "geometric topology" - mathml: - - "τ(x)" - urls: - - "https://mathworld.wolfram.com/WhiteheadTorsion.html" - - "https://en.wikipedia.org/wiki/Whitehead_torsion" - - "https://www.encyclopediaofmath.org/index.php/Whitehead_torsion" - - - concept: whittaker-function - arity: 2 - en: whittaker function $1 $2 - property: "indexed function" - area: "special functions" - mathml: - - "Mκ,μ(z)" - - "Wκ,μ(z)" - urls: - - "https://mathworld.wolfram.com/WhittakerFunction.html" - - "https://en.wikipedia.org/wiki/Whittaker_function" - - "https://dlmf.nist.gov/13#PT3" - - "https://www.encyclopediaofmath.org/index.php/Whittaker_functions" + property: symbol + subject-area: "measure theory" + mathml: + - "dV" + urls: + - "https://mathworld.wolfram.com/VolumeElement.html" + - "https://en.wikipedia.org/wiki/Volume_element" + + - concept: walsh-function + arity: 1 + arguments: [a1] + speech: + en: walsh function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "W(x)" + urls: + - "https://mathworld.wolfram.com/WalshFunction.html" + - "https://en.wikipedia.org/wiki/Walsh_function" + - "https://www.encyclopediaofmath.org/index.php/Walsh_functions" + + - concept: wavelet-transform + arity: 2 + arguments: [a1, a2] + speech: + en: wavelet transform a1 a2 + property: "embellished function" + subject-area: "functional analysis" + mathml: + - "Wψy" + notation: "mrow [ msub W a1 /msub a2 ]" + urls: + - "https://mathworld.wolfram.com/WaveletTransform.html" + - "https://en.wikipedia.org/wiki/Wavelet_transform" + - "https://en.wikipedia.org/wiki/Embedded_Zerotrees_of_Wavelet_transforms" + alias: + - integral-wavelet-transform + + - concept: way-below + arity: 2 + arguments: [a1, a2] + speech: + en: a1 way below a2 + property: infix + subject-area: "domain theory" + mathml: + - "X≪Y" + urls: + - "http://mizar.org/fm/1997-6/pdf6-1/waybel_3.pdf" + - "https://en.wikipedia.org/wiki/Domain_theory" + alias: + - way-inside + - order-of-approximation + + - concept: weak-convergence + arity: 2 + arguments: [a1, a2] + speech: + en: a1 weak convergence a2 + property: infix + subject-area: "analysis" + mathml: + - "X→wY" + - "X⇀Y" + urls: + - "https://mathworld.wolfram.com/WeakConvergence.html" + - "https://en.wikipedia.org/wiki/Weak_convergence_(Hilbert_space)" + + - concept: weber-function + arity: 1 + arguments: [a1] + speech: + en: weber function of a1 + property: "indexed function" + subject-area: "special functions" + mathml: + - "𝐄ν(x)" + urls: + - "https://mathworld.wolfram.com/WeberFunctions.html" + - "https://dlmf.nist.gov/11.10#E2" + - "https://www.encyclopediaofmath.org/index.php/Weber_function" + + - concept: weierstrass-elliptic-function + arity: 1 + arguments: [a1] + speech: + en: weierstrass elliptic function of a1 + property: function + subject-area: "special functions" + mathml: + - "℘(x)" + urls: + - "https://mathworld.wolfram.com/WeierstrassEllipticFunction.html" + - "https://en.wikipedia.org/wiki/Weierstrass%27s_elliptic_functions" + - "https://dlmf.nist.gov/23.2#ii" + - "https://ncatlab.org/nlab/show/Weierstrass+elliptic+function" + - "https://www.encyclopediaofmath.org/index.php/Weierstrass_elliptic_functions" + + - concept: weierstrass-sigma-function + arity: 1 + arguments: [a1] + speech: + en: weierstrass sigma function of a1 + property: function + subject-area: "special functions" + mathml: + - "σ(x)" + urls: + - "https://mathworld.wolfram.com/WeierstrassSigmaFunction.html" + - "https://dlmf.nist.gov/23.1" + - "https://dlmf.nist.gov/23.2#E6" + - "https://dlmf.nist.gov/23.3#SS1.p3" + + - concept: weierstrass-zeta-function + arity: 1 + arguments: [a1] + speech: + en: weierstrass zeta function of a1 + property: function + subject-area: "special functions" + mathml: + - "ζ(x)" + urls: + - "https://mathworld.wolfram.com/WeierstrassZetaFunction.html" + - "https://dlmf.nist.gov/23.1" + - "https://dlmf.nist.gov/23.2#E5" + - "https://dlmf.nist.gov/23.3#SS1.p3" + + - concept: weight + arity: 1 + arguments: [a1] + speech: + en: weight of a1 + property: function + subject-area: "group theory" + mathml: + - "wt(x)" + urls: + - "https://en.wikipedia.org/wiki/Weight_(strings)" + - "https://ncatlab.org/nlab/show/weight" + - "https://www.encyclopediaofmath.org/index.php/Weight" + + - concept: weighted-lehmer-mean + arity: ">=0" + speech: + en: weighted lehmer mean of a1 a2 ... + property: "indexed function" + subject-area: "means" + mathml: + - "Lp(x,y,z)" + urls: + - "https://mathworld.wolfram.com/LehmerMean.html" + - "https://en.wikipedia.org/wiki/Lehmer_mean" + + - concept: weighted-mean + arity: 1 + arguments: [a1] + speech: + en: weighted mean of a1 + property: fenced + subject-area: "special functions" + mathml: + - "⟨x⟩" + urls: + - "https://mathworld.wolfram.com/WeightedMean.html" + - "https://en.wikipedia.org/wiki/Weighted_arithmetic_mean" + alias: + - weighted-arithmetic-mean + - weighted-average + + - concept: wheel-graph + arity: 1 + arguments: [a1] + speech: + en: wheel graph of a1 + property: "indexed symbol" + subject-area: "graph theory" + mathml: + - "Wn" + urls: + - "https://mathworld.wolfram.com/WheelGraph.html" + - "https://en.wikipedia.org/wiki/Wheel_graph" + + - concept: whitehead-group + arity: 1 + arguments: [a1] + speech: + en: whitehead group of a1 + property: function + subject-area: "group theory" + mathml: + - "Wh(x)" + urls: + - "https://mathworld.wolfram.com/WhiteheadGroup.html" + - "https://en.wikipedia.org/wiki/Whitehead_torsion" + - "https://www.encyclopediaofmath.org/index.php/Whitehead_group" + + - concept: whitehead-bracket + arity: 2 + arguments: [a1, a2] + speech: + en: whitehead bracket a1 a2 + property: fenced + subject-area: "lie algebra" + mathml: + - "[x,y]" + urls: + - "https://en.wikipedia.org/wiki/Whitehead_product" + - "https://ncatlab.org/nlab/show/Whitehead+product" + - "https://www.encyclopediaofmath.org/index.php/Whitehead_product" + + - concept: whitehead-torsion + arity: 1 + arguments: [a1] + speech: + en: whitehead torsion of a1 + property: function + subject-area: "geometric topology" + mathml: + - "τ(x)" + urls: + - "https://mathworld.wolfram.com/WhiteheadTorsion.html" + - "https://en.wikipedia.org/wiki/Whitehead_torsion" + - "https://www.encyclopediaofmath.org/index.php/Whitehead_torsion" + + - concept: whittaker-function + arity: 2 + arguments: [a1, a2] + speech: + en: whittaker function a1 a2 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Mκ,μ(z)" + - "Wκ,μ(z)" + urls: + - "https://mathworld.wolfram.com/WhittakerFunction.html" + - "https://en.wikipedia.org/wiki/Whittaker_function" + - "https://dlmf.nist.gov/13#PT3" + - "https://www.encyclopediaofmath.org/index.php/Whittaker_functions" - - concept: whittaker-function - arity: 3 - en: whittaker function $1 $2 of $3 - property: "indexed function" - area: "special functions" - mathml: - - "Mκ,μ(z)" - - "Wκ,μ(z)" - urls: - - "https://mathworld.wolfram.com/WhittakerFunction.html" - - "https://en.wikipedia.org/wiki/Whittaker_function" - - "https://dlmf.nist.gov/13#PT3" - - "https://www.encyclopediaofmath.org/index.php/Whittaker_functions" - - - concept: wiener-algebra - arity: 0 + - concept: whittaker-function + arity: 3 + arguments: [a1, a2, a3] + speech: + en: whittaker function a1 a2 of a3 + property: "indexed function" + subject-area: "special functions" + mathml: + - "Mκ,μ(z)" + - "Wκ,μ(z)" + urls: + - "https://mathworld.wolfram.com/WhittakerFunction.html" + - "https://en.wikipedia.org/wiki/Whittaker_function" + - "https://dlmf.nist.gov/13#PT3" + - "https://www.encyclopediaofmath.org/index.php/Whittaker_functions" + + - concept: wiener-algebra + arity: 0 + arguments: [] + speech: en: wiener algebra - property: symbol - area: "Fourier analysis" - mathml: - - "A(T)" - urls: - - "https://mathworld.wolfram.com/WienerAlgebra.html" - - "https://en.wikipedia.org/wiki/Wiener_algebra" - - - concept: wiener-process - arity: 1 - en: wiener process of $1 - property: "indexed symbol" - area: "martingale theory" - mathml: - - "Wn" - urls: - - "https://mathworld.wolfram.com/WienerProcess.html" - - "https://en.wikipedia.org/wiki/Wiener_process" - - "https://www.encyclopediaofmath.org/index.php/Wiener_process" - - - concept: wiener-sausage - arity: 2 - en: wiener sausage of radius $1 and length $2 - property: "indexed symbol" - area: "mathematical physics" - mathml: - - "Wδ(t)" - urls: - - "https://mathworld.wolfram.com/WienerSausage.html" - - "https://en.wikipedia.org/wiki/Wiener_sausage" - - "https://www.encyclopediaofmath.org/index.php/Wiener_sausage" - - - concept: wilson-polynomial - arity: 1 - en: $1th wilson polynomial - property: "indexed function" - area: "orthogonal polynomials" - mathml: - - "Wn" - urls: - - "https://mathworld.wolfram.com/WilsonPolynomial.html" - - "https://en.wikipedia.org/wiki/Wilson_polynomials" - - "https://dlmf.nist.gov/18.25#T1.t1.r2" - - "https://www.encyclopediaofmath.org/index.php/Wilson_polynomials" - - - concept: wilson-quotient - arity: 1 - en: wilson quotient of $1 - property: function - area: "number theory" - mathml: - - "W(x)" - urls: - - "https://mathworld.wolfram.com/WilsonQuotient.html" - - "https://en.wikipedia.org/wiki/Wilson_quotient" - - - concept: winding-number - arity: 1 - en: winding number of $1 - property: "function, symbol" - area: "algebraic topology" - mathml: - - "𝒩(x)" - - "w(x)" - urls: - - "https://en.wikipedia.org/wiki/Winding_number" - - "https://dlmf.nist.gov/1.9#E32" - - "https://ncatlab.org/nlab/show/winding+number" - - "https://planetmath.org/windingnumber" - - "https://www.encyclopediaofmath.org/index.php/Winding_number" - - - concept: window-function - arity: 1 - en: window function of $1 - property: function - area: "fourier analysis" - mathml: - - "w(x)" - urls: - - "https://mathworld.wolfram.com/WindowFunction.html" - - "https://en.wikipedia.org/wiki/Window_function" - - "https://www.encyclopediaofmath.org/index.php/Window_function" - - - concept: wishart-distribution - arity: 0 + property: symbol + subject-area: "Fourier analysis" + mathml: + - "A(T)" + urls: + - "https://mathworld.wolfram.com/WienerAlgebra.html" + - "https://en.wikipedia.org/wiki/Wiener_algebra" + + - concept: wiener-process + arity: 1 + arguments: [a1] + speech: + en: wiener process of a1 + property: "indexed symbol" + subject-area: "martingale theory" + mathml: + - "Wn" + urls: + - "https://mathworld.wolfram.com/WienerProcess.html" + - "https://en.wikipedia.org/wiki/Wiener_process" + - "https://www.encyclopediaofmath.org/index.php/Wiener_process" + + - concept: wiener-sausage + arity: 2 + arguments: [a1, a2] + speech: + en: wiener sausage of radius a1 and length a2 + property: "indexed symbol" + subject-area: "mathematical physics" + mathml: + - "Wδ(t)" + urls: + - "https://mathworld.wolfram.com/WienerSausage.html" + - "https://en.wikipedia.org/wiki/Wiener_sausage" + - "https://www.encyclopediaofmath.org/index.php/Wiener_sausage" + + - concept: wilson-polynomial + arity: 1 + arguments: [a1] + speech: + en: a1th wilson polynomial + property: "indexed function" + subject-area: "orthogonal polynomials" + mathml: + - "Wn" + urls: + - "https://mathworld.wolfram.com/WilsonPolynomial.html" + - "https://en.wikipedia.org/wiki/Wilson_polynomials" + - "https://dlmf.nist.gov/18.25#T1.t1.r2" + - "https://www.encyclopediaofmath.org/index.php/Wilson_polynomials" + + - concept: wilson-quotient + arity: 1 + arguments: [a1] + speech: + en: wilson quotient of a1 + property: function + subject-area: "number theory" + mathml: + - "W(x)" + urls: + - "https://mathworld.wolfram.com/WilsonQuotient.html" + - "https://en.wikipedia.org/wiki/Wilson_quotient" + + - concept: winding-number + arity: 1 + arguments: [a1] + speech: + en: winding number of a1 + property: "function, symbol" + subject-area: "algebraic topology" + mathml: + - "𝒩(x)" + - "w(x)" + urls: + - "https://en.wikipedia.org/wiki/Winding_number" + - "https://dlmf.nist.gov/1.9#E32" + - "https://ncatlab.org/nlab/show/winding+number" + - "https://planetmath.org/windingnumber" + - "https://www.encyclopediaofmath.org/index.php/Winding_number" + + - concept: window-function + arity: 1 + arguments: [a1] + speech: + en: window function of a1 + property: function + subject-area: "fourier analysis" + mathml: + - "w(x)" + urls: + - "https://mathworld.wolfram.com/WindowFunction.html" + - "https://en.wikipedia.org/wiki/Window_function" + - "https://www.encyclopediaofmath.org/index.php/Window_function" + + - concept: wishart-distribution + arity: 0 + arguments: [] + speech: en: wishart distribution - property: symbol - area: "probability theory" - mathml: - - "Wp" - urls: - - "https://mathworld.wolfram.com/WishartDistribution.html" - - "https://en.wikipedia.org/wiki/Wishart_distribution" - - "https://www.encyclopediaofmath.org/index.php/Wishart_distribution" - - - concept: witt-polynomials - arity: 1 - en: witt polynomials of $1 - property: "indexed function" - area: "ring theory" - mathml: - - "Wx" - urls: - - "https://en.wikipedia.org/wiki/Witt_vector" - - "https://www.encyclopediaofmath.org/index.php/Witt_vector" - - - concept: witt-vector - arity: ">=0" - en: witt vector of $1 - property: fenced - area: "ring theory" - mathml: - - "W(X)" - urls: - - "https://en.wikipedia.org/wiki/Witt_vector" - - "https://www.encyclopediaofmath.org/index.php/Witt_vector" - - - concept: woodall-number - arity: 1 - en: woodall number of $1 - property: "indexed symbol" - area: "number theory" - mathml: - - "Wx" - urls: - - "https://mathworld.wolfram.com/WoodallNumber.html" - - "https://en.wikipedia.org/wiki/Woodall_number" - - "https://en.wikipedia.org/wiki/Woodall_prime" - - - concept: wright-function - arity: 1 - en: wright function of $1 - property: function - area: "special functions" - mathml: - - "ϕ(x)" - urls: - - "https://mathworld.wolfram.com/WrightFunction.html" - - - concept: wright-omega-function - arity: 1 - en: wright omega function of $1 - property: function - area: "special functions" - mathml: - - "ω(x)" - urls: - - "https://en.wikipedia.org/wiki/Wright_Omega_function" - alias: - - wright-function - - - concept: writhe - arity: 1 - en: writhe of $1 - property: function - area: "knot theory" - mathml: - - "Wr(x)" - urls: - - "https://mathworld.wolfram.com/Writhe.html" - - "https://en.wikipedia.org/wiki/Writhe" - - "https://ncatlab.org/nlab/show/writhe" - - - concept: wronskian - arity: 2 - en: wronskian of $1, $2 - property: operator - area: "special functions" - mathml: - - "𝒲(f,g)" - - "W(f,g)" - urls: - - "https://mathworld.wolfram.com/Wronskian.html" - - "https://en.wikipedia.org/wiki/Wronskian" - - "https://dlmf.nist.gov/1.13#E4" - - "https://ncatlab.org/nlab/show/Wronskian" - - "https://www.encyclopediaofmath.org/index.php/Wronskian" - - - concept: yang-mill-functional - arity: 1 - en: yang mill functional of $1 - property: function - area: "gauge theory" - mathml: - - "ℒ(x)" - urls: - - "https://mathworld.wolfram.com/Yang-MillsFunctional.html" - - "https://www.encyclopediaofmath.org/index.php/Yang-Mills_functional" - - "https://www.encyclopediaofmath.org/index.php/YangâXXXXMills_functional" - - - concept: z-matrix - arity: 0 + property: symbol + subject-area: "probability theory" + mathml: + - "Wp" + urls: + - "https://mathworld.wolfram.com/WishartDistribution.html" + - "https://en.wikipedia.org/wiki/Wishart_distribution" + - "https://www.encyclopediaofmath.org/index.php/Wishart_distribution" + + - concept: witt-polynomials + arity: 1 + arguments: [a1] + speech: + en: witt polynomials of a1 + property: "indexed function" + subject-area: "ring theory" + mathml: + - "Wx" + urls: + - "https://en.wikipedia.org/wiki/Witt_vector" + - "https://www.encyclopediaofmath.org/index.php/Witt_vector" + + - concept: witt-vector + arity: ">=0" + speech: + en: witt vector of a1 + property: fenced + subject-area: "ring theory" + mathml: + - "W(X)" + urls: + - "https://en.wikipedia.org/wiki/Witt_vector" + - "https://www.encyclopediaofmath.org/index.php/Witt_vector" + + - concept: woodall-number + arity: 1 + arguments: [a1] + speech: + en: woodall number of a1 + property: "indexed symbol" + subject-area: "number theory" + mathml: + - "Wx" + urls: + - "https://mathworld.wolfram.com/WoodallNumber.html" + - "https://en.wikipedia.org/wiki/Woodall_number" + - "https://en.wikipedia.org/wiki/Woodall_prime" + + - concept: wright-function + arity: 1 + arguments: [a1] + speech: + en: wright function of a1 + property: function + subject-area: "special functions" + mathml: + - "ϕ(x)" + urls: + - "https://mathworld.wolfram.com/WrightFunction.html" + + - concept: wright-omega-function + arity: 1 + arguments: [a1] + speech: + en: wright omega function of a1 + property: function + subject-area: "special functions" + mathml: + - "ω(x)" + urls: + - "https://en.wikipedia.org/wiki/Wright_Omega_function" + alias: + - wright-function + + - concept: writhe + arity: 1 + arguments: [a1] + speech: + en: writhe of a1 + property: function + subject-area: "knot theory" + mathml: + - "Wr(x)" + urls: + - "https://mathworld.wolfram.com/Writhe.html" + - "https://en.wikipedia.org/wiki/Writhe" + - "https://ncatlab.org/nlab/show/writhe" + + - concept: wronskian + arity: 2 + arguments: [a1, a2] + speech: + en: wronskian of a1, a2 + property: operator + subject-area: "special functions" + mathml: + - "𝒲(f,g)" + - "W(f,g)" + urls: + - "https://mathworld.wolfram.com/Wronskian.html" + - "https://en.wikipedia.org/wiki/Wronskian" + - "https://dlmf.nist.gov/1.13#E4" + - "https://ncatlab.org/nlab/show/Wronskian" + - "https://www.encyclopediaofmath.org/index.php/Wronskian" + + - concept: yang-mill-functional + arity: 1 + arguments: [a1] + speech: + en: yang mill functional of a1 + property: function + subject-area: "gauge theory" + mathml: + - "ℒ(x)" + urls: + - "https://mathworld.wolfram.com/Yang-MillsFunctional.html" + - "https://www.encyclopediaofmath.org/index.php/Yang-Mills_functional" + - "https://www.encyclopediaofmath.org/index.php/YangâXXXXMills_functional" + + - concept: z-matrix + arity: 0 + arguments: [] + speech: en: z matrix - property: symbol - area: "linear algebra" - mathml: - - "Z" - urls: - - "https://en.wikipedia.org/wiki/Z-matrix_(mathematics)" - - - concept: z-matrix-molecule - arity: 1 - en: z matrix molecule of $1 - property: mtable - area: "chemistry" - mathml: - - "......" - urls: - - "https://en.wikipedia.org/wiki/Z-matrix_(chemistry)" - - - concept: z-transform - arity: 1 - en: z transform of $1 - property: function - area: "combinatorics" - mathml: - - "Z(x)" - urls: - - "https://mathworld.wolfram.com/z-Transform.html" - - "https://mathworld.wolfram.com/Z-Transform.html" - - "https://en.wikipedia.org/wiki/Z-transform" - - "https://www.encyclopediaofmath.org/index.php/Z-transform" - - - concept: zernike-polynomial - arity: 4 - en: $1 $2 zernike polynomial of $3, $4 - property: "indexed function" - area: "orthogonal polynomials" - mathml: - - "Znm(ρ,φ)" - urls: - - "https://mathworld.wolfram.com/ZernikePolynomial.html" - - "https://en.wikipedia.org/wiki/Zernike_polynomials" - - "https://www.encyclopediaofmath.org/index.php/Zernike_polynomials" - - - concept: zero-ideal - arity: 0 + property: symbol + subject-area: "linear algebra" + mathml: + - "Z" + urls: + - "https://en.wikipedia.org/wiki/Z-matrix_(mathematics)" + + - concept: z-matrix-molecule + arity: 1 + arguments: [a1] + speech: + en: z matrix molecule of a1 + property: mtable + subject-area: "chemistry" + mathml: + - "......" + urls: + - "https://en.wikipedia.org/wiki/Z-matrix_(chemistry)" + + - concept: z-transform + arity: 1 + arguments: [a1] + speech: + en: z transform of a1 + property: function + subject-area: "combinatorics" + mathml: + - "Z(x)" + urls: + - "https://mathworld.wolfram.com/z-Transform.html" + - "https://mathworld.wolfram.com/Z-Transform.html" + - "https://en.wikipedia.org/wiki/Z-transform" + - "https://www.encyclopediaofmath.org/index.php/Z-transform" + + - concept: zernike-polynomial + arity: 4 + arguments: [a1, a2, a3, a4] + speech: + en: a1 a2 zernike polynomial of a3, a4 + property: "indexed function" + subject-area: "orthogonal polynomials" + mathml: + - "Znm(ρ,φ)" + urls: + - "https://mathworld.wolfram.com/ZernikePolynomial.html" + - "https://en.wikipedia.org/wiki/Zernike_polynomials" + - "https://www.encyclopediaofmath.org/index.php/Zernike_polynomials" + + - concept: zero-ideal + arity: 0 + arguments: [] + speech: en: zero ideal - property: symbol - area: "ring theory" - mathml: - - "{0}" - urls: - - "https://mathworld.wolfram.com/ZeroIdeal.html" - - "https://ncatlab.org/nlab/show/zero+ideal" - - - concept: zero-matrix - arity: 2 - en: $1 $2 zero matrix - property: "indexed symbol" - area: "linear algebra" - mathml: - - "0ij" - urls: - - "https://en.wikipedia.org/wiki/Zero_matrix" - - - concept: zero-morphism - arity: 2 - en: zero morphism $1 $2 - property: "indexed symbol" - area: "category theory" - mathml: - - "0AB" - notation: "msub mn 0 mrow X,Y" - urls: - - "https://en.wikipedia.org/wiki/Zero_morphism" - - "https://ncatlab.org/nlab/show/zero+morphism" - - - concept: zero-object - arity: 0 + property: symbol + subject-area: "ring theory" + mathml: + - "{0}" + urls: + - "https://mathworld.wolfram.com/ZeroIdeal.html" + - "https://ncatlab.org/nlab/show/zero+ideal" + + - concept: zero-matrix + arity: 2 + arguments: [a1, a2] + speech: + en: a1 a2 zero matrix + property: "indexed symbol" + subject-area: "linear algebra" + mathml: + - "0ij" + urls: + - "https://en.wikipedia.org/wiki/Zero_matrix" + + - concept: zero-morphism + arity: 2 + arguments: [a1, a2] + speech: + en: zero morphism a1 a2 + property: "indexed symbol" + subject-area: "category theory" + mathml: + - "0AB" + notation: "msub mn 0 mrow X,Y" + urls: + - "https://en.wikipedia.org/wiki/Zero_morphism" + - "https://ncatlab.org/nlab/show/zero+morphism" + + - concept: zero-object + arity: 0 + arguments: [] + speech: en: zero object - property: symbol - area: "algebra" - mathml: - - "{0}" - urls: - - "https://en.wikipedia.org/wiki/Zero_object_(algebra)" - - "https://ncatlab.org/nlab/show/zero+object" - - - concept: zero-ring - arity: 0 + property: symbol + subject-area: "algebra" + mathml: + - "{0}" + urls: + - "https://en.wikipedia.org/wiki/Zero_object_(algebra)" + - "https://ncatlab.org/nlab/show/zero+object" + + - concept: zero-ring + arity: 0 + arguments: [] + speech: en: zero ring - property: symbol - area: "ring theory" - mathml: - - "{0}" - - "0" - urls: - - "https://mathworld.wolfram.com/ZeroRing.html" - - "https://en.wikipedia.org/wiki/Zero_ring" - - - concept: zero-vector - arity: 0 + property: symbol + subject-area: "ring theory" + mathml: + - "{0}" + - "0" + urls: + - "https://mathworld.wolfram.com/ZeroRing.html" + - "https://en.wikipedia.org/wiki/Zero_ring" + + - concept: zero-vector + arity: 0 + arguments: [] + speech: en: zero vector - property: constant - area: "linear algebra" - mathml: - - "0" - urls: - - "https://mathworld.wolfram.com/ZeroVector.html" - - - concept: zeta-function - arity: 1 - en: zeta function of $1 - property: function - area: "number theory" - mathml: - - "ζ(x)" - urls: - - "https://mathworld.wolfram.com/ZetaFunction.html" - - "https://en.wikipedia.org/wiki/List_of_zeta_functions" - - "https://en.wikipedia.org/wiki/Zeta_function_(operator)" - - "https://ncatlab.org/nlab/show/zeta+function" - - - concept: zig-zag-product - arity: 2 - en: $1 zig zag product $2 - property: infix - area: "graph theory" - mathml: - - "X∘Y" - urls: - - "https://en.wikipedia.org/wiki/Zig-zag_product" + property: constant + subject-area: "linear algebra" + mathml: + - "0" + urls: + - "https://mathworld.wolfram.com/ZeroVector.html" + + - concept: zeta-function + arity: 1 + arguments: [a1] + speech: + en: zeta function of a1 + property: function + subject-area: "number theory" + mathml: + - "ζ(x)" + urls: + - "https://mathworld.wolfram.com/ZetaFunction.html" + - "https://en.wikipedia.org/wiki/List_of_zeta_functions" + - "https://en.wikipedia.org/wiki/Zeta_function_(operator)" + - "https://ncatlab.org/nlab/show/zeta+function" + + - concept: zig-zag-product + arity: 2 + arguments: [a1, a2] + speech: + en: a1 zig zag product a2 + property: infix + subject-area: "graph theory" + mathml: + - "X∘Y" + urls: + - "https://en.wikipedia.org/wiki/Zig-zag_product" From 8eacacacde73e53edb77cc03dfc20dcbbc3b5335 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 14:01:58 +0100 Subject: [PATCH 21/33] open index 1 --- intent-open-concepts/index.md | 17 +++++++++-------- 1 file changed, 9 insertions(+), 8 deletions(-) diff --git a/intent-open-concepts/index.md b/intent-open-concepts/index.md index 2ecfd3d1..490797a1 100644 --- a/intent-open-concepts/index.md +++ b/intent-open-concepts/index.md @@ -35,6 +35,7 @@ span.cb {margin-right: 2em; white-space:nowrap} .markdown-body table {font-size:85%} .markdown-body table tr.row0, .markdown-body table th.row0 {background-color:#F6F8FA} .markdown-body table tr.row1 {background-color:#FEFFFE} +.markdown-body table tr.subj {background-color:beige;font-size:110%;text-align:left;} a.link {font-weight:500} a.self {color: black; font-weight:500} [arg] { background-color: #ddfafa;} @@ -123,9 +124,8 @@ Additional contributions are welcome:

-{%- for section in site.data.open.concepts -%} - -### {{section.title}} +{% assign cpts = site.data.open.concepts | sort: "subject-area" %} +{% assign subjt = "" %} @@ -137,12 +137,15 @@ Additional contributions are welcome: {%- endfor -%} - -{%- for c in section.intents -%} +{%- for c in cpts -%} +{%- if c.subject-area != subjt -%} +{%- assign subjt = c.subject-area -%} + +{%- endif -%} {%- assign clss = forloop.index| modulo:2 -%} {%- assign arityr = c.arity | replace: ">=", "⩾" -%} {%- assign arityu = c.arity | replace: ">=", "GEQ" -%} @@ -183,7 +186,6 @@ Additional contributions are welcome: Aliases: {% for al in c.alias -%}{{al}}{%- unless forloop.last -%}
{% endunless -%}{%- endfor -%} {%-endif -%} {%- endif -%} -{%- if forloop.first-%}{%-endif -%} {%- if forloop.first-%} -
Speech Template ({{language.language-code}})CommentsSubject Sources
{{subjt}}
{{c.area}} {%- if c.urls -%} {% for u in c.urls %} @@ -244,7 +246,6 @@ arXiv Aliases: {% for al in c.alias -%}{{al}}{%- unless forloop.last -%}, {% endunless -%}{%- endfor -%} {%-endif -%} {{c.area}} {%- if c.urls -%} {% for u in c.urls %} @@ -276,7 +277,7 @@ arXiv
-{%- endfor -%} + ### Key From 1a88ef2637155fb43d90604bce2ddbca25f13c9b Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 14:07:47 +0100 Subject: [PATCH 22/33] open index 2 --- intent-open-concepts/index.md | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/intent-open-concepts/index.md b/intent-open-concepts/index.md index 490797a1..aec05517 100644 --- a/intent-open-concepts/index.md +++ b/intent-open-concepts/index.md @@ -144,7 +144,13 @@ Additional contributions are welcome: {%- for c in cpts -%} {%- if c.subject-area != subjt -%} {%- assign subjt = c.subject-area -%} -
{{subjt}}
+{%- if c.subject-area == null -%} +00 Unclassified +{%- else -%} +{{subjt}} +{%- endif -%} +
[{{cond.condition}}]: -{% if cond[language.language-code] -%} -{%- for l in cond[language.language-code] -%} +{% if cond.speech[language.language-code] -%} +{%- for l in cond.speech[language.language-code] -%} {{l}} {%- unless forloop.last -%}
{% endunless -%} {% endfor %} {%- else -%} @@ -226,12 +226,12 @@ arXiv 		{{c.property}}{%- unless c.default == false or c.arity == 0-%}*{%- endunless -%} -{%- if c[language.language-code] -%} -{%- for l in c[language.language-code] -%} +{%- if c.speech[language.language-code] -%} +{%- for l in c.speech[language.language-code] -%} {{l}} {%- unless forloop.last -%}
{% endunless -%} {% endfor %} {%- else -%} -{%- for l in c.en -%} +{%- for l in c.speech.en -%} {{l}} ({{language.language-code}}){%- unless forloop.last -%}
{% endunless -%} {% endfor %} {% endif %} From ba6648234429b562eb0d3f742851e62b57669fd7 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 18:30:42 +0100 Subject: [PATCH 24/33] space after comma to please the linter --- _data/core.yml | 98 +++++++++++++++++++++++++------------------------- 1 file changed, 49 insertions(+), 49 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index 30460c88..eb0d49fe 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -217,7 +217,7 @@ concepts: - concept: closed-open-interval subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: interval between a1 (included) and a2 @@ -226,7 +226,7 @@ concepts: - concept: open-closed-interval subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: interval between a1 and a2, included @@ -235,7 +235,7 @@ concepts: - concept: open-interval subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: open interval between a1 and a2 @@ -244,7 +244,7 @@ concepts: - concept: closed-interval subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: closed interval between a1 and a2 @@ -298,7 +298,7 @@ concepts: - concept: fraction subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: fraction a1 over a2 end fraction @@ -306,7 +306,7 @@ concepts: - concept: mixed-fraction subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: a1 and a2 @@ -317,7 +317,7 @@ concepts: - concept: quotient subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: integer part of a1 divided by a2 @@ -326,7 +326,7 @@ concepts: - concept: evaluated-at subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: a1 evaluated-at a2 @@ -347,7 +347,7 @@ concepts: - concept: remainder subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: the remainder of a1 divided by a2 @@ -372,7 +372,7 @@ concepts: - concept: power subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix conditions: - condition: "a2=2" @@ -392,7 +392,7 @@ concepts: - concept: root subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function conditions: - condition: "a2=2" @@ -411,7 +411,7 @@ concepts: - concept: greatest-common-divisor subject-area: functions and inverses arity: ">=2" - arguments: [a1,a2,...] + arguments: [a1, a2,...] property: function speech: en: greatest common divisor of a1, a2, ... @@ -420,7 +420,7 @@ concepts: - concept: least-common-multiple subject-area: functions and inverses arity: ">=2" - arguments: [a1,a2,...] + arguments: [a1, a2,...] property: function speech: en: lest common multiple of a1, a2, ... @@ -429,7 +429,7 @@ concepts: - concept: least-common-denominator subject-area: functions and inverses arity: ">=2" - arguments: [a1,a2,...] + arguments: [a1, a2,...] property: function speech: en: "least common denominator of a1, a2, ..." @@ -482,7 +482,7 @@ concepts: - concept: polar-coordinate subject-area: functions and inverses arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "polar coordinate a1 comma a2" @@ -493,7 +493,7 @@ concepts: - concept: spherical-coordinate subject-area: functions and inverses arity: 3 - arguments: [a1,a2,a3] + arguments: [a1, a2, a3] property: function speech: en: "spherical coordinate a1 comma a2, comma a3" @@ -504,7 +504,7 @@ concepts: - concept: cartesian-coordinate subject-area: functions and inverses arity: ">=2" - arguments: [a1,a2,...] + arguments: [a1, a2,...] property: function speech: en: "cartesian coordinate a1 comma a2 ..." @@ -514,7 +514,7 @@ concepts: - concept: coordinate subject-area: functions and inverses arity: ">=2" - arguments: [a1,a2,...] + arguments: [a1, a2,...] property: function speech: en: "coordinate a1 comma a2 ..." @@ -573,7 +573,7 @@ concepts: - concept: definite-integral subject-area: calculus arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: ??? speech: en: "integral from a1 to a2" @@ -584,7 +584,7 @@ concepts: - concept: derivative subject-area: calculus arity: 3 - arguments: [a1,a2,a3] + arguments: [a1, a2, a3] property: ??? speech: en: @@ -617,7 +617,7 @@ concepts: - concept: partial-derivative subject-area: calculus arity: ">=3" - arguments: [a1,a2,a3,...] + arguments: [a1, a2, a3,...] property: ??? speech: en: @@ -672,7 +672,7 @@ concepts: - concept: tends-to subject-area: calculus arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "a1 tends to a2" @@ -682,7 +682,7 @@ concepts: - concept: tends-to-from-above subject-area: calculus arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "a1 tends to from above a2" @@ -692,7 +692,7 @@ concepts: - concept: tends-to-from-below subject-area: calculus arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "a1 tends to from below a2" @@ -732,7 +732,7 @@ concepts: - concept: set-difference subject-area: sets arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "set difference of a1 and a2" @@ -744,7 +744,7 @@ concepts: - concept: set-difference subject-area: sets arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "\"a1 minus a2\" or \"a2 subtracted from a1\"" @@ -810,7 +810,7 @@ concepts: - concept: sum subject-area: sequences and series arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "sum over a1 of a2" @@ -820,7 +820,7 @@ concepts: - concept: sum subject-area: sequences and series arity: 3 - arguments: [a1,a2,a3] + arguments: [a1, a2, a3] property: function speech: en: "sum from a1 to a2 of a3" @@ -840,7 +840,7 @@ concepts: - concept: product subject-area: sequences and series arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "product over a1 of a2" @@ -850,7 +850,7 @@ concepts: - concept: product subject-area: sequences and series arity: 3 - arguments: [a1,a2,a3] + arguments: [a1, a2, a3] property: function speech: en: "product from a1 to a2 of a3" @@ -1193,7 +1193,7 @@ concepts: - concept: logarithm subject-area: elementary classical functions arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "log base a2 of a1" @@ -1249,7 +1249,7 @@ concepts: - concept: conditional-probability subject-area: Statistics and Probability arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "probability of a1 given a2" @@ -1368,7 +1368,7 @@ concepts: - concept: dimensional-product subject-area: Linear Algebra arity: ">=2" - arguments: [a1,a2,...] + arguments: [a1, a2,...] property: infix default: false speech: @@ -1475,7 +1475,7 @@ concepts: - concept: line-segment subject-area: Geometry arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: prefix speech: en: @@ -1486,7 +1486,7 @@ concepts: - concept: directed-line-segment subject-area: Geometry arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: prefix speech: en: @@ -1497,7 +1497,7 @@ concepts: - concept: line subject-area: Geometry arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: prefix speech: en: @@ -1508,7 +1508,7 @@ concepts: - concept: ray subject-area: Geometry arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: prefix speech: en: @@ -1519,7 +1519,7 @@ concepts: - concept: arc subject-area: Geometry arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: prefix speech: en: @@ -1616,7 +1616,7 @@ concepts: - concept: time-separator subject-area: Separators arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: a1 a2 @@ -1638,7 +1638,7 @@ concepts: - concept: ordered-pair subject-area: General Concepts arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "the pair a1 and a2" @@ -1646,7 +1646,7 @@ concepts: - concept: indexed-by subject-area: General Concepts arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "a1 indexed by a2" @@ -1668,7 +1668,7 @@ concepts: - concept: rate subject-area: General Concepts arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "a1 per a2" @@ -1679,7 +1679,7 @@ concepts: - concept: translation subject-area: General Concepts arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "translation by a1 comma a2" @@ -1689,7 +1689,7 @@ concepts: - concept: constraint subject-area: General Concepts arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "fraction 2 over x minus 1 with constraint x not equal to 1" @@ -1699,7 +1699,7 @@ concepts: - concept: binomial-coefficient subject-area: General Concepts arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "a1 choose a2" @@ -1732,7 +1732,7 @@ concepts: - concept: pochhammer subject-area: General Concepts arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "a2 permutation of a1" @@ -1764,7 +1764,7 @@ concepts: - concept: permutation-cycle subject-area: General Concepts arity: ">=2" - arguments: [a1,a2,...] + arguments: [a1, a2,...] property: function speech: en: "permutation cycle of a1 a2 ..." @@ -1788,7 +1788,7 @@ concepts: - concept: embellished-name subject-area: General Concepts arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: infix speech: en: "a1 with annotation a2" @@ -1809,7 +1809,7 @@ concepts: - concept: annotation subject-area: Grouping arity: 2 - arguments: [a1,a2] + arguments: [a1, a2] property: function speech: en: "a1 which is a2" From d77c8cc2f5307629665451f60cfa64790c7cad52 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 19:02:52 +0100 Subject: [PATCH 25/33] reduce indent to please linter --- _data/core.yml | 394 ++++++++++++++++++++++++------------------------- 1 file changed, 197 insertions(+), 197 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index eb0d49fe..c396df2e 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -6,208 +6,208 @@ defaultfixity: - - fixity: function - concepts: - - concept: curl - characters: [∇] - - concept: divergence - characters: [∇] - - concept: gradient - characters: [∇] - - concept: laplacian - characters: [∆] + - fixity: function + concepts: + - concept: curl + characters: [∇] + - concept: divergence + characters: [∇] + - concept: gradient + characters: [∇] + - concept: laplacian + characters: [∆] - - fixity: prefix - concepts: - - concept: angle - characters: [∠] - - concept: angle-measure - characters: [∡] - - concept: change - characters: ["Δ"] - - concept: for-all - characters: [∀] - - concept: measured-angle - characters: [∡] - - concept: minus - characters: ["-", "−"] - - concept: not - characters: [¬] - - concept: number-of - characters: ["#"] - - concept: partial-derivative - characters: [∂] - - concept: right-angle - characters: [∟] - - concept: square-root-of - characters: [√] - - concept: there-does-not-exist - characters: [∄] - - concept: there-exists - characters: [∃] + - fixity: prefix + concepts: + - concept: angle + characters: [∠] + - concept: angle-measure + characters: [∡] + - concept: change + characters: ["Δ"] + - concept: for-all + characters: [∀] + - concept: measured-angle + characters: [∡] + - concept: minus + characters: ["-", "−"] + - concept: not + characters: [¬] + - concept: number-of + characters: ["#"] + - concept: partial-derivative + characters: [∂] + - concept: right-angle + characters: [∟] + - concept: square-root-of + characters: [√] + - concept: there-does-not-exist + characters: [∄] + - concept: there-exists + characters: [∃] - - fixity: infix - concepts: - - concept: and - characters: [⁤∧] - - concept: applied-to - characters: [⁡U+2061] - - concept: approximately - characters: [≈] - - concept: congruent - characters: [≅] - - concept: cartesian-product - characters: [×] - - concept: composed-with - characters: [∘] - - concept: cross-product - characters: [×] - - concept: defined-as - characters: ["≝", "=", "≔"] - - concept: dimensional-product - characters: [×] - link: dimensional-product*infix - - concept: divided-by - characters: [/, ÷, ":"] - - concept: divides - characters: ["|", "∣"] - - concept: does-not-belong-to - characters: [∉] - - concept: does-not-divide - characters: [∤] - - concept: dot-product - characters: ["·"] - - concept: downwards-diagonal-ellipsis - characters: ["⋱"] - - concept: direct-product - characters: [×] - - concept: element-of - characters: [∈, ∊] - - concept: ellipsis - characters: ["…", "⋯"] - - concept: equals - characters: ["="] - - concept: equivalent-to - characters: [≡] - - concept: evaluates-to - characters: ["→"] - - concept: given - characters: ["|"] - - concept: greater-than - characters: [">"] - - concept: greater-than-or-equal-to - characters: [≥, ≧] - - concept: identically-equals - characters: [≡] - - concept: if-and-only-if - characters: ["⟺"] - - concept: implies - characters: [⇒] - - concept: inner-product - characters: [⋅] - - concept: intersection - characters: [∩] - - concept: less-than - characters: ["<"] - - concept: less-than-or-equal-to - characters: [≤, ≦] - - concept: list-separator - characters: [",", ";"] - - concept: maps-to - characters: ["→"] - - concept: member-of - characters: [∈, ∊] - - concept: minus - characters: ["-", "−"] - - concept: minus-or-plus - characters: [∓] - - concept: not-subset - characters: [⊄] - - concept: not-superset - characters: [⊅] - - concept: not-equal-to - characters: [≠] - - concept: not-member-of - characters: [∉] - - concept: not-parallel-to - characters: [∦] - - concept: obtained-from - characters: [←] - - concept: or - characters: [∨] - - concept: outer-product - characters: [⊗] - - concept: parallel-to - characters: [∥] - - concept: perpendicular - characters: ["⟂"] - - concept: plus - characters: [+, U+2064] - - concept: plus-or-minus - characters: [±] - - concept: precedes - characters: [≺] - - concept: proportional - characters: [∝, ∷, ∼, ~] - - concept: range-separator - characters: ["-", "‐", "‑", "–", "—"] - - concept: ratio - characters: [":", "∶"] - - concept: set-difference - characters: ["∼", "~", "-", "−", "\\"] - - concept: similar - characters: [≅] - - concept: subset - characters: [⊂] - - concept: subset-or-equal - characters: [⊆] - - concept: succeeds - characters: [≻] - - concept: such-that - characters: [":", "|"] - - concept: superset - characters: [⊃] - - concept: superset-or-equal - characters: [⊇] - - concept: tilde - characters: [~] - - concept: times - characters: ["*", "·", "×", "∗"] - - concept: union - characters: [∪] - - concept: upwards-diagonal-ellipsis - characters: ["⋰"] - - concept: vertical-ellipsis - characters: ["⋮"] - - concept: xor - characters: [⊕] + - fixity: infix + concepts: + - concept: and + characters: [⁤∧] + - concept: applied-to + characters: [⁡U+2061] + - concept: approximately + characters: [≈] + - concept: congruent + characters: [≅] + - concept: cartesian-product + characters: [×] + - concept: composed-with + characters: [∘] + - concept: cross-product + characters: [×] + - concept: defined-as + characters: ["≝", "=", "≔"] + - concept: dimensional-product + characters: [×] + link: dimensional-product*infix + - concept: divided-by + characters: [/, ÷, ":"] + - concept: divides + characters: ["|", "∣"] + - concept: does-not-belong-to + characters: [∉] + - concept: does-not-divide + characters: [∤] + - concept: dot-product + characters: ["·"] + - concept: downwards-diagonal-ellipsis + characters: ["⋱"] + - concept: direct-product + characters: [×] + - concept: element-of + characters: [∈, ∊] + - concept: ellipsis + characters: ["…", "⋯"] + - concept: equals + characters: ["="] + - concept: equivalent-to + characters: [≡] + - concept: evaluates-to + characters: ["→"] + - concept: given + characters: ["|"] + - concept: greater-than + characters: [">"] + - concept: greater-than-or-equal-to + characters: [≥, ≧] + - concept: identically-equals + characters: [≡] + - concept: if-and-only-if + characters: ["⟺"] + - concept: implies + characters: [⇒] + - concept: inner-product + characters: [⋅] + - concept: intersection + characters: [∩] + - concept: less-than + characters: ["<"] + - concept: less-than-or-equal-to + characters: [≤, ≦] + - concept: list-separator + characters: [",", ";"] + - concept: maps-to + characters: ["→"] + - concept: member-of + characters: [∈, ∊] + - concept: minus + characters: ["-", "−"] + - concept: minus-or-plus + characters: [∓] + - concept: not-subset + characters: [⊄] + - concept: not-superset + characters: [⊅] + - concept: not-equal-to + characters: [≠] + - concept: not-member-of + characters: [∉] + - concept: not-parallel-to + characters: [∦] + - concept: obtained-from + characters: [←] + - concept: or + characters: [∨] + - concept: outer-product + characters: [⊗] + - concept: parallel-to + characters: [∥] + - concept: perpendicular + characters: ["⟂"] + - concept: plus + characters: [+, U+2064] + - concept: plus-or-minus + characters: [±] + - concept: precedes + characters: [≺] + - concept: proportional + characters: [∝, ∷, ∼, ~] + - concept: range-separator + characters: ["-", "‐", "‑", "–", "—"] + - concept: ratio + characters: [":", "∶"] + - concept: set-difference + characters: ["∼", "~", "-", "−", "\\"] + - concept: similar + characters: [≅] + - concept: subset + characters: [⊂] + - concept: subset-or-equal + characters: [⊆] + - concept: succeeds + characters: [≻] + - concept: such-that + characters: [":", "|"] + - concept: superset + characters: [⊃] + - concept: superset-or-equal + characters: [⊇] + - concept: tilde + characters: [~] + - concept: times + characters: ["*", "·", "×", "∗"] + - concept: union + characters: [∪] + - concept: upwards-diagonal-ellipsis + characters: ["⋰"] + - concept: vertical-ellipsis + characters: ["⋮"] + - concept: xor + characters: [⊕] - - fixity: postfix - concepts: - - concept: factorial - characters: ["!"] - - concept: percent - characters: ["%"] + - fixity: postfix + concepts: + - concept: factorial + characters: ["!"] + - concept: percent + characters: ["%"] - - fixity: nofix - concepts: - - concept: diameter - characters: ["d"] - - concept: distance - characters: ["d", "D"] - - concept: probability - characters: ["P"] - - concept: radius - characters: ["r"] - - concept: volume - characters: ["V"] + - fixity: nofix + concepts: + - concept: diameter + characters: ["d"] + - concept: distance + characters: ["d", "D"] + - concept: probability + characters: ["P"] + - concept: radius + characters: ["r"] + - concept: volume + characters: ["V"] - - fixity: silent - concepts: - - concept: invisible-separator - characters: [⁣U+2063] - - concept: invisible-times - characters: [⁢U+2062] + - fixity: silent + concepts: + - concept: invisible-separator + characters: [⁣U+2063] + - concept: invisible-times + characters: [⁢U+2062] concepts: From 838e5193e621ccd9adeee71eaed8e3a237f6b5d4 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 19:05:01 +0100 Subject: [PATCH 26/33] space after comma to please the linter --- _data/core.yml | 26 +++++++++++++------------- 1 file changed, 13 insertions(+), 13 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index c396df2e..381e5cd4 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -356,7 +356,7 @@ concepts: - concept: max subject-area: functions and inverses arity: ">=1" - arguments: [a1,...] + arguments: [a1, ...] property: function speech: en: "max of a1, ..." @@ -364,7 +364,7 @@ concepts: - concept: min subject-area: functions and inverses arity: ">=1" - arguments: [a1,...] + arguments: [a1, ...] property: function speech: en: "min of a1, ..." @@ -411,7 +411,7 @@ concepts: - concept: greatest-common-divisor subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2,...] + arguments: [a1, a2, ...] property: function speech: en: greatest common divisor of a1, a2, ... @@ -420,7 +420,7 @@ concepts: - concept: least-common-multiple subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2,...] + arguments: [a1, a2, ...] property: function speech: en: lest common multiple of a1, a2, ... @@ -429,7 +429,7 @@ concepts: - concept: least-common-denominator subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2,...] + arguments: [a1, a2, ...] property: function speech: en: "least common denominator of a1, a2, ..." @@ -504,7 +504,7 @@ concepts: - concept: cartesian-coordinate subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2,...] + arguments: [a1, a2, ...] property: function speech: en: "cartesian coordinate a1 comma a2 ..." @@ -514,7 +514,7 @@ concepts: - concept: coordinate subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2,...] + arguments: [a1, a2, ...] property: function speech: en: "coordinate a1 comma a2 ..." @@ -617,7 +617,7 @@ concepts: - concept: partial-derivative subject-area: calculus arity: ">=3" - arguments: [a1, a2, a3,...] + arguments: [a1, a2, a3, ...] property: ??? speech: en: @@ -785,14 +785,14 @@ concepts: - concept: list subject-area: sets arity: ">=0" - arguments: [a1,...] + arguments: [a1, ...] speech: en: "list of a1, ..." - concept: tuple subject-area: sets arity: ">=0" - arguments: [a1,...] + arguments: [a1, ...] speech: en: "tuple of a1, ..." @@ -1368,7 +1368,7 @@ concepts: - concept: dimensional-product subject-area: Linear Algebra arity: ">=2" - arguments: [a1, a2,...] + arguments: [a1, a2, ...] property: infix default: false speech: @@ -1579,7 +1579,7 @@ concepts: - concept: point subject-area: Geometry arity: ">=1" - arguments: [a1,...] + arguments: [a1, ...] property: ??? speech: en: @@ -1764,7 +1764,7 @@ concepts: - concept: permutation-cycle subject-area: General Concepts arity: ">=2" - arguments: [a1, a2,...] + arguments: [a1, a2, ...] property: function speech: en: "permutation cycle of a1 a2 ..." From fdda0a240495900bfee91f34a8bce262aca15c9d Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 19:18:11 +0100 Subject: [PATCH 27/33] indent comments to please the linter --- _data/core.yml | 631 +++++++++++++++++++++++++------------------------ 1 file changed, 316 insertions(+), 315 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index 381e5cd4..9e703bd4 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -258,7 +258,7 @@ concepts: speech: en: inverse of a1 comments: - - "`inverse` can be used for function inverses, matrix inverses, etc." + - "`inverse` can be used for function inverses, matrix inverses, etc." - concept: inverse subject-area: functions and inverses @@ -311,8 +311,8 @@ concepts: speech: en: a1 and a2 comments: - - "a1 is a positive integer and a2 is a fraction with positive numerical components. - The second argument can be an `mfrac` (normal or beveled) or can be a linear fraction using `/`" + - "a1 is a positive integer and a2 is a fraction with positive numerical components. + The second argument can be an `mfrac` (normal or beveled) or can be a linear fraction using `/`" - concept: quotient subject-area: functions and inverses @@ -331,19 +331,19 @@ concepts: speech: en: a1 evaluated-at a2 comments: - - "Two common notations are - x2|3 - and - - - - x2 - | - - x=3 - - - " + - "Two common notations are + x2|3 + and + + + + x2 + | + + x=3 + + + " - concept: remainder subject-area: functions and inverses arity: 2 @@ -546,10 +546,10 @@ concepts: speech: en: rounded-value of a1 comments: - - "This sometimes uses the notation - ⌊x⌉ - or - [x]" + - "This sometimes uses the notation + ⌊x⌉ + or + [x]" - concept: fractional-part subject-area: functions and inverses @@ -568,7 +568,7 @@ concepts: speech: en: "integral over a1" comments: - - "integral sign is not an argument" + - "integral sign is not an argument" - concept: definite-integral subject-area: calculus @@ -578,7 +578,7 @@ concepts: speech: en: "integral from a1 to a2" comments: - - "integral sign is not an argument" + - "integral sign is not an argument" - concept: derivative @@ -591,27 +591,27 @@ concepts: - "(verbose) the a3 derivative of a1 with respect to a2" - "(terse) d a1 by d a2 " comments: - - "the terse reading only makes sense for Leibniz notation such as - d2ydx2 - or - d2dx2f(x). - It does not make sense for other notations such as - f''(x) - " - - "The first of these examples might be marked up as" - - | - ``` - - - d2 - y - - - d - x2 - - - ``` + - "the terse reading only makes sense for Leibniz notation such as + d2ydx2 + or + d2dx2f(x). + It does not make sense for other notations such as + f''(x) + " + - "The first of these examples might be marked up as" + - | + ``` + + + d2 + y + + + d + x2 + + + ``` - concept: partial-derivative @@ -623,19 +623,19 @@ concepts: en: - "partial a1 partial a2 [partial a4 ...]" comments: - - | - ``` - - - ∂3 - sin(x)y - - - ∂2 - x∂y - - - ``` + - | + ``` + + + ∂3 + sin(x)y + + + ∂2 + x∂y + + + ``` - concept: limit subject-area: calculus @@ -645,29 +645,29 @@ concepts: speech: en: "limit as a1" comments: - - "limit is not an argument, but intent should be on `msub` or `munder`" - - "There are several arrows used for limits. " - - "Example: - - lim - x↗0 - - - might be spoken as \"limit as x tends to from below 0\" and marked up as:" - - | - ``` - - lim - - x - ↗ - 0 - - - ``` - - "Another notation that might be spoken similarly is - limx→0- - " + - "limit is not an argument, but intent should be on `msub` or `munder`" + - "There are several arrows used for limits. " + - "Example: + + lim + x↗0 + + + might be spoken as \"limit as x tends to from below 0\" and marked up as:" + - | + ``` + + lim + + x + ↗ + 0 + + + ``` + - "Another notation that might be spoken similarly is + limx→0- + " - concept: tends-to subject-area: calculus @@ -677,7 +677,7 @@ concepts: speech: en: "a1 tends to a2" comments: - - "see \"limit\" example" + - "see \"limit\" example" - concept: tends-to-from-above subject-area: calculus @@ -687,7 +687,7 @@ concepts: speech: en: "a1 tends to from above a2" comments: - - "see \"limit\" example" + - "see \"limit\" example" - concept: tends-to-from-below subject-area: calculus @@ -697,7 +697,7 @@ concepts: speech: en: "a1 tends to from below a2" comments: - - "see \"limit\" example" + - "see \"limit\" example" ## ====================== 4.4.5 Sets ============================ - concept: set @@ -708,26 +708,26 @@ concepts: speech: en: "set of a1" comments: - - | - the argument to `set` is typically an `mrow`. For example: - - ``` - - - { - - 2 - , - 4 - , - 6 - , - 8 - - } - - - ``` + - | + the argument to `set` is typically an `mrow`. For example: + + ``` + + + { + + 2 + , + 4 + , + 6 + , + 8 + + } + + + ``` - concept: set-difference subject-area: sets @@ -737,9 +737,9 @@ concepts: speech: en: "set difference of a1 and a2" comments: - - "This can be spoken in many ways. See other entry for infix speech." - - "There are several notations that are used and their order of appearance differs: - A-B, A\\B" + - "This can be spoken in many ways. See other entry for infix speech." + - "There are several notations that are used and their order of appearance differs: + A-B, A\\B" - concept: set-difference subject-area: sets @@ -749,8 +749,8 @@ concepts: speech: en: "\"a1 minus a2\" or \"a2 subtracted from a1\"" comments: - - "This can be spoken in many ways. See other entry for functional speech." - - "See functional form for some notational usages." + - "This can be spoken in many ways. See other entry for functional speech." + - "See functional form for some notational usages." - concept: complement subject-area: sets @@ -760,9 +760,9 @@ concepts: speech: en: "complement of a1" comments: - - "This can be spoken in many ways. See other entry for functional speech." - - "Two notations used for complement are: - AC, A'" + - "This can be spoken in many ways. See other entry for functional speech." + - "Two notations used for complement are: + AC, A'" - concept: empty-set subject-area: sets @@ -771,7 +771,7 @@ concepts: speech: en: "empty set" comments: - - "Three notations used for empty set are: { }, ∅, and ∅" + - "Three notations used for empty set are: { }, ∅, and ∅" - concept: cardinality @@ -780,7 +780,7 @@ concepts: arguments: [a1] property: function comments: - - "often used with matchfix single vertical bars" + - "often used with matchfix single vertical bars" - concept: list subject-area: sets @@ -805,7 +805,7 @@ concepts: speech: en: "sum of a1" comments: - - usually on `` + - usually on `` - concept: sum subject-area: sequences and series @@ -815,7 +815,7 @@ concepts: speech: en: "sum over a1 of a2" comments: - - usually on `` or `` + - usually on `` or `` - concept: sum subject-area: sequences and series @@ -825,7 +825,7 @@ concepts: speech: en: "sum from a1 to a2 of a3" comments: - - usually on `` or `` + - usually on `` or `` - concept: product subject-area: sequences and series @@ -835,7 +835,7 @@ concepts: speech: en: "product of a1" comments: - - usually on `` + - usually on `` - concept: product subject-area: sequences and series @@ -845,7 +845,7 @@ concepts: speech: en: "product over a1 of a2" comments: - - usually on `` or `` + - usually on `` or `` - concept: product subject-area: sequences and series @@ -855,7 +855,7 @@ concepts: speech: en: "product from a1 to a2 of a3" comments: - - usually on `` or `` + - usually on `` or `` ## ====================== 4.4.7 elementary classical functions ====================== @@ -868,7 +868,7 @@ concepts: en: "sine a1" fr: "sinus a1" comments: - - used as 'sin', 'sen' + - used as 'sin', 'sen' - concept: cosine subject-area: elementary classical functions @@ -890,7 +890,7 @@ concepts: - "(verbose) tangent a1" - "(terse) tan a1" comments: - - used as 'tan', 'tg' + - used as 'tan', 'tg' - concept: secant subject-area: elementary classical functions @@ -902,7 +902,7 @@ concepts: - "(verbose) secant a1" - "(terse) seech a1" comments: - - used as 'sec' + - used as 'sec' - concept: cosecant subject-area: elementary classical functions @@ -914,7 +914,7 @@ concepts: - "(verbose) cosecant a1" - "(terse) co-seech a1" comments: - - used as 'csc' + - used as 'csc' - concept: cotangent subject-area: elementary classical functions @@ -926,7 +926,7 @@ concepts: - "(verbose) cotangent a1" - "(terse) co-tan a1" comments: - - used as 'cot' + - used as 'cot' ## inverse trig functions @@ -939,8 +939,8 @@ concepts: en: - "(verbose) arcsine a1" comments: - - "used as 'arcsin', 'arc sin'" - - "this is distinct from sin inverse (sin-1)" + - "used as 'arcsin', 'arc sin'" + - "this is distinct from sin inverse (sin-1)" - concept: arccosine subject-area: elementary classical functions @@ -951,7 +951,7 @@ concepts: en: - "(verbose) arccosine a1" comments: - - "used as 'arccos', 'arc cos'" + - "used as 'arccos', 'arc cos'" - concept: arctangent subject-area: elementary classical functions @@ -962,7 +962,7 @@ concepts: en: - "(verbose) arctangent a1" comments: - - "used as 'arctan', 'arc tan'" + - "used as 'arctan', 'arc tan'" - concept: arcsecant subject-area: elementary classical functions @@ -973,7 +973,7 @@ concepts: en: - "(verbose) arcsecant a1" comments: - - "used as 'arcsec', 'arc sec'" + - "used as 'arcsec', 'arc sec'" - concept: arccosecant subject-area: elementary classical functions @@ -984,7 +984,7 @@ concepts: en: - "(verbose) arc-cosecant a1" comments: - - "used as 'arccos', 'arc cos'" + - "used as 'arccos', 'arc cos'" - concept: arccotangent subject-area: elementary classical functions @@ -995,7 +995,7 @@ concepts: en: - "(verbose) arc-cotangent a1" comments: - - "used as 'arccos', 'arc cos'" + - "used as 'arccos', 'arc cos'" ## hyperbolic trig functions - concept: hyperbolic-sine @@ -1004,8 +1004,8 @@ concepts: arguments: [a1] property: function comments: - - "youtube" - - "used as 'sinh'" + - "youtube" + - "used as 'sinh'" speech: en: - "short form 'shine a1'" @@ -1019,8 +1019,8 @@ concepts: arguments: [a1] property: function comments: - - "youtube" - - "used as 'cosh'" + - "youtube" + - "used as 'cosh'" speech: en: - "short form 'cosh a1'" @@ -1034,8 +1034,8 @@ concepts: arguments: [a1] property: function comments: - - "youtube" - - "used as 'tanh'" + - "youtube" + - "used as 'tanh'" speech: en: - "short form American 'tanch a1'" @@ -1047,8 +1047,8 @@ concepts: arguments: [a1] property: function comments: - - "youtube" - - "used as 'sech'" + - "youtube" + - "used as 'sech'" speech: en: - "short form American 'sech a1'" @@ -1060,8 +1060,8 @@ concepts: arguments: [a1] property: function comments: - - "youtube" - - "used as 'cosech'" + - "youtube" + - "used as 'cosech'" speech: en: - "short form American 'cosech a1'" @@ -1074,8 +1074,8 @@ concepts: arguments: [a1] property: function comments: - - "youtube" - - "used as 'coth'" + - "youtube" + - "used as 'coth'" speech: en: - "short form American 'coth a1'" @@ -1090,7 +1090,7 @@ concepts: arguments: [a1] property: function comments: - - "used as 'asinh'" + - "used as 'asinh'" speech: en: - "short form 'arc shine a1'" @@ -1104,7 +1104,7 @@ concepts: arguments: [a1] property: function comments: - - "used as 'acosh'" + - "used as 'acosh'" speech: en: - "short form 'arc cosh a1'" @@ -1118,7 +1118,7 @@ concepts: arguments: [a1] property: function comments: - - "used as 'atanh'" + - "used as 'atanh'" speech: en: - "short form American 'arc tanch a1'" @@ -1130,7 +1130,7 @@ concepts: arguments: [a1] property: function comments: - - "used as 'asech'" + - "used as 'asech'" speech: en: - "short form American 'arc sech a1'" @@ -1142,7 +1142,7 @@ concepts: arguments: [a1] property: function comments: - - "used as 'acsch'" + - "used as 'acsch'" speech: en: - "short form American 'arc cosech a1'" @@ -1155,7 +1155,7 @@ concepts: arguments: [a1] property: function comments: - - "used as 'acoth'" + - "used as 'acoth'" speech: en: - "short form American 'arc coth a1'" @@ -1210,7 +1210,7 @@ concepts: speech: en: "mean of a1" comments: - - "This might be display as x¯" + - "This might be display as x¯" - concept: standard-deviation subject-area: Statistics and Probability @@ -1254,23 +1254,23 @@ concepts: speech: en: "probability of a1 given a2" comments: - - | - The intent should be on the `mrow` that includes the "P" - - ``` - - - P - ( - - A - | - B - - ) - - - ``` + - | + The intent should be on the `mrow` that includes the "P" + + ``` + + + P + ( + + A + | + B + + ) + + + ``` ## ====================== 4.4.9 Linear Algebra ====================== - concept: vector @@ -1285,7 +1285,7 @@ concepts: arguments: [a1] property: function comments: - - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly + - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly - concept: determinant subject-area: Linear Algebra @@ -1293,7 +1293,7 @@ concepts: arguments: [a1] property: function comments: - - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly + - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly - concept: adjugate subject-area: Linear Algebra @@ -1301,7 +1301,7 @@ concepts: arguments: [a1] property: function comments: - - "sometimes used when computing an inverse matrix" + - "sometimes used when computing an inverse matrix" - concept: magnitude subject-area: Linear Algebra @@ -1309,7 +1309,7 @@ concepts: arguments: [a1] property: function comments: - - "often used with matchfix single or double vertical bars" + - "often used with matchfix single or double vertical bars" - concept: norm subject-area: Linear Algebra @@ -1317,7 +1317,7 @@ concepts: arguments: [a1] property: function comments: - - "often used with matchfix double vertical bars" + - "often used with matchfix double vertical bars" - concept: span subject-area: Linear Algebra @@ -1325,7 +1325,7 @@ concepts: arguments: [a1] property: function comments: - - "often used with matchfix angle brackets" + - "often used with matchfix angle brackets" - concept: unit-vector subject-area: Linear Algebra @@ -1333,7 +1333,7 @@ concepts: arguments: [a1] property: prefix comments: - - "Example: x^" + - "Example: x^" speech: en: "unit vector x" @@ -1342,7 +1342,7 @@ concepts: arity: 0 arguments: [] comments: - - "This is typically represented as 'I' or bold-faced '𝐈'" + - "This is typically represented as 'I' or bold-faced '𝐈'" speech: en: "identity matrix" @@ -1374,8 +1374,8 @@ concepts: speech: en: "a1 by a2 ..." comments: - - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name. - A common use would be describe the size of a matrix. For example m×n." + - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name. + A common use would be describe the size of a matrix. For example m×n." ## ====================== 4.4.10 Constants and Sets ====================== @@ -1466,7 +1466,7 @@ concepts: en: "golden ratio" fr: "d" comments: - - "Often denoted as φ" + - "Often denoted as φ" @@ -1481,7 +1481,7 @@ concepts: en: - "line segment a1 a2" comments: - - "Example: (`mover`): AB_" + - "Example: (`mover`): AB_" - concept: directed-line-segment subject-area: Geometry @@ -1492,7 +1492,7 @@ concepts: en: - "directed line segment a1 a2" comments: - - "Example: (`mover`): AB→" + - "Example: (`mover`): AB→" - concept: line subject-area: Geometry @@ -1503,7 +1503,7 @@ concepts: en: - "line a1 a2" comments: - - "Example: (`mover`): AB↔" + - "Example: (`mover`): AB↔" - concept: ray subject-area: Geometry @@ -1514,7 +1514,7 @@ concepts: en: - "ray a1 a2" comments: - - "Example: (`mover`): AB→" + - "Example: (`mover`): AB→" - concept: arc subject-area: Geometry @@ -1525,7 +1525,7 @@ concepts: en: - "arc a1 a2" comments: - - "Example: (`mover`): AB⌒" + - "Example: (`mover`): AB⌒" - concept: length subject-area: Geometry @@ -1536,19 +1536,19 @@ concepts: en: - "length of a1" comments: - - "It may be necessary to 'nest' the intent as shown here for the example: - - A - B - " - - "The markup for this is:" - - | - ``` - - A - B - - ``` + - "It may be necessary to 'nest' the intent as shown here for the example: + + A + B + " + - "The markup for this is:" + - | + ``` + + A + B + + ``` - concept: area subject-area: Geometry @@ -1559,23 +1559,24 @@ concepts: en: - "area of a1" comments: - - "There are many notations. Here's one: - [ABCD]" - - "The markup for this is:" - - | - ``` - - [ - - A - B - C - D - ] - - - ``` - - "It may be necessary to 'nest' the intent as shown in the `length` intent" + - "There are many notations. Here's one: + [ABCD]" + - "The markup for this is:" + - | + ``` + + [ + + A + B + C + D + ] + + + ``` + - "It may be necessary to 'nest' the intent as shown in the `length` intent" + - concept: point subject-area: Geometry arity: ">=1" @@ -1596,7 +1597,7 @@ concepts: en: - "volume of a1" comments: - - "See comments for `length` and `volume` for examples of how this might be marked up" + - "See comments for `length` and `volume` for examples of how this might be marked up" - concept: blank subject-area: Fill in the blank @@ -1606,12 +1607,12 @@ concepts: en: - "blank" comments: - - "blanks can be represented in many ways in MathML. Some examples:" - - "`__`" - - "`?`" - - "`□`" - - "``" - - "``
``
``" + - "blanks can be represented in many ways in MathML. Some examples:" + - "`__`" + - "`?`" + - "`□`" + - "``" + - "``
``
``" - concept: time-separator subject-area: Separators @@ -1621,8 +1622,8 @@ concepts: speech: en: a1 a2 comments: - - "separates hours and minutes and is typically silent" - - "Example: 2:31" + - "separates hours and minutes and is typically silent" + - "Example: 2:31" - concept: fenced-group @@ -1633,7 +1634,7 @@ concepts: speech: en: "fenced-group of a1" comments: - - "this includes parens, brackets, and braces" + - "this includes parens, brackets, and braces" - concept: ordered-pair subject-area: General Concepts @@ -1651,7 +1652,7 @@ concepts: speech: en: "a1 indexed by a2" comments: - - "this is typically a subscript and might also be spoken as 'a1 sub a2'" + - "this is typically a subscript and might also be spoken as 'a1 sub a2'" - concept: highlight subject-area: General Concepts @@ -1661,8 +1662,8 @@ concepts: speech: en: "a1 highlighted" comments: - - "this typically would be used inside of a larger expression and not on its own" - - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" + - "this typically would be used inside of a larger expression and not on its own" + - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" - concept: rate @@ -1673,8 +1674,8 @@ concepts: speech: en: "a1 per a2" comments: - - "Typically used with units" - - "Used with `mfrac` or `/`" + - "Typically used with units" + - "Used with `mfrac` or `/`" - concept: translation subject-area: General Concepts @@ -1684,7 +1685,7 @@ concepts: speech: en: "translation by a1 comma a2" comments: - - "Example: T(1,3)" + - "Example: T(1,3)" - concept: constraint subject-area: General Concepts @@ -1694,7 +1695,7 @@ concepts: speech: en: "fraction 2 over x minus 1 with constraint x not equal to 1" comments: - - "Example: 2x-1, x≠1" + - "Example: 2x-1, x≠1" - concept: binomial-coefficient subject-area: General Concepts @@ -1704,30 +1705,30 @@ concepts: speech: en: "a1 choose a2" comments: - - "There are many notations used for the binomial coefficient. Here are some of them: - - ( - - n + - "There are many notations used for the binomial coefficient. Here are some of them: + + ( + + n + k + + ) + , + + + C k - - ) - , - - - C - k - n - - , - - - C - k - - n - - " + n + + , + + + C + k + + n + + " - concept: pochhammer subject-area: General Concepts @@ -1737,29 +1738,29 @@ concepts: speech: en: "a2 permutation of a1" comments: - - "There are many notations for this: some of them are - - Pkn - ,  - Pkn - ,  - Pkn - ,  - Pn,k - ,  - P(n,k) - ,  - nk - " - - "The first of these would be marked up as:" - - | - ``` - - P - k - n - - ``` + - "There are many notations for this: some of them are + + Pkn + ,  + Pkn + ,  + Pkn + ,  + Pn,k + ,  + P(n,k) + ,  + nk + " + - "The first of these would be marked up as:" + - | + ``` + + P + k + n + + ``` - concept: permutation-cycle subject-area: General Concepts @@ -1769,21 +1770,21 @@ concepts: speech: en: "permutation cycle of a1 a2 ..." comments: - - "A common notation for a permutation cycle is ( - 132 - )" - - "This would be marked up as:" - - | - ``` - ( - - 1 - 3 - 2 - - ) - ``` + - "A common notation for a permutation cycle is ( + 132 + )" + - "This would be marked up as:" + - | + ``` + ( + + 1 + 3 + 2 + + ) + ``` - concept: embellished-name subject-area: General Concepts @@ -1793,7 +1794,7 @@ concepts: speech: en: "a1 with annotation a2" comments: - - "used with `mover` or `munder`" + - "used with `mover` or `munder`" - concept: fenced-group @@ -1804,7 +1805,7 @@ concepts: speech: en: "fenced-group of a1" comments: - - "this includes parens, brackets, and braces" + - "this includes parens, brackets, and braces" - concept: annotation subject-area: Grouping @@ -1814,8 +1815,8 @@ concepts: speech: en: "a1 which is a2" comments: - - "used with `mover` or `munder`" - - "Example: H2O⏟water" + - "used with `mover` or `munder`" + - "Example: H2O⏟water" - concept: braced-group subject-area: Grouping @@ -1825,8 +1826,8 @@ concepts: speech: en: "grouped a1 end-grouped" comments: - - "used with `mover` or `munder`" - - "Example: 13-16⏟" + - "used with `mover` or `munder`" + - "Example: 13-16⏟" - concept: repeating-decimal subject-area: Grouping @@ -1836,23 +1837,23 @@ concepts: speech: en: "repeating decimal a1" comments: - - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits." - - "Example: 122=0.045_" - - "This right hand side of this might be might be marked up as:" - - | - ``` - 0.0 - - 45 - _ - - ``` - - "or using the elementary math elements in MathML full as" - - | - ``` - - - 0.045 - - ``` + - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits." + - "Example: 122=0.045_" + - "This right hand side of this might be might be marked up as:" + - | + ``` + 0.0 + + 45 + _ + + ``` + - "or using the elementary math elements in MathML full as" + - | + ``` + + + 0.045 + + ``` From b2ec9534116764f7fe3ce6387ab1d88a60c2abc8 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 19:21:51 +0100 Subject: [PATCH 28/33] max line length 240 to please the linter --- _data/core.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/_data/core.yml b/_data/core.yml index 9e703bd4..db22dddf 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -1560,7 +1560,7 @@ concepts: - "area of a1" comments: - "There are many notations. Here's one: - [ABCD]" + [ABCD]" - "The markup for this is:" - | ``` From 7a57b6c4f4c2cc861129eb82de98b0b8c551b6e7 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sat, 29 Aug 2026 20:45:13 +0100 Subject: [PATCH 29/33] show arg list in conditions case --- intent-core-concepts/index.md | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 974e29db..28e4f067 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -200,7 +200,13 @@ if c.link {%- for cond in c.conditions -%}
{{c.concept}}{{arityr}}{{arityr}}
+[ +{%- for arg in c.arguments -%} +{{arg}} +{%- unless forloop.last -%},{% endunless -%} +{%- endfor -%} +]		{{c.property}}{%- unless c.default == false or c.arity == 0 -%}*{%- endunless -%} From c680c30815502c24e6bbb8321cc46cb30039de04 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Sun, 30 Aug 2026 19:22:06 +0100 Subject: [PATCH 30/33] prefix arguments with $ --- _data/core.yml | 584 ++++----- _data/open.yml | 3338 ++++++++++++++++++++++++------------------------ 2 files changed, 1961 insertions(+), 1961 deletions(-) diff --git a/_data/core.yml b/_data/core.yml index db22dddf..e5696010 100644 --- a/_data/core.yml +++ b/_data/core.yml @@ -217,119 +217,119 @@ concepts: - concept: closed-open-interval subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: interval between a1 (included) and a2 - fr: intervalle ouvert à droite entre a1 et a2 + en: interval between $a1 (included) and $a2 + fr: intervalle ouvert à droite entre $a1 et $a2 - concept: open-closed-interval subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: interval between a1 and a2, included + en: interval between $a1 and $a2, included fr: intervalle ouvert à gauche... - concept: open-interval subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: open interval between a1 and a2 + en: open interval between $a1 and $a2 fr: intervalle ouvert - concept: closed-interval subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: closed interval between a1 and a2 - fr: intervalle fermé entre a1 et a2 + en: closed interval between $a1 and $a2 + fr: intervalle fermé entre $a1 et $a2 - concept: inverse subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function* speech: - en: inverse of a1 + en: inverse of $a1 comments: - "`inverse` can be used for function inverses, matrix inverses, etc." - concept: inverse subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: postfix speech: - en: a1 inverse + en: $a1 inverse - concept: domain subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: domain of a1 - fr: domaine de définition de a1 + en: domain of $a1 + fr: domaine de définition de $a1 - concept: codomain subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: codomain of a1 - fr: ensemble d'arrivée de a1 + en: codomain of $a1 + fr: ensemble d'arrivée de $a1 - concept: image subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function* speech: - en: image of a1 - fr: image de a1 + en: image of $a1 + fr: image de $a1 - concept: fraction subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: fraction a1 over a2 end fraction + en: fraction $a1 over $a2 end fraction - concept: mixed-fraction subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: a1 and a2 + en: $a1 and $a2 comments: - - "a1 is a positive integer and a2 is a fraction with positive numerical components. + - "$a1 is a positive integer and $a2 is a fraction with positive numerical components. The second argument can be an `mfrac` (normal or beveled) or can be a linear fraction using `/`" - concept: quotient subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: integer part of a1 divided by a2 - fr: quotient de a1 par a2 + en: integer part of $a1 divided by $a2 + fr: quotient de $a1 par $a2 - concept: evaluated-at subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: a1 evaluated-at a2 + en: $a1 evaluated-at $a2 comments: - "Two common notations are x2|3 @@ -347,145 +347,145 @@ concepts: - concept: remainder subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: the remainder of a1 divided by a2 - fr: reste de la divsion de a1 par a2 + en: the remainder of $a1 divided by $a2 + fr: reste de la divsion de $a1 par $a2 - concept: max subject-area: functions and inverses arity: ">=1" - arguments: [a1, ...] + arguments: [$a1, ...] property: function speech: - en: "max of a1, ..." + en: "max of $a1, ..." - concept: min subject-area: functions and inverses arity: ">=1" - arguments: [a1, ...] + arguments: [$a1, ...] property: function speech: - en: "min of a1, ..." + en: "min of $a1, ..." - concept: power subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix conditions: - - condition: "a2=2" + - condition: "$a2=2" speech: - en: "a1 squared" - fr: "a1 carré" - - condition: "a2=3" + en: "$a1 squared" + fr: "$a1 carré" + - condition: "$a2=3" speech: - en: "a1 cubed" - fr: "a1 cube" + en: "$a1 cubed" + fr: "$a1 cube" - condition: "" speech: - en: "a1 to the a2th power" - fr: "a1 à la a2" + en: "$a1 to the $a2th power" + fr: "$a1 à la $a2" - concept: root subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function conditions: - - condition: "a2=2" + - condition: "$a2=2" speech: - en: "square root of a1" - - condition: "a2=3" + en: "square root of $a1" + - condition: "$a2=3" speech: - en: "cube root of a1" - - condition: "a2=4" + en: "cube root of $a1" + - condition: "$a2=4" speech: - en: "fourth root of a1" + en: "fourth root of $a1" - condition: "" speech: - en: "a2th root of a1" + en: "$a2th root of $a1" - concept: greatest-common-divisor subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2, ...] + arguments: [$a1, $a2, ...] property: function speech: - en: greatest common divisor of a1, a2, ... - fr: plus grand commun diviseur de a1, a2, ... + en: greatest common divisor of $a1, $a2, ... + fr: plus grand commun diviseur de $a1, $a2, ... - concept: least-common-multiple subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2, ...] + arguments: [$a1, $a2, ...] property: function speech: - en: lest common multiple of a1, a2, ... - fr: plus grand commun diviseur de a1, a2, ... + en: lest common multiple of $a1, $a2, ... + fr: plus grand commun diviseur de $a1, $a2, ... - concept: least-common-denominator subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2, ...] + arguments: [$a1, $a2, ...] property: function speech: - en: "least common denominator of a1, a2, ..." + en: "least common denominator of $a1, $a2, ..." - concept: absolute-value subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: absolute value of a1 - fr: valeur absolue de a1 - de: Betrag von a1 + en: absolute value of $a1 + fr: valeur absolue de $a1 + de: Betrag von $a1 - concept: complex-conjugate subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: complex conjugate of a1 - fr: a1 conjugé + en: complex conjugate of $a1 + fr: $a1 conjugé - concept: complex-arg subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: arg of a1 + en: arg of $a1 - concept: real-part subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - real part of a1 - - imaginary part of a1 + - real part of $a1 + - imaginary part of $a1 - concept: imaginary-part subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: imaginary part of a1 + en: imaginary part of $a1 - concept: polar-coordinate subject-area: functions and inverses arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "polar coordinate a1 comma a2" + en: "polar coordinate $a1 comma $a2" comment: - "The first argument is the radius, the second argument is the polar angle, the third arguments is the azimuthal angle." - "Example: (r, θ)" @@ -493,10 +493,10 @@ concepts: - concept: spherical-coordinate subject-area: functions and inverses arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] property: function speech: - en: "spherical coordinate a1 comma a2, comma a3" + en: "spherical coordinate $a1 comma $a2, comma $a3" comment: - "The first argument is the radius, the second argument is the angle." - "Example: (r,Φ,θ)" @@ -504,20 +504,20 @@ concepts: - concept: cartesian-coordinate subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2, ...] + arguments: [$a1, $a2, ...] property: function speech: - en: "cartesian coordinate a1 comma a2 ..." + en: "cartesian coordinate $a1 comma $a2 ..." comment: - "Example: (1,2)" - concept: coordinate subject-area: functions and inverses arity: ">=2" - arguments: [a1, a2, ...] + arguments: [$a1, $a2, ...] property: function speech: - en: "coordinate a1 comma a2 ..." + en: "coordinate $a1 comma $a2 ..." comment: - "This a generic coordinate that doesn't specify the coordinate system. It takes 2 or more arguments." - "Example: (1,2)" @@ -525,26 +525,26 @@ concepts: - concept: floor subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: floor of a1 + en: floor of $a1 - concept: ceiling subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: ceiling of a1 + en: ceiling of $a1 - concept: round subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: rounded-value of a1 + en: rounded-value of $a1 comments: - "This sometimes uses the notation ⌊x⌉ @@ -554,29 +554,29 @@ concepts: - concept: fractional-part subject-area: functions and inverses arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: fractional part of a1 + en: fractional part of $a1 ## ====================== 4.4.4 Calculus ============================ - concept: definite-integral subject-area: calculus arity: 1 - arguments: [a1] + arguments: [$a1] property: ??? speech: - en: "integral over a1" + en: "integral over $a1" comments: - "integral sign is not an argument" - concept: definite-integral subject-area: calculus arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: ??? speech: - en: "integral from a1 to a2" + en: "integral from $a1 to $a2" comments: - "integral sign is not an argument" @@ -584,12 +584,12 @@ concepts: - concept: derivative subject-area: calculus arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] property: ??? speech: en: - - "(verbose) the a3 derivative of a1 with respect to a2" - - "(terse) d a1 by d a2 " + - "(verbose) the $a3 derivative of $a1 with respect to $a2" + - "(terse) d <$a3 if $a3 != 1> $a1 by d $a2 <$a3 if $a3 != 1>" comments: - "the terse reading only makes sense for Leibniz notation such as d2ydx2 @@ -617,11 +617,11 @@ concepts: - concept: partial-derivative subject-area: calculus arity: ">=3" - arguments: [a1, a2, a3, ...] + arguments: [$a1, $a2, $a3, ...] property: ??? speech: en: - - "partial a1 partial a2 [partial a4 ...]" + - "partial $a1 partial $a2 <$a3 if $a3 != 1> [partial $a4 <$a5 if $a5 != 1> ...]" comments: - | ``` @@ -640,10 +640,10 @@ concepts: - concept: limit subject-area: calculus arity: 1 - arguments: [a1] + arguments: [$a1] property: prefix speech: - en: "limit as a1" + en: "limit as $a1" comments: - "limit is not an argument, but intent should be on `msub` or `munder`" - "There are several arrows used for limits. " @@ -672,30 +672,30 @@ concepts: - concept: tends-to subject-area: calculus arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: "a1 tends to a2" + en: "$a1 tends to $a2" comments: - "see \"limit\" example" - concept: tends-to-from-above subject-area: calculus arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: "a1 tends to from above a2" + en: "$a1 tends to from above $a2" comments: - "see \"limit\" example" - concept: tends-to-from-below subject-area: calculus arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: "a1 tends to from below a2" + en: "$a1 tends to from below $a2" comments: - "see \"limit\" example" @@ -703,10 +703,10 @@ concepts: - concept: set subject-area: sets arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "set of a1" + en: "set of $a1" comments: - | the argument to `set` is typically an `mrow`. For example: @@ -732,10 +732,10 @@ concepts: - concept: set-difference subject-area: sets arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "set difference of a1 and a2" + en: "set difference of $a1 and $a2" comments: - "This can be spoken in many ways. See other entry for infix speech." - "There are several notations that are used and their order of appearance differs: @@ -744,10 +744,10 @@ concepts: - concept: set-difference subject-area: sets arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: "\"a1 minus a2\" or \"a2 subtracted from a1\"" + en: "\"$a1 minus $a2\" or \"$a2 subtracted from $a1\"" comments: - "This can be spoken in many ways. See other entry for functional speech." - "See functional form for some notational usages." @@ -755,10 +755,10 @@ concepts: - concept: complement subject-area: sets arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "complement of a1" + en: "complement of $a1" comments: - "This can be spoken in many ways. See other entry for functional speech." - "Two notations used for complement are: @@ -777,7 +777,7 @@ concepts: - concept: cardinality subject-area: sets arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "often used with matchfix single vertical bars" @@ -785,75 +785,75 @@ concepts: - concept: list subject-area: sets arity: ">=0" - arguments: [a1, ...] + arguments: [$a1, ...] speech: - en: "list of a1, ..." + en: "list of $a1, ..." - concept: tuple subject-area: sets arity: ">=0" - arguments: [a1, ...] + arguments: [$a1, ...] speech: - en: "tuple of a1, ..." + en: "tuple of $a1, ..." ## ====================== 4.4.6 sequence and series ============================ - concept: sum subject-area: sequences and series arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "sum of a1" + en: "sum of $a1" comments: - usually on `` - concept: sum subject-area: sequences and series arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "sum over a1 of a2" + en: "sum over $a1 of $a2" comments: - usually on `` or `` - concept: sum subject-area: sequences and series arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] property: function speech: - en: "sum from a1 to a2 of a3" + en: "sum from $a1 to $a2 of $a3" comments: - usually on `` or `` - concept: product subject-area: sequences and series arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "product of a1" + en: "product of $a1" comments: - usually on `` - concept: product subject-area: sequences and series arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "product over a1 of a2" + en: "product over $a1 of $a2" comments: - usually on `` or `` - concept: product subject-area: sequences and series arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] property: function speech: - en: "product from a1 to a2 of a3" + en: "product from $a1 to $a2 of $a3" comments: - usually on `` or `` @@ -862,69 +862,69 @@ concepts: - concept: sine subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "sine a1" - fr: "sinus a1" + en: "sine $a1" + fr: "sinus $a1" comments: - used as 'sin', 'sen' - concept: cosine subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) cosine a1" - - "(terse) cos a1" + - "(verbose) cosine $a1" + - "(terse) cos $a1" - concept: tangent subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) tangent a1" - - "(terse) tan a1" + - "(verbose) tangent $a1" + - "(terse) tan $a1" comments: - used as 'tan', 'tg' - concept: secant subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) secant a1" - - "(terse) seech a1" + - "(verbose) secant $a1" + - "(terse) seech $a1" comments: - used as 'sec' - concept: cosecant subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) cosecant a1" - - "(terse) co-seech a1" + - "(verbose) cosecant $a1" + - "(terse) co-seech $a1" comments: - used as 'csc' - concept: cotangent subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) cotangent a1" - - "(terse) co-tan a1" + - "(verbose) cotangent $a1" + - "(terse) co-tan $a1" comments: - used as 'cot' @@ -933,11 +933,11 @@ concepts: - concept: arcsine subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) arcsine a1" + - "(verbose) arcsine $a1" comments: - "used as 'arcsin', 'arc sin'" - "this is distinct from sin inverse (sin-1)" @@ -945,55 +945,55 @@ concepts: - concept: arccosine subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) arccosine a1" + - "(verbose) arccosine $a1" comments: - "used as 'arccos', 'arc cos'" - concept: arctangent subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) arctangent a1" + - "(verbose) arctangent $a1" comments: - "used as 'arctan', 'arc tan'" - concept: arcsecant subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) arcsecant a1" + - "(verbose) arcsecant $a1" comments: - "used as 'arcsec', 'arc sec'" - concept: arccosecant subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) arc-cosecant a1" + - "(verbose) arc-cosecant $a1" comments: - "used as 'arccos', 'arc cos'" - concept: arccotangent subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "(verbose) arc-cotangent a1" + - "(verbose) arc-cotangent $a1" comments: - "used as 'arccos', 'arc cos'" @@ -1001,85 +1001,85 @@ concepts: - concept: hyperbolic-sine subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "youtube" - "used as 'sinh'" speech: en: - - "short form 'shine a1'" + - "short form 'shine $a1'" fr: - - "sinus hyperbolique a1" + - "sinus hyperbolique $a1" - concept: hyperbolic-cosine subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "youtube" - "used as 'cosh'" speech: en: - - "short form 'cosh a1'" + - "short form 'cosh $a1'" fr: - - "cosh a1" - - "kosh a1" + - "cosh $a1" + - "kosh $a1" - concept: hyperbolic-tangent subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "youtube" - "used as 'tanh'" speech: en: - - "short form American 'tanch a1'" - - "short form British 'than a1'" + - "short form American 'tanch $a1'" + - "short form British 'than $a1'" - concept: hyperbolic-secant subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "youtube" - "used as 'sech'" speech: en: - - "short form American 'sech a1'" - - "short form British 'shek a1'" + - "short form American 'sech $a1'" + - "short form British 'shek $a1'" - concept: hyperbolic-cosecant subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "youtube" - "used as 'cosech'" speech: en: - - "short form American 'cosech a1'" - - "short form British 'coshek a1'" + - "short form American 'cosech $a1'" + - "short form British 'coshek $a1'" - concept: hyperbolic-cotangent subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "youtube" - "used as 'coth'" speech: en: - - "short form American 'coth a1'" - - "short form British 'coath a1'" + - "short form American 'coth $a1'" + - "short form British 'coath $a1'" @@ -1087,116 +1087,116 @@ concepts: - concept: arc-hyperbolic-sine subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "used as 'asinh'" speech: en: - - "short form 'arc shine a1'" + - "short form 'arc shine $a1'" fr: - - "sinus hyperbolique a1" + - "sinus hyperbolique $a1" - concept: arc-hyperbolic-cosine subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "used as 'acosh'" speech: en: - - "short form 'arc cosh a1'" + - "short form 'arc cosh $a1'" fr: - - "cosh a1" - - "kosh a1" + - "cosh $a1" + - "kosh $a1" - concept: arc-hyperbolic-tangent subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "used as 'atanh'" speech: en: - - "short form American 'arc tanch a1'" - - "short form British 'arc than a1'" + - "short form American 'arc tanch $a1'" + - "short form British 'arc than $a1'" - concept: arc-hyperbolic-secant subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "used as 'asech'" speech: en: - - "short form American 'arc sech a1'" - - "short form British 'arc shek a1'" + - "short form American 'arc sech $a1'" + - "short form British 'arc shek $a1'" - concept: arc-hyperbolic-cosecant subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "used as 'acsch'" speech: en: - - "short form American 'arc cosech a1'" - - "short form British 'arc coshek a1'" + - "short form American 'arc cosech $a1'" + - "short form British 'arc coshek $a1'" - concept: arc-hyperbolic-cotangent subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "used as 'acoth'" speech: en: - - "short form American 'arc coth a1'" - - "short form British 'arc coath a1'" + - "short form American 'arc coth $a1'" + - "short form British 'arc coath $a1'" ## exponential related functions - concept: exponential subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "exponential of a1" + - "exponential of $a1" - concept: natural-logarithm subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "natural log of a1" - - "log of a1" + - "natural log of $a1" + - "log of $a1" - concept: logarithm subject-area: elementary classical functions arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "log of a1" + en: "log of $a1" - concept: logarithm subject-area: elementary classical functions arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "log base a2 of a1" + en: "log base $a2 of $a1" @@ -1205,54 +1205,54 @@ concepts: - concept: mean subject-area: Statistics and Probability arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "mean of a1" + en: "mean of $a1" comments: - "This might be display as x¯" - concept: standard-deviation subject-area: Statistics and Probability arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "standard deviation of a1" + en: "standard deviation of $a1" - concept: variance subject-area: Statistics and Probability arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "variance of a1" + en: "variance of $a1" - concept: median subject-area: Statistics and Probability arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "median of a1" + en: "median of $a1" - concept: mode subject-area: Statistics and Probability arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "mode of a1" + en: "mode of $a1" - concept: conditional-probability subject-area: Statistics and Probability arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "probability of a1 given a2" + en: "probability of $a1 given $a2" comments: - | The intent should be on the `mrow` that includes the "P" @@ -1276,13 +1276,13 @@ concepts: - concept: vector subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: function - concept: matrix subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly @@ -1290,7 +1290,7 @@ concepts: - concept: determinant subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - when used with an `mtable` argument, it is a good idea to use the `:matrix` property on the `mtable` to insure it speaks correctly @@ -1298,7 +1298,7 @@ concepts: - concept: adjugate subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "sometimes used when computing an inverse matrix" @@ -1306,7 +1306,7 @@ concepts: - concept: magnitude subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "often used with matchfix single or double vertical bars" @@ -1314,7 +1314,7 @@ concepts: - concept: norm subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "often used with matchfix double vertical bars" @@ -1322,7 +1322,7 @@ concepts: - concept: span subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: function comments: - "often used with matchfix angle brackets" @@ -1330,7 +1330,7 @@ concepts: - concept: unit-vector subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: prefix comments: - "Example: x^" @@ -1349,30 +1349,30 @@ concepts: - concept: transpose subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: postfix speech: - en: "a1 transpose" - fr: "a1 transposée" + en: "$a1 transpose" + fr: "$a1 transposée" - concept: transpose subject-area: Linear Algebra arity: 1 - arguments: [a1] + arguments: [$a1] property: function default: false speech: - en: "transpose of a1" - fr: "transposée de a1" + en: "transpose of $a1" + fr: "transposée de $a1" - concept: dimensional-product subject-area: Linear Algebra arity: ">=2" - arguments: [a1, a2, ...] + arguments: [$a1, $a2, ...] property: infix default: false speech: - en: "a1 by a2 ..." + en: "$a1 by $a2 ..." comments: - "This is typically used with the `×` operator and can be placed on that character as a 0-arity concept name. A common use would be describe the size of a matrix. For example m×n." @@ -1475,66 +1475,66 @@ concepts: - concept: line-segment subject-area: Geometry arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: prefix speech: en: - - "line segment a1 a2" + - "line segment $a1 $a2" comments: - "Example: (`mover`): AB_" - concept: directed-line-segment subject-area: Geometry arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: prefix speech: en: - - "directed line segment a1 a2" + - "directed line segment $a1 $a2" comments: - "Example: (`mover`): AB→" - concept: line subject-area: Geometry arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: prefix speech: en: - - "line a1 a2" + - "line $a1 $a2" comments: - "Example: (`mover`): AB↔" - concept: ray subject-area: Geometry arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: prefix speech: en: - - "ray a1 a2" + - "ray $a1 $a2" comments: - "Example: (`mover`): AB→" - concept: arc subject-area: Geometry arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: prefix speech: en: - - "arc a1 a2" + - "arc $a1 $a2" comments: - "Example: (`mover`): AB⌒" - concept: length subject-area: Geometry arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "length of a1" + - "length of $a1" comments: - "It may be necessary to 'nest' the intent as shown here for the example: @@ -1553,11 +1553,11 @@ concepts: - concept: area subject-area: Geometry arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "area of a1" + - "area of $a1" comments: - "There are many notations. Here's one: [ABCD]" @@ -1580,22 +1580,22 @@ concepts: - concept: point subject-area: Geometry arity: ">=1" - arguments: [a1, ...] + arguments: [$a1, ...] property: ??? speech: en: - - "point a1 [comma a2 ...]" + - "point $a1 [comma $a2 ...]" comment: - "Example: (1,2,3)" - concept: volume subject-area: Geometry arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: en: - - "volume of a1" + - "volume of $a1" comments: - "See comments for `length` and `volume` for examples of how this might be marked up" @@ -1617,10 +1617,10 @@ concepts: - concept: time-separator subject-area: Separators arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: a1 a2 + en: $a1 $a2 comments: - "separates hours and minutes and is typically silent" - "Example: 2:31" @@ -1629,38 +1629,38 @@ concepts: - concept: fenced-group subject-area: General Concepts arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "fenced-group of a1" + en: "fenced-group of $a1" comments: - "this includes parens, brackets, and braces" - concept: ordered-pair subject-area: General Concepts arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "the pair a1 and a2" + en: "the pair $a1 and $a2" - concept: indexed-by subject-area: General Concepts arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: "a1 indexed by a2" + en: "$a1 indexed by $a2" comments: - - "this is typically a subscript and might also be spoken as 'a1 sub a2'" + - "this is typically a subscript and might also be spoken as '$a1 sub $a2'" - concept: highlight subject-area: General Concepts arity: 1 - arguments: [a1] + arguments: [$a1] property: postfix speech: - en: "a1 highlighted" + en: "$a1 highlighted" comments: - "this typically would be used inside of a larger expression and not on its own" - "this might be used with `` or similar. It might also be used with color changes, although may be done with CSS" @@ -1669,10 +1669,10 @@ concepts: - concept: rate subject-area: General Concepts arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: "a1 per a2" + en: "$a1 per $a2" comments: - "Typically used with units" - "Used with `mfrac` or `/`" @@ -1680,17 +1680,17 @@ concepts: - concept: translation subject-area: General Concepts arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "translation by a1 comma a2" + en: "translation by $a1 comma $a2" comments: - "Example: T(1,3)" - concept: constraint subject-area: General Concepts arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: en: "fraction 2 over x minus 1 with constraint x not equal to 1" @@ -1700,10 +1700,10 @@ concepts: - concept: binomial-coefficient subject-area: General Concepts arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: "a1 choose a2" + en: "$a1 choose $a2" comments: - "There are many notations used for the binomial coefficient. Here are some of them: @@ -1733,10 +1733,10 @@ concepts: - concept: pochhammer subject-area: General Concepts arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "a2 permutation of a1" + en: "$a2 permutation of $a1" comments: - "There are many notations for this: some of them are @@ -1765,10 +1765,10 @@ concepts: - concept: permutation-cycle subject-area: General Concepts arity: ">=2" - arguments: [a1, a2, ...] + arguments: [$a1, $a2, ...] property: function speech: - en: "permutation cycle of a1 a2 ..." + en: "permutation cycle of $a1 $a2 ..." comments: - "A common notation for a permutation cycle is ( 132 @@ -1789,10 +1789,10 @@ concepts: - concept: embellished-name subject-area: General Concepts arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: infix speech: - en: "a1 with annotation a2" + en: "$a1 with annotation $a2" comments: - "used with `mover` or `munder`" @@ -1800,20 +1800,20 @@ concepts: - concept: fenced-group subject-area: Grouping arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "fenced-group of a1" + en: "fenced-group of $a1" comments: - "this includes parens, brackets, and braces" - concept: annotation subject-area: Grouping arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] property: function speech: - en: "a1 which is a2" + en: "$a1 which is $a2" comments: - "used with `mover` or `munder`" - "Example: H2O⏟water" @@ -1821,10 +1821,10 @@ concepts: - concept: braced-group subject-area: Grouping arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "grouped a1 end-grouped" + en: "grouped $a1 end-grouped" comments: - "used with `mover` or `munder`" - "Example: 13-16⏟" @@ -1832,10 +1832,10 @@ concepts: - concept: repeating-decimal subject-area: Grouping arity: 1 - arguments: [a1] + arguments: [$a1] property: function speech: - en: "repeating decimal a1" + en: "repeating decimal $a1" comments: - "typically used in when there is a bar over the repeating part of a decimal or dots over the first and last digits." - "Example: 122=0.045_" diff --git a/_data/open.yml b/_data/open.yml index 5f2d46bd..b9eced09 100644 --- a/_data/open.yml +++ b/_data/open.yml @@ -19,9 +19,9 @@ concepts: - concept: abelian-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: abelian integral of a1 + en: abelian integral of $a1 property: indexed subject-area: "complex analysis" mathml: @@ -33,9 +33,9 @@ concepts: - concept: abundance arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: abundance of a1 + en: abundance of $a1 property: prefix subject-area: "number theory" mathml: @@ -45,9 +45,9 @@ concepts: - concept: abundancy arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: abundancy index of a1 + en: abundancy index of $a1 property: mixfix subject-area: "number theory" mathml: @@ -59,9 +59,9 @@ concepts: - concept: ackermann-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: ackermann function of a1 + en: ackermann function of $a1 property: function subject-area: "computability theory" mathml: @@ -73,9 +73,9 @@ concepts: - concept: ad arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a d a1 + en: a d $a1 property: postfix. prefix subject-area: "calendar units" mathml: @@ -85,9 +85,9 @@ concepts: - concept: additive-inverse arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: additive inverse of a1 + en: additive inverse of $a1 property: prefix subject-area: "abstract algebra" mathml: @@ -143,9 +143,9 @@ concepts: - concept: adjoint arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: adjoint of a1 + en: adjoint of $a1 property: subject-area: mathml: @@ -159,9 +159,9 @@ concepts: - concept: adjoint-action arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: adjoint action of a1 + en: adjoint action of $a1 property: "function/msub" subject-area: "lie algebra" mathml: @@ -177,9 +177,9 @@ concepts: - concept: adjoint-representation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: adjoint representation of a1 + en: adjoint representation of $a1 property: function subject-area: "lie algebra" mathml: @@ -191,9 +191,9 @@ concepts: - concept: adjugate arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: adjugate of a1 + en: adjugate of $a1 property: function subject-area: "linear algebra" mathml: @@ -203,9 +203,9 @@ concepts: - concept: affine-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: affine group of a1 + en: affine group of $a1 property: function subject-area: "group theory" mathml: @@ -217,9 +217,9 @@ concepts: - concept: affine-hull arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: affine hull of a1 + en: affine hull of $a1 property: function subject-area: "affine geometry" mathml: @@ -243,9 +243,9 @@ concepts: - concept: airy-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: airy function of a1 + en: airy function of $a1 property: function subject-area: "special functions" mathml: @@ -262,9 +262,9 @@ concepts: - concept: albanese-variety arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: albanese variety of a1 + en: albanese variety of $a1 property: function subject-area: "algebraic geometry" mathml: @@ -304,9 +304,9 @@ concepts: - concept: algebraic-closure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: algebraic closure of a1 + en: algebraic closure of $a1 property: mover/msup subject-area: "algebra" mathml: @@ -319,9 +319,9 @@ concepts: - concept: almost-surely arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: almost surely of a1 + en: almost surely of $a1 property: subject-area: "probability theory" mathml: @@ -331,9 +331,9 @@ concepts: - concept: alternating-factorial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: alternating factorial of a1 + en: alternating factorial of $a1 property: function subject-area: "functions" mathml: @@ -343,9 +343,9 @@ concepts: - concept: alternating-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: alternating group of a1 + en: alternating group of $a1 property: function subject-area: "group theory" mathml: @@ -358,9 +358,9 @@ concepts: - concept: alternation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 alternation a2 + en: $a1 alternation $a2 property: infix subject-area: "logic" mathml: @@ -376,9 +376,9 @@ concepts: - concept: alternative-denial arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 alternative denial a2 + en: $a1 alternative denial $a2 property: infix, prefix subject-area: "propositional calculus" mathml: @@ -394,9 +394,9 @@ concepts: - concept: amalgam arity: 5 - arguments: [a1, a2, a3, a4, a5] + arguments: [$a1, $a2, $a3, $a4, $a5] speech: - en: amalgam of a1 a2 a3 a4 a5 + en: amalgam of $a1 $a2 $a3 $a4 $a5 property: fenced, 5-tuple subject-area: "model theory" mathml: @@ -407,9 +407,9 @@ concepts: - concept: amalgamated-product arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: Free product with amalgamation of a1 and a3 with respect to a2 + en: Free product with amalgamation of $a1 and $a3 with respect to $a2 property: indexed infix subject-area: "group theory" mathml: @@ -438,9 +438,9 @@ concepts: - concept: anger-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: anger function of a1 + en: anger function of $a1 property: function subject-area: "special functions" mathml: @@ -453,9 +453,9 @@ concepts: - concept: angle-of-parallelism arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: angle of parallelism of a1 + en: angle of parallelism of $a1 property: function subject-area: "hyperbolic geometry" mathml: @@ -494,9 +494,9 @@ concepts: - concept: anharmonic-ratio arity: 4 - arguments: [a1, a2, a3, a4] + arguments: [$a1, $a2, $a3, $a4] speech: - en: "anharmonic ratio of a1 , a2 , a3 , a4" + en: "anharmonic ratio of $a1 , $a2 , $a3 , $a4" property: fenced subject-area: "geometry" mathml: @@ -508,9 +508,9 @@ concepts: - concept: annihilator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: annihilator of a1 + en: annihilator of $a1 property: function subject-area: "ring theory" mathml: @@ -522,9 +522,9 @@ concepts: - concept: annulus arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: annulus of a1 + en: annulus of $a1 property: function subject-area: "complex analysis" mathml: @@ -536,9 +536,9 @@ concepts: - concept: antiparticle arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: antiparticle of a1 + en: antiparticle of $a1 property: mover subject-area: "particle physics" mathml: @@ -551,9 +551,9 @@ concepts: - concept: apartness-relation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 apartness relation a2 + en: $a1 apartness relation $a2 property: infix subject-area: "constructive mathematics" mathml: @@ -579,9 +579,9 @@ concepts: - concept: arcminute arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: arcminute of a1 + en: arcminute of $a1 property: unit subject-area: "SI-mentioned units" mathml: @@ -599,9 +599,9 @@ concepts: - concept: arcsecond arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: arcsecond of a1 + en: arcsecond of $a1 property: unit subject-area: "SI-mentioned units" mathml: @@ -630,9 +630,9 @@ concepts: - concept: arf-invariant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: arf invariant of a1 + en: arf invariant of $a1 property: function subject-area: "geometric topology" mathml: @@ -644,9 +644,9 @@ concepts: - concept: argument arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: argument of a1 + en: argument of $a1 property: function subject-area: "complex analysis" mathml: @@ -656,9 +656,9 @@ concepts: - concept: arithmetic-geometric-mean arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: arithmetic geometric mean of a1 + en: arithmetic geometric mean of $a1 property: function subject-area: "special functions" mathml: @@ -672,9 +672,9 @@ concepts: - concept: associated-legendre-polynomial arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: associated legendre polynomial of degree a1 and order a2 + en: associated legendre polynomial of degree $a1 and order $a2 property: function subject-area: "special functions" mathml: @@ -686,9 +686,9 @@ concepts: - concept: associator arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: associator of a1, a2, a3 + en: associator of $a1, $a2, $a3 property: fenced subject-area: "algebra" mathml: @@ -701,9 +701,9 @@ concepts: - concept: automorphism-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: automorphism group of a1 + en: automorphism group of $a1 property: function subject-area: "group theory" mathml: @@ -714,9 +714,9 @@ concepts: - concept: backward-difference arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: backward difference of a1 + en: backward difference of $a1 property: operator subject-area: "special functions" mathml: @@ -745,9 +745,9 @@ concepts: - concept: barrel arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 barrels + en: $a1 barrels property: unit subject-area: "imperial units" mathml: @@ -759,7 +759,7 @@ concepts: - concept: bateman-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: bateman function property: function @@ -773,7 +773,7 @@ concepts: - concept: baumslag-solitar-group arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: baumslag solitar group property: function @@ -786,9 +786,9 @@ concepts: - concept: bc arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 b c + en: $a1 b c property: postfix subject-area: "calendar units" mathml: @@ -798,9 +798,9 @@ concepts: - concept: beatty-sequence arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th beatty sequence + en: $a1th beatty sequence property: "indexed symbol" subject-area: "number theory" mathml: @@ -811,9 +811,9 @@ concepts: - concept: bell-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th bell number + en: $a1th bell number property: "indexed symbol" subject-area: "number theory" mathml: @@ -827,10 +827,10 @@ concepts: - concept: bell-polynomial arity: ">=0" speech: - en: a1th bell polynomial of a2, a3, ... + en: $a1th bell polynomial of $a2, $a3, ... property: "indexed function" subject-area: "polynomials" - notation: "mrow msub B a1 (a2, ... $n" + notation: "mrow msub B $a1 ($a2, ... $n" urls: - "https://mathworld.wolfram.com/BellPolynomial.html" - "https://en.wikipedia.org/wiki/Bell_polynomials" @@ -838,9 +838,9 @@ concepts: - concept: berezin-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: berezin integral of a1 + en: berezin integral of $a1 property: indexed subject-area: "mathematical physics" mathml: @@ -852,9 +852,9 @@ concepts: - concept: bergman-space arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1th bergman space of a2 + en: $a1th bergman space of $a2 property: "indexed function" subject-area: "complex analysis" mathml: @@ -866,9 +866,9 @@ concepts: - concept: bernoulli-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th bernoulli number + en: $a1th bernoulli number property: "indexed symbol" subject-area: "number theory" mathml: @@ -883,9 +883,9 @@ concepts: - concept: bernoulli-polynomial arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: bernoulli polynomial a1 a2 + en: bernoulli polynomial $a1 $a2 property: "indexed function" subject-area: "number theory" mathml: @@ -899,9 +899,9 @@ concepts: - concept: bessel-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1th bessel function of a2 + en: $a1th bessel function of $a2 property: "indexed function" subject-area: "special functions" mathml: @@ -914,9 +914,9 @@ concepts: - concept: bessel-function-of-second-kind arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1th bessel function of second kind of a2 + en: $a1th bessel function of second kind of $a2 property: "indexed function" subject-area: "special functions" mathml: @@ -928,9 +928,9 @@ concepts: - concept: bessel-polynomial arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1th bessel polynomial of a2 + en: $a1th bessel polynomial of $a2 property: "indexed function" subject-area: "special functions" mathml: @@ -943,9 +943,9 @@ concepts: - concept: beta-distribution arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: beta distribution of a1 + en: beta distribution of $a1 property: function subject-area: "probability theory" mathml: @@ -959,9 +959,9 @@ concepts: - concept: beta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: beta function of a1 + en: beta function of $a1 property: function subject-area: "special functions" mathml: @@ -980,9 +980,9 @@ concepts: - concept: betti-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th betti number + en: $a1th betti number property: "indexed symbol" subject-area: "graph theory" mathml: @@ -995,9 +995,9 @@ concepts: - concept: biconditional arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 biconditional a2 + en: $a1 biconditional $a2 property: infix subject-area: "logic" mathml: @@ -1013,9 +1013,9 @@ concepts: - concept: big-O arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: big O of a1 + en: big O of $a1 property: prefix subject-area: "complexity" mathml: @@ -1026,9 +1026,9 @@ concepts: - concept: bigeometric-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: bigeometric integral of a1 + en: bigeometric integral of $a1 property: indexed subject-area: "calculus" mathml: @@ -1038,9 +1038,9 @@ concepts: - concept: bijection arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: bijection, a1, of a2 to a3 + en: bijection, $a1, of $a2 to $a3 property: mixfix subject-area: "set theory" mathml: @@ -1063,9 +1063,9 @@ concepts: - concept: binomial-coefficient arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: binomial coefficient a1 choose a2 + en: binomial coefficient $a1 choose $a2 property: "indexed function" subject-area: "combinatorics" mathml: @@ -1082,9 +1082,9 @@ concepts: - concept: binomial-distribution arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: binomial distribution a1 a2 + en: binomial distribution $a1 $a2 property: function subject-area: "probability theory" mathml: @@ -1111,9 +1111,9 @@ concepts: - concept: bipolar-set arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: bipolar set of a1 + en: bipolar set of $a1 property: msup subject-area: "functional analysis" mathml: @@ -1125,9 +1125,9 @@ concepts: - concept: biquaternion arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: biquaternion of a1 + en: biquaternion of $a1 property: mtable subject-area: "ring theory" mathml: @@ -1137,9 +1137,9 @@ concepts: - concept: blaschke-product arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: blaschke product of a1 + en: blaschke product of $a1 property: function subject-area: "complex analysis" mathml: @@ -1208,9 +1208,9 @@ concepts: - concept: boundary arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: boundary of a1 + en: boundary of $a1 property: function subject-area: "topology" mathml: @@ -1227,9 +1227,9 @@ concepts: - concept: bounded-variation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: bounded variation of a1 + en: bounded variation of $a1 property: function subject-area: "analysis" mathml: @@ -1240,9 +1240,9 @@ concepts: - concept: box-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 box product a2 + en: $a1 box product $a2 property: infix subject-area: "graph theory" mathml: @@ -1254,9 +1254,9 @@ concepts: - concept: brauer-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: brauer group of a1 + en: brauer group of $a1 property: function subject-area: "group theory" mathml: @@ -1282,9 +1282,9 @@ concepts: - concept: burnside-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: burnside group of a1 + en: burnside group of $a1 property: function subject-area: "group theory" mathml: @@ -1307,9 +1307,9 @@ concepts: - concept: calderon-toeplitz-operator arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: calderon toeplitz operator a1 a2 + en: calderon toeplitz operator $a1 $a2 property: "indexed symbol" subject-area: "operator theory" mathml: @@ -1319,7 +1319,7 @@ concepts: - concept: canonical-commutation-relation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: canonical commutation relation property: fenced @@ -1331,9 +1331,9 @@ concepts: - concept: cap-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 cap product a2 + en: $a1 cap product $a2 property: infix subject-area: "algebraic topology" mathml: @@ -1344,9 +1344,9 @@ concepts: - concept: cardinality arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cardinality of a1 + en: cardinality of $a1 property: many subject-area: "set theory" mathml: @@ -1361,9 +1361,9 @@ concepts: - concept: carmichael-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: carmichael function of a1 + en: carmichael function of $a1 property: function subject-area: "number theory" mathml: @@ -1374,9 +1374,9 @@ concepts: - concept: cartesian-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 cartesian product a2 + en: $a1 cartesian product $a2 property: infix subject-area: "set theory" mathml: @@ -1416,9 +1416,9 @@ concepts: - concept: catalan-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th catalan number + en: $a1th catalan number property: "indexed symbol" subject-area: "combinatorics" mathml: @@ -1468,9 +1468,9 @@ concepts: - concept: cauchy-principal-value arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cauchy principal value of a1 + en: cauchy principal value of $a1 property: function subject-area: "analysis" mathml: @@ -1483,9 +1483,9 @@ concepts: - concept: cauchy-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 cauchy product a2 + en: $a1 cauchy product $a2 property: infix subject-area: "analysis" mathml: @@ -1508,9 +1508,9 @@ concepts: - concept: cayley-table arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cayley table of a1 + en: cayley table of $a1 property: mtable subject-area: "group theory" mathml: @@ -1522,9 +1522,9 @@ concepts: - concept: ceiling arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: ceiling of a1 + en: ceiling of $a1 property: fenced, function subject-area: "number theory" mathml: @@ -1538,9 +1538,9 @@ concepts: - concept: center arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: center of a1 + en: center of $a1 property: function subject-area: "algebra" mathml: @@ -1554,9 +1554,9 @@ concepts: - concept: centralizer arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: centralizer of a1 + en: centralizer of $a1 property: function subject-area: "group theory" mathml: @@ -1569,9 +1569,9 @@ concepts: - concept: chain arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 chains + en: $a1 chains property: unit subject-area: "imperial units" mathml: @@ -1595,9 +1595,9 @@ concepts: - concept: character arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: character of a1 + en: character of $a1 property: "indexed function" subject-area: "group theory" mathml: @@ -1612,9 +1612,9 @@ concepts: - concept: characteristic arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: characteristic of a1 + en: characteristic of $a1 property: function subject-area: "ring theory" mathml: @@ -1627,9 +1627,9 @@ concepts: - concept: characteristic-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: characteristic function of a1 + en: characteristic function of $a1 property: "indexed function, function" subject-area: "probability theory" mathml: @@ -1648,9 +1648,9 @@ concepts: - concept: characteristic-subgroup arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 characteristic subgroup a2 + en: $a1 characteristic subgroup $a2 property: infix subject-area: "group theory" mathml: @@ -1661,9 +1661,9 @@ concepts: - concept: charlier-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: charlier polynomial of a1 + en: charlier polynomial of $a1 property: function subject-area: "special functions" mathml: @@ -1676,9 +1676,9 @@ concepts: - concept: chebyshev-polynomial-of-first-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: chebyshev polynomial of first kind of a1 + en: chebyshev polynomial of first kind of $a1 property: function subject-area: "number theory" mathml: @@ -1694,9 +1694,9 @@ concepts: - concept: chebyshev-polynomial-of-second-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: chebyshev polynomial of second kind of a1 + en: chebyshev polynomial of second kind of $a1 property: function subject-area: "number theory" mathml: @@ -1711,9 +1711,9 @@ concepts: - concept: cheeger-constant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cheeger constant of a1 + en: cheeger constant of $a1 property: function subject-area: "Riemannian geometry" mathml: @@ -1723,9 +1723,9 @@ concepts: - concept: cheeger-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cheeger number of a1 + en: cheeger number of $a1 property: function subject-area: "graph theory" mathml: @@ -1738,9 +1738,9 @@ concepts: - concept: chemical-equilibrium arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 chemical equilibrium a2 + en: $a1 chemical equilibrium $a2 property: infix subject-area: "chemistry" mathml: @@ -1766,9 +1766,9 @@ concepts: - concept: chord arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: chord of a1 + en: chord of $a1 property: function subject-area: "geometry" mathml: @@ -1778,9 +1778,9 @@ concepts: - concept: christoffel-symbol-of-first-kind arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: christoffel symbol of first kind of a1, a2, a3 + en: christoffel symbol of first kind of $a1, $a2, $a3 property: "indexed symbol" subject-area: "Riemannian geometry" mathml: @@ -1793,9 +1793,9 @@ concepts: - concept: christoffel-symbol-of-second-kind arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: christoffel symbol of second kind of a1 a2 a3 + en: christoffel symbol of second kind of $a1 $a2 $a3 property: "indexed symbol" subject-area: "Riemannian geometry" mathml: @@ -1808,9 +1808,9 @@ concepts: - concept: chromatic-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: chromatic polynomial of a1 + en: chromatic polynomial of $a1 property: function subject-area: "graph theory" mathml: @@ -1823,9 +1823,9 @@ concepts: - concept: classifying-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: classifying space of a1 + en: classifying space of $a1 property: function subject-area: "group theory" mathml: @@ -1838,9 +1838,9 @@ concepts: - concept: clausen-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: clausen function of a1 + en: clausen function of $a1 property: function subject-area: "special functions" mathml: @@ -1850,9 +1850,9 @@ concepts: - concept: clebsch-gordan-coefficient arity: 8 - arguments: [a1, a2, a3, a4, a6, a7, a8] + arguments: [$a1, $a2, $a3, $a4, $a6, $a7, $a8] speech: - en: clebsch gordan coefficient a1 a2 a3 a4 a5 a6 a7 a8 + en: clebsch gordan coefficient $a1 $a2 $a3 $a4 $a5 $a6 $a7 $a8 property: fenced subject-area: "special functions" mathml: @@ -1866,9 +1866,9 @@ concepts: - concept: clifford-algebra arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: clifford algebra of a1 + en: clifford algebra of $a1 property: function subject-area: "universal algebra" mathml: @@ -1892,9 +1892,9 @@ concepts: - concept: clique-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: clique number of a1 + en: clique number of $a1 property: function subject-area: "graph theory" mathml: @@ -1904,9 +1904,9 @@ concepts: - concept: closed-ball arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: closed ball a1 a2 + en: closed ball $a1 $a2 property: mixfix subject-area: "topology" mathml: @@ -1919,7 +1919,7 @@ concepts: - concept: closed-interval arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: closed interval property: fenced @@ -1932,9 +1932,9 @@ concepts: - concept: closed-neighbourhood arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: closed neighbourhood of a2 in a1 + en: closed neighbourhood of $a2 in $a1 property: "indexed function, function" subject-area: "graph theory" mathml: @@ -1944,9 +1944,9 @@ concepts: - concept: closure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: closure of a1 + en: closure of $a1 property: "function, msup" subject-area: "abstract algebra,, topology" mathml: @@ -1962,9 +1962,9 @@ concepts: - concept: codimension arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: codimension of a1 + en: codimension of $a1 property: function subject-area: "linear algebra" mathml: @@ -1977,9 +1977,9 @@ concepts: - concept: cofinality arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cofinality of a1 + en: cofinality of $a1 property: function subject-area: "order theory" mathml: @@ -2005,9 +2005,9 @@ concepts: - concept: coherence arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: coherence of a1 + en: coherence of $a1 property: "indexed function" subject-area: "signal processing, quantum physics" mathml: @@ -2019,9 +2019,9 @@ concepts: - concept: coimage arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: coimage of a1 + en: coimage of $a1 property: function subject-area: "abstract algebra" mathml: @@ -2032,9 +2032,9 @@ concepts: - concept: cokernel arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cokernel of a1 + en: cokernel of $a1 property: function subject-area: "category theory" mathml: @@ -2048,20 +2048,20 @@ concepts: - concept: column-vector arity: ">=0" speech: - en: column vector of a1 a2 ... + en: column vector of $a1 $a2 ... property: mtable subject-area: "linear algebra" mathml: - - "(xyz)" + - "(xyz)" urls: - "https://mathworld.wolfram.com/ColumnVector.html" - "https://en.wikipedia.org/wiki/Column_vector" - concept: comma-category arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: comma category a1 a2 + en: comma category $a1 $a2 property: mixfix subject-area: "category theory" mathml: @@ -2071,7 +2071,7 @@ concepts: - concept: commutator arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: commutator property: fenced @@ -2086,17 +2086,17 @@ concepts: - concept: commutator-subgroup arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: commutator subgroup of a1 + en: commutator subgroup of $a1 property: msup, fenced subject-area: "abstract algebra" mathml: - "X'" - "X(1)" - "[X,X]" - notationb: "msup a1 (1)" - notationa: "mrow [ a1, a1 ]" + notationb: "msup $a1 (1)" + notationa: "mrow [ $a1, $a1 ]" urls: - "https://mathworld.wolfram.com/CommutatorSubgroup.html" - "https://en.wikipedia.org/wiki/Commutator_subgroup" @@ -2108,9 +2108,9 @@ concepts: - concept: companion-lehmer-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: companion lehmer number of a1 + en: companion lehmer number of $a1 property: "indexed function" subject-area: "number theory" mathml: @@ -2122,9 +2122,9 @@ concepts: - concept: comparability arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 comparability a2 + en: $a1 comparability $a2 property: infix subject-area: "order theory" mathml: @@ -2136,7 +2136,7 @@ concepts: - concept: complement-of-interval arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: complement of interval property: fenced @@ -2148,9 +2148,9 @@ concepts: - concept: complementary-nome arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: complementary nome of a1 + en: complementary nome of $a1 property: function subject-area: "special functions" mathml: @@ -2161,7 +2161,7 @@ concepts: - concept: complete-graph arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: complete graph property: symbol @@ -2176,14 +2176,14 @@ concepts: - concept: complex-conjugate arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: complex conjugate of a1 + en: complex conjugate of $a1 property: msup subject-area: "complex analysis" mathml: - "X*" - notationa: "mover a1 ¯" + notationa: "mover $a1 ¯" urls: - "https://mathworld.wolfram.com/ComplexConjugate.html" - "https://en.wikipedia.org/wiki/Complex_conjugate" @@ -2207,9 +2207,9 @@ concepts: - concept: complexification arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: complexification of a1 + en: complexification of $a1 property: msup subject-area: "complex manifolds" mathml: @@ -2224,9 +2224,9 @@ concepts: - concept: composition arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 composition a2 + en: $a1 composition $a2 property: infix subject-area: "algebra" mathml: @@ -2242,7 +2242,7 @@ concepts: - concept: compound-interest-nominal-rate arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: nominal rate property: msup @@ -2255,9 +2255,9 @@ concepts: - concept: concentration arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: concentration of a1 + en: concentration of $a1 property: fenced subject-area: "chemistry" mathml: @@ -2267,9 +2267,9 @@ concepts: - concept: condition-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: condition number of a1 + en: condition number of $a1 property: function subject-area: "numerical analysis" mathml: @@ -2281,9 +2281,9 @@ concepts: - concept: conditional-expectation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: conditional expectation a1 a2 + en: conditional expectation $a1 $a2 property: mixfix subject-area: "probability theory" mathml: @@ -2294,9 +2294,9 @@ concepts: - concept: conditional-probability arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: conditional probability a1 a2 + en: conditional probability $a1 $a2 property: mixfix subject-area: "probability theory" mathml: @@ -2308,9 +2308,9 @@ concepts: - concept: conductor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: conductor of a1 + en: conductor of $a1 property: function subject-area: "algebraic number theory" mathml: @@ -2320,9 +2320,9 @@ concepts: - concept: contraction-operator arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 contraction operator a2 + en: $a1 contraction operator $a2 property: infix subject-area: "algebraic geometry" mathml: @@ -2332,9 +2332,9 @@ concepts: - concept: contrast-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: contrast function a1 a2 + en: contrast function $a1 $a2 property: mixfix subject-area: "statistics" mathml: @@ -2346,9 +2346,9 @@ concepts: - concept: configuration arity: 4 - arguments: [a1, a2, a3, a4] + arguments: [$a1, $a2, $a3, $a4] speech: - en: "configuration a1 sub a2, a3 sub a4" + en: "configuration $a1 sub $a2, $a3 sub $a4" property: mixfix subject-area: "geometry" mathml: @@ -2360,9 +2360,9 @@ concepts: - concept: congruence-relation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 congruence relation a2 + en: $a1 congruence relation $a2 property: infix subject-area: "algebra, geometry" mathml: @@ -2382,9 +2382,9 @@ concepts: - concept: conjugacy-class arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: conjugacy class of a1 + en: conjugacy class of $a1 property: function subject-area: "group theory" mathml: @@ -2396,9 +2396,9 @@ concepts: - concept: conjugate-transpose arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: conjugate transpose of a1 + en: conjugate transpose of $a1 property: msup subject-area: "linear algebra" mathml: @@ -2410,9 +2410,9 @@ concepts: - concept: connected-sum arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 connected sum a2 + en: $a1 connected sum $a2 property: infix subject-area: "topology" mathml: @@ -2424,9 +2424,9 @@ concepts: - concept: connectivity arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: connectivity of a1 + en: connectivity of $a1 property: function subject-area: "graph theory" mathml: @@ -2451,9 +2451,9 @@ concepts: - concept: containment arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 containment a2 + en: $a1 containment $a2 property: infix subject-area: "computer science" mathml: @@ -2467,9 +2467,9 @@ concepts: - concept: contingency-table arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: contingency table of a1 + en: contingency table of $a1 property: mtable subject-area: "statistics" mathml: @@ -2482,9 +2482,9 @@ concepts: - concept: continued-fraction arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: continued fraction a1 + en: continued fraction $a1 property: mixfix subject-area: "number theory" mathml: @@ -2533,9 +2533,9 @@ concepts: - concept: converge arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 converges + en: $a1 converges property: postfix subject-area: "computer science" mathml: @@ -2547,9 +2547,9 @@ concepts: - concept: converse arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: converse of a1 + en: converse of $a1 property: msup subject-area: "relational algebra" mathml: @@ -2561,9 +2561,9 @@ concepts: - concept: converse-graph arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: converse graph of a1 + en: converse graph of $a1 property: msup subject-area: "graph theory" mathml: @@ -2578,9 +2578,9 @@ concepts: - concept: convolution arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 convolution a2 + en: $a1 convolution $a2 property: infix subject-area: "functional analysis" mathml: @@ -2614,9 +2614,9 @@ concepts: - concept: coprime arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 coprime a2 + en: $a1 coprime $a2 property: infix subject-area: "number theory" mathml: @@ -2630,9 +2630,9 @@ concepts: - concept: coproduct arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: coproduct of a1 and a2 + en: coproduct of $a1 and $a2 property: indexed subject-area: "topology, category theory" mathml: @@ -2646,9 +2646,9 @@ concepts: - concept: correlation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: correlation of a1 + en: correlation of $a1 property: function subject-area: "statistics" mathml: @@ -2672,9 +2672,9 @@ concepts: - concept: cosine-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cosine integral of a1 + en: cosine integral of $a1 property: operator subject-area: "special-functions" mathml: @@ -2702,9 +2702,9 @@ concepts: - concept: covariance arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: covariance of a1 + en: covariance of $a1 property: function subject-area: "statistics" mathml: @@ -2718,9 +2718,9 @@ concepts: - concept: covariant-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: covariant derivative of a1 + en: covariant derivative of $a1 property: "indexed operator" subject-area: "differential geometry" mathml: @@ -2733,9 +2733,9 @@ concepts: - concept: covariation arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: covariation of a1 and a2 over a3 + en: covariation of $a1 and $a2 over $a3 property: indexed fenced subject-area: "stochastic processes" mathml: @@ -2747,9 +2747,9 @@ concepts: - concept: covering-relation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 covering relation a2 + en: $a1 covering relation $a2 property: infix subject-area: "order theory" mathml: @@ -2761,9 +2761,9 @@ concepts: - concept: cross-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 cross product a2 + en: $a1 cross product $a2 property: infix subject-area: "linear algebra" mathml: @@ -2778,9 +2778,9 @@ concepts: - concept: cross-ratio arity: 4 - arguments: [a1, a2, a3, a4] + arguments: [$a1, $a2, $a3, $a4] speech: - en: "cross ratio of a1, a2, a3, a4" + en: "cross ratio of $a1, $a2, $a3, $a4" property: fenced subject-area: "geometry" mathml: @@ -2793,9 +2793,9 @@ concepts: - concept: crossing-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: crossing number of a1 + en: crossing number of $a1 property: function subject-area: "graph theory" mathml: @@ -2807,9 +2807,9 @@ concepts: - concept: cullen-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th cullen number + en: $a1th cullen number property: "indexed symbol" subject-area: "number theory" mathml: @@ -2820,9 +2820,9 @@ concepts: - concept: cumulant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cumulant of a1 + en: cumulant of $a1 property: "indexed symbol" subject-area: "probability theory" mathml: @@ -2836,9 +2836,9 @@ concepts: - concept: cumulative-distribution-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cumulative distribution function of a1 + en: cumulative distribution function of $a1 property: "indexed symbol" subject-area: "probability theory" mathml: @@ -2852,9 +2852,9 @@ concepts: - concept: cup-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 cup product a2 + en: $a1 cup product $a2 property: infix subject-area: "algebraic topology" mathml: @@ -2865,15 +2865,15 @@ concepts: - concept: curl arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: curl of a1 + en: curl of $a1 property: function subject-area: "vector calculus" mathml: - "curlX" - "rotX" - notationa: "mrow ∇ × a1" + notationa: "mrow ∇ × $a1" urls: - "https://mathworld.wolfram.com/Curl.html" - "https://en.wikipedia.org/wiki/Curl_(mathematics)" @@ -2882,9 +2882,9 @@ concepts: - concept: current arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: current of a1 + en: current of $a1 property: fenced subject-area: "differential topology" mathml: @@ -2897,9 +2897,9 @@ concepts: - concept: curvature arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: curvature of a1 + en: curvature of $a1 property: function subject-area: "differential geometry" mathml: @@ -2913,9 +2913,9 @@ concepts: - concept: cycle arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cycle a1 + en: cycle $a1 property: fenced subject-area: "combinatorics" mathml: @@ -2939,9 +2939,9 @@ concepts: - concept: cyclotomic-field arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: cyclotomic field of a1 + en: cyclotomic field of $a1 property: embellished symbol subject-area: "number theory" mathml: @@ -2954,9 +2954,9 @@ concepts: - concept: cyclotomic-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th cyclotomic polynomial + en: $a1th cyclotomic polynomial property: "indexed symbol" subject-area: "number theory" mathml: @@ -2968,9 +2968,9 @@ concepts: - concept: dalembert-operator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dalembert operator of a1 + en: dalembert operator of $a1 property: prefix subject-area: "partial differential equations" mathml: @@ -2985,9 +2985,9 @@ concepts: - concept: davenport-constant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: davenport constant of a1 + en: davenport constant of $a1 property: function subject-area: "group theory" mathml: @@ -2999,9 +2999,9 @@ concepts: - concept: dawson-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dawson function of a1 + en: dawson function of $a1 property: function subject-area: "special-functions" mathml: @@ -3019,9 +3019,9 @@ concepts: - concept: decrease arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: decrease of a1 + en: decrease of $a1 property: postfix subject-area: "physics" mathml: @@ -3031,9 +3031,9 @@ concepts: - concept: decrease-tends-to arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 decrease tends to a2 + en: $a1 decrease tends to $a2 property: infix subject-area: "calculus" mathml: @@ -3044,9 +3044,9 @@ concepts: - concept: dedekind-eta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dedekind eta function of a1 + en: dedekind eta function of $a1 property: function subject-area: "special functions" mathml: @@ -3058,9 +3058,9 @@ concepts: - concept: dedekind-zeta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dedekind zeta function of a1 + en: dedekind zeta function of $a1 property: function subject-area: "special functions" mathml: @@ -3070,9 +3070,9 @@ concepts: - concept: deductive-closure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: deductive closure of a1 + en: deductive closure of $a1 property: function subject-area: "logic" mathml: @@ -3083,9 +3083,9 @@ concepts: - concept: defined-as arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 defined as a2 + en: $a1 defined as $a2 property: infix subject-area: "general" mathml: @@ -3103,9 +3103,9 @@ concepts: - concept: degree arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: degree of a1 + en: degree of $a1 property: prefix, postfix subject-area: "physics, geometry" mathml: @@ -3119,9 +3119,9 @@ concepts: - concept: degree-of-graph arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: degree of graph of a1 + en: degree of graph of $a1 property: function subject-area: "graph theory" mathml: @@ -3147,9 +3147,9 @@ concepts: - concept: degree-of-mapping arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: degree of mapping of a1 + en: degree of mapping of $a1 property: function subject-area: "topology" mathml: @@ -3161,9 +3161,9 @@ concepts: - concept: degree-of-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: degree of polynomial of a1 + en: degree of polynomial of $a1 property: function subject-area: "polynomials" mathml: @@ -3175,9 +3175,9 @@ concepts: - concept: dependence-relation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 dependence relation a2 + en: $a1 dependence relation $a2 property: infix subject-area: "linear algebra" mathml: @@ -3187,9 +3187,9 @@ concepts: - concept: dereference arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dereference of a1 + en: dereference of $a1 property: prefix subject-area: "programming languages" mathml: @@ -3199,9 +3199,9 @@ concepts: - concept: derivation-tree arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: derivation a1, a2 + en: derivation $a1, $a2 property: mfrac subject-area: "logic" mathml: @@ -3211,9 +3211,9 @@ concepts: - concept: derived-category arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: derived category of a1 + en: derived category of $a1 property: function subject-area: "category theory" mathml: @@ -3238,9 +3238,9 @@ concepts: - concept: diagonal-intersection arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: diagonal intersection of a1 + en: diagonal intersection of $a1 property: function subject-area: "set theory" mathml: @@ -3250,9 +3250,9 @@ concepts: - concept: diagonal-matrix arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: diagonal matrix of a1 + en: diagonal matrix of $a1 property: function subject-area: "linear algebra" mathml: @@ -3262,9 +3262,9 @@ concepts: - concept: diameter arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: diameter of a1 + en: diameter of $a1 property: symbol, prefix unit subject-area: "geometry" mathml: @@ -3277,9 +3277,9 @@ concepts: - concept: dickman-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dickman function of a1 + en: dickman function of $a1 property: function subject-area: "special functions" mathml: @@ -3293,9 +3293,9 @@ concepts: - concept: different-ideal arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: different ideal of a1 + en: different ideal of $a1 property: function subject-area: "algebraic number theory" mathml: @@ -3307,9 +3307,9 @@ concepts: - concept: differential-entropy arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: differential entropy of a1 + en: differential entropy of $a1 property: function subject-area: "information theory" mathml: @@ -3323,16 +3323,16 @@ concepts: - concept: differential-operator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: differential operator with respect to a1 + en: differential operator with respect to $a1 property: prefix subject-area: "calculus" mathml: - "Dx" - "∂x" - "ddx" - notationa: "mfrac d mrow d a1" + notationa: "mfrac d mrow d $a1" urls: - "https://mathworld.wolfram.com/DifferentialOperator.html" - "https://en.wikipedia.org/wiki/Differential_operator" @@ -3360,9 +3360,9 @@ concepts: - concept: dihedral-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th dihedral group + en: $a1th dihedral group property: symbol subject-area: "group theory" mathml: @@ -3375,9 +3375,9 @@ concepts: - concept: dilation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 dilation a2 + en: $a1 dilation $a2 property: infix subject-area: "mathematical morphology" mathml: @@ -3387,9 +3387,9 @@ concepts: - concept: dilogarithm arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dilogarithm of a1 + en: dilogarithm of $a1 property: function subject-area: "special functions" mathml: @@ -3405,9 +3405,9 @@ concepts: - concept: dimension arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dimension of a1 + en: dimension of $a1 property: "function, fenced" subject-area: "linear algebra, graph theory" mathml: @@ -3431,9 +3431,9 @@ concepts: - concept: dirac-delta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dirac delta function of a1 + en: dirac delta function of $a1 property: function subject-area: "analysis" mathml: @@ -3465,9 +3465,9 @@ concepts: - concept: dirac-measure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dirac measure of a1 + en: dirac measure of $a1 property: function subject-area: "measure theory" mathml: @@ -3477,9 +3477,9 @@ concepts: - concept: dirac-operator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dirac operator of a1 + en: dirac operator of $a1 property: function subject-area: "differential operators" mathml: @@ -3491,9 +3491,9 @@ concepts: - concept: direct-limit arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: direct limit of a1 + en: direct limit of $a1 property: prefix subject-area: "category theory" mathml: @@ -3505,9 +3505,9 @@ concepts: - concept: direct-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 direct product a2 + en: $a1 direct product $a2 property: infix subject-area: "abstract algebra" mathml: @@ -3521,9 +3521,9 @@ concepts: - concept: direct-sum arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 direct sum a2 + en: $a1 direct sum $a2 property: infix subject-area: "abstract algebra" mathml: @@ -3540,9 +3540,9 @@ concepts: - concept: directional-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: directional derivative of a1 + en: directional derivative of $a1 property: "function, mixfix" subject-area: "differential calculus" mathml: @@ -3556,9 +3556,9 @@ concepts: - concept: dirichlet-character arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dirichlet character of a1 + en: dirichlet character of $a1 property: function subject-area: "special-functions" mathml: @@ -3571,9 +3571,9 @@ concepts: - concept: dirichlet-convolution arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 dirichlet convolution a2 + en: $a1 dirichlet convolution $a2 property: infix subject-area: "number theory" mathml: @@ -3598,9 +3598,9 @@ concepts: - concept: dirichlet-eta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dirichlet eta function of a1 + en: dirichlet eta function of $a1 property: function subject-area: "analytic number theory" mathml: @@ -3612,9 +3612,9 @@ concepts: - concept: dirichlet-kernel arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dirichlet kernel of a1 + en: dirichlet kernel of $a1 property: function subject-area: "mathematical analysis" mathml: @@ -3626,9 +3626,9 @@ concepts: - concept: dirichlet-l-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dirichlet l function of a1 + en: dirichlet l function of $a1 property: function subject-area: "special-functions" mathml: @@ -3641,9 +3641,9 @@ concepts: - concept: discrete-valuation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: discrete valuation of a1 + en: discrete valuation of $a1 property: function subject-area: "commutative algebra" mathml: @@ -3654,9 +3654,9 @@ concepts: - concept: discriminant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: discriminant of a1 + en: discriminant of $a1 property: function subject-area: "polynomials" mathml: @@ -3671,9 +3671,9 @@ concepts: - concept: disjoint-union arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: disjoint union of a1 + en: disjoint union of $a1 property: indexed subject-area: "set theory" mathml: @@ -3687,9 +3687,9 @@ concepts: - concept: disjoint-union arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: disjoint union of a1 and a2 + en: disjoint union of $a1 and $a2 property: infix subject-area: "set theory" mathml: @@ -3703,7 +3703,7 @@ concepts: - concept: distance arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: distance property: fenced @@ -3715,9 +3715,9 @@ concepts: - concept: diverge arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 diverges + en: $a1 diverges property: postfix subject-area: "computer science" mathml: @@ -3729,9 +3729,9 @@ concepts: - concept: divergence arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: divergence of a1 + en: divergence of $a1 property: "function, mixfix" subject-area: "vector calculus" mathml: @@ -3748,7 +3748,7 @@ concepts: - concept: divided-difference arity: ">=0" speech: - en: divided difference of a1 .. + en: divided difference of $a1 .. property: "fenced, mixfix" subject-area: "special functions" mathml: @@ -3763,9 +3763,9 @@ concepts: - concept: divisible-by arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 divisible by a2 + en: $a1 divisible by $a2 property: infix subject-area: "number theory" mathml: @@ -3776,16 +3776,16 @@ concepts: - "https://youtu.be/9dyK_op-Ocw?t=251" - "https://en.wikipedia.org/wiki/Divisor" - "https://ru.wikipedia.org/wiki/%D0%94%D0%B5%D0%BB%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C" - - "https://youtu.be/a3wyG2mkmxc?t=32" + - "https://youtu.be/$a3wyG2mkmxc?t=32" alias: - divides - concept: divisor-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: divisor function of a1 + en: divisor function of $a1 property: indexed subject-area: "number theory" mathml: @@ -3800,9 +3800,9 @@ concepts: - concept: domain arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: domain of a1 + en: domain of $a1 property: function subject-area: "set theory" mathml: @@ -3826,9 +3826,9 @@ concepts: - concept: domination-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: domination number of a1 + en: domination number of $a1 property: function subject-area: "graph theory" mathml: @@ -3843,9 +3843,9 @@ concepts: - concept: dot-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 dot product a2 + en: $a1 dot product $a2 property: infix subject-area: "linear algebra" mathml: @@ -3858,9 +3858,9 @@ concepts: - concept: double-bond arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 double bond a2 + en: $a1 double bond $a2 property: infix subject-area: "chemistry" mathml: @@ -3870,9 +3870,9 @@ concepts: - concept: double-category arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 double category a2 + en: $a1 double category $a2 property: infix subject-area: "category theory" mathml: @@ -3882,9 +3882,9 @@ concepts: - concept: double-factorial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: double factorial of a1 + en: double factorial of $a1 property: postfix subject-area: "combinatorics" mathml: @@ -3913,9 +3913,9 @@ concepts: - concept: drinfeld-center arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: drinfeld center of a1 + en: drinfeld center of $a1 property: prefix subject-area: "category theory" mathml: @@ -3927,9 +3927,9 @@ concepts: - concept: dual-basis arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dual basis of a1 + en: dual basis of $a1 property: msup subject-area: "linear algebra" mathml: @@ -3945,9 +3945,9 @@ concepts: - concept: dual-bundle arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dual bundle of a1 + en: dual bundle of $a1 property: msup subject-area: "vector bundles" mathml: @@ -3961,9 +3961,9 @@ concepts: - concept: dual-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: dual space of a1 + en: dual space of $a1 property: msup subject-area: "linear algebra" mathml: @@ -3978,9 +3978,9 @@ concepts: - concept: duodecimal arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: duodecimal of a1 + en: duodecimal of $a1 property: unit subject-area: "arithmetic" mathml: @@ -3996,9 +3996,9 @@ concepts: - concept: e-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: e function of a1 + en: e function of $a1 property: function subject-area: "special functions" mathml: @@ -4026,9 +4026,9 @@ concepts: - concept: edge-cover-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: edge cover number of a1 + en: edge cover number of $a1 property: function subject-area: "graph theory" mathml: @@ -4039,9 +4039,9 @@ concepts: - concept: effective-domain arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: effective domain of a1 + en: effective domain of $a1 property: function subject-area: "convex analysis" mathml: @@ -4051,9 +4051,9 @@ concepts: - concept: efficiency arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: efficiency of a1 + en: efficiency of $a1 property: function subject-area: "statistics" mathml: @@ -4079,9 +4079,9 @@ concepts: - concept: elliptic-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: elliptic function of a1 + en: elliptic function of $a1 property: function subject-area: "special functions" mathml: @@ -4110,9 +4110,9 @@ concepts: - concept: endomorphism-monoid arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: endomorphism monoid of a1 + en: endomorphism monoid of $a1 property: function subject-area: "category theory" mathml: @@ -4150,9 +4150,9 @@ concepts: - concept: entropy arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: entropy of a1 + en: entropy of $a1 property: unit subject-area: "physics" mathml: @@ -4166,9 +4166,9 @@ concepts: - concept: epigraph arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: epigraph of a1 + en: epigraph of $a1 property: function subject-area: "analysis" mathml: @@ -4190,9 +4190,9 @@ concepts: - concept: equalizer arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: equalizer of a1 + en: equalizer of $a1 property: function subject-area: "set theory" mathml: @@ -4207,9 +4207,9 @@ concepts: - concept: equivalence-class arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: equivalence class of a1 + en: equivalence class of $a1 property: fenced subject-area: "set theory" mathml: @@ -4223,9 +4223,9 @@ concepts: - concept: equivalence-relation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 equivalence relation a2 + en: $a1 equivalence relation $a2 property: infix subject-area: "set theory" mathml: @@ -4240,9 +4240,9 @@ concepts: - concept: equivariant-cohomology arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: equivariant cohomology a1 a2 + en: equivariant cohomology $a1 $a2 property: function subject-area: "algebraic topology" mathml: @@ -4267,9 +4267,9 @@ concepts: - concept: error-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: error function of a1 + en: error function of $a1 property: function subject-area: "special functions" mathml: @@ -4284,9 +4284,9 @@ concepts: - concept: essential-extension arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 essential extension a2 + en: $a1 essential extension $a2 property: infix subject-area: "abstract algebra" mathml: @@ -4301,9 +4301,9 @@ concepts: - concept: essential-infimum arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: essential infimum of a1 + en: essential infimum of $a1 property: function subject-area: "measure theory" mathml: @@ -4315,9 +4315,9 @@ concepts: - concept: essential-supremum arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: essential supremum of a1 + en: essential supremum of $a1 property: function subject-area: "measure theory" mathml: @@ -4344,9 +4344,9 @@ concepts: - concept: etale-cohomology arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: etale cohomology of a1 + en: etale cohomology of $a1 property: function subject-area: "algebraic topology" mathml: @@ -4358,9 +4358,9 @@ concepts: - concept: euclid-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: euclid number a1 + en: euclid number $a1 property: symbol subject-area: "number theory" mathml: @@ -4371,9 +4371,9 @@ concepts: - concept: euclidean-distance arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: euclidean distance of a1 + en: euclidean distance of $a1 property: function subject-area: "geometry" mathml: @@ -4400,9 +4400,9 @@ concepts: - concept: euler-characteristic arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: euler characteristic of a1 + en: euler characteristic of $a1 property: function subject-area: "algebraic topology" mathml: @@ -4415,9 +4415,9 @@ concepts: - concept: euler-class arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: euler class of a1 + en: euler class of $a1 property: function subject-area: "algebraic topology" mathml: @@ -4470,9 +4470,9 @@ concepts: - concept: euler-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: euler polynomial of a1 + en: euler polynomial of $a1 property: function subject-area: "special-functions" mathml: @@ -4485,9 +4485,9 @@ concepts: - concept: euler-totient-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: euler totient function of a1 + en: euler totient function of $a1 property: function subject-area: "number theory" mathml: @@ -4515,9 +4515,9 @@ concepts: - concept: eulerian-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: eulerian number of a1 + en: eulerian number of $a1 property: function subject-area: "combinatorics" mathml: @@ -4529,9 +4529,9 @@ concepts: - concept: exclusive-or arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 exclusive or a2 + en: $a1 exclusive or $a2 property: infix subject-area: "logic" mathml: @@ -4551,9 +4551,9 @@ concepts: - concept: expectation-value arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: expectation value of a1 + en: expectation value of $a1 property: fenced subject-area: "quantum physics" mathml: @@ -4565,9 +4565,9 @@ concepts: - concept: expected-value arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: expected value of a1 + en: expected value of $a1 property: function subject-area: "probability theory" mathml: @@ -4585,9 +4585,9 @@ concepts: - concept: exponential-factorial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: exponential factorial of a1 + en: exponential factorial of $a1 property: postfix subject-area: "number theory" mathml: @@ -4598,9 +4598,9 @@ concepts: - concept: exponential-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: exponential integral of a1 + en: exponential integral of $a1 property: subject-area: mathml: @@ -4616,9 +4616,9 @@ concepts: - concept: exterior arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: exterior of a1 + en: exterior of $a1 property: "function, msup" subject-area: "topology" mathml: @@ -4630,9 +4630,9 @@ concepts: - concept: exterior-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: exterior derivative of a1 + en: exterior derivative of $a1 property: operator subject-area: "differential forms" mathml: @@ -4643,9 +4643,9 @@ concepts: - concept: exterior-algebra arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: exterior algebra of a1 + en: exterior algebra of $a1 property: function subject-area: "multilinear algebra" mathml: @@ -4655,9 +4655,9 @@ concepts: - concept: exterior-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 exterior product a2 + en: $a1 exterior product $a2 property: infix subject-area: "multilinear algebra" mathml: @@ -4670,9 +4670,9 @@ concepts: - concept: f-distribution arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: f distribution of a1 + en: f distribution of $a1 property: "indexed symbol" subject-area: "probability theory" mathml: @@ -4683,9 +4683,9 @@ concepts: - concept: faber-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th faber polynomial + en: $a1th faber polynomial property: function subject-area: "polynomials" mathml: @@ -4697,9 +4697,9 @@ concepts: - concept: falling-factorial arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: falling factorial a1 a2 + en: falling factorial $a1 $a2 property: mixfix subject-area: "combinatorics" mathml: @@ -4717,9 +4717,9 @@ concepts: - concept: fatou-set arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fatou set of a1 + en: fatou set of $a1 property: function subject-area: "complex dynamics" mathml: @@ -4767,9 +4767,9 @@ concepts: - concept: fermat-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th fermat number + en: $a1th fermat number property: "indexed symbol" subject-area: "number theory" mathml: @@ -4780,9 +4780,9 @@ concepts: - concept: fermat-quotient arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fermat quotient of a1 + en: fermat quotient of $a1 property: function subject-area: "number theory" mathml: @@ -4793,9 +4793,9 @@ concepts: - concept: fermi-dirac-distribution arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fermi dirac distribution of a1 + en: fermi dirac distribution of $a1 property: function subject-area: "quantum statistics" mathml: @@ -4807,9 +4807,9 @@ concepts: - concept: feynman-slash arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: feynman slash of a1 + en: feynman slash of $a1 property: menclose subject-area: "quantum field theory" mathml: @@ -4819,9 +4819,9 @@ concepts: - concept: fibonacci-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th fibonacci number + en: $a1th fibonacci number property: "indexed symbol" subject-area: "number theory" mathml: @@ -4835,9 +4835,9 @@ concepts: - concept: fibonacci-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fibonacci polynomial of a1 + en: fibonacci polynomial of $a1 property: "indexed function" subject-area: "polynomials" mathml: @@ -4849,9 +4849,9 @@ concepts: - concept: fibre-product arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fibre product of a1 + en: fibre product of $a1 property: indexed infix subject-area: "category theory" mathml: @@ -4866,9 +4866,9 @@ concepts: - concept: field-extension arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 field extension a2 + en: $a1 field extension $a2 property: infix subject-area: "algebra" mathml: @@ -4881,7 +4881,7 @@ concepts: - concept: field-of-sets arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: field of sets property: fenced @@ -4906,9 +4906,9 @@ concepts: - concept: fisher-information arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fisher information of a1 + en: fisher information of $a1 property: function subject-area: "statistics" mathml: @@ -4937,9 +4937,9 @@ concepts: - concept: floor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: floor of a1 + en: floor of $a1 property: fenced, function subject-area: "number theory" mathml: @@ -4954,9 +4954,9 @@ concepts: - concept: fock-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fock space of a1 + en: fock space of $a1 property: function subject-area: "quantum mechanics" mathml: @@ -4968,9 +4968,9 @@ concepts: - concept: forward-difference arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: a1th forward difference of a3 over a2 + en: $a1th forward difference of $a3 over $a2 property: operator subject-area: "numerical analysis" mathml: @@ -4981,9 +4981,9 @@ concepts: - concept: fourier-cosine-transform arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fourier cosine transform of a1 + en: fourier cosine transform of $a1 property: operator subject-area: "functional analysis" mathml: @@ -4995,9 +4995,9 @@ concepts: - concept: fourier-sine-transform arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fourier sine transform of a1 + en: fourier sine transform of $a1 property: operator subject-area: "functional analysis" mathml: @@ -5009,9 +5009,9 @@ concepts: - concept: fourier-transform arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fourier transform of a1 + en: fourier transform of $a1 property: mover subject-area: "fourier analysis" mathml: @@ -5026,9 +5026,9 @@ concepts: - concept: fox-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fox derivative of a1 + en: fox derivative of $a1 property: mfrac subject-area: "geometric topology" mathml: @@ -5040,9 +5040,9 @@ concepts: - concept: fox-wright-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: fox wright function a1 a2 + en: fox wright function $a1 $a2 property: mmultiscripts subject-area: "special functions" mathml: @@ -5054,9 +5054,9 @@ concepts: - concept: fractional-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fractional derivative of a1 + en: fractional derivative of $a1 property: operator subject-area: "fractional caclulus" mathml: @@ -5067,9 +5067,9 @@ concepts: - concept: fractional-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fractional integral of a1 + en: fractional integral of $a1 property: operator subject-area: "fractional caclulus" mathml: @@ -5081,9 +5081,9 @@ concepts: - concept: fractional-part arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fractional part of a1 + en: fractional part of $a1 property: "function, fenced" subject-area: "arithmetic" mathml: @@ -5100,9 +5100,9 @@ concepts: - concept: franel-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th franel number + en: $a1th franel number property: "indexed symbol" subject-area: "combinatorics" mathml: @@ -5112,9 +5112,9 @@ concepts: - concept: frattini-subgroup arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: frattini subgroup of a1 + en: frattini subgroup of $a1 property: function subject-area: "group theory" mathml: @@ -5127,9 +5127,9 @@ concepts: - concept: frechet-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: frechet derivative of a1 + en: frechet derivative of $a1 property: operator subject-area: "banach spaces" mathml: @@ -5157,9 +5157,9 @@ concepts: - concept: fredholm-determinant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fredholm determinant of a1 + en: fredholm determinant of $a1 property: function subject-area: "mathematical physics" mathml: @@ -5171,9 +5171,9 @@ concepts: - concept: free-algebra arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: free algebra a1 a2 + en: free algebra $a1 $a2 property: mixfix subject-area: "ring theory" mathml: @@ -5185,9 +5185,9 @@ concepts: - concept: free-module arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 free module on a2 + en: $a1 free module on $a2 property: mixfix, msup subject-area: "module theory" mathml: @@ -5201,9 +5201,9 @@ concepts: - concept: free-monoid arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: free monoid of a1 + en: free monoid of $a1 property: msup subject-area: "abstract algebra" mathml: @@ -5215,9 +5215,9 @@ concepts: - concept: free-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 free product a2 + en: $a1 free product $a2 property: infix subject-area: "group theory" mathml: @@ -5229,9 +5229,9 @@ concepts: - concept: fresnel-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: fresnel integral of a1 + en: fresnel integral of $a1 property: operator subject-area: "special functions" mathml: @@ -5249,9 +5249,9 @@ concepts: - concept: frobenius-norm arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: frobenius norm of a1 + en: frobenius norm of $a1 property: indexed fenced subject-area: "linear algebra" mathml: @@ -5265,7 +5265,7 @@ concepts: - concept: frolicher-nijenhuis-bracket arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: frolicher nijenhuis bracket property: fenced @@ -5278,9 +5278,9 @@ concepts: - concept: functional-congruence arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: functional congruence of a1 and a2 mod a3 + en: functional congruence of $a1 and $a2 mod $a3 property: mixfix subject-area: "number theory" mathml: @@ -5292,7 +5292,7 @@ concepts: - concept: functor-category arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: functor category property: msup, fenced @@ -5318,9 +5318,9 @@ concepts: - concept: g-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: g function of a1 + en: g function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -5333,9 +5333,9 @@ concepts: - concept: gabor-transform arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: gabor transform of a1 + en: gabor transform of $a1 property: operator subject-area: "integral transforms" mathml: @@ -5347,9 +5347,9 @@ concepts: - concept: gain-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: gain function of a1 + en: gain function of $a1 property: function subject-area: "graph theory" mathml: @@ -5361,9 +5361,9 @@ concepts: - concept: galilean-transformation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: galilean transformation of a1 + en: galilean transformation of $a1 property: function subject-area: "physics" mathml: @@ -5375,9 +5375,9 @@ concepts: - concept: galois-field arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: galois field of a1 + en: galois field of $a1 property: function subject-area: "finite fields" mathml: @@ -5393,9 +5393,9 @@ concepts: - concept: galois-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: galois group of a1 + en: galois group of $a1 property: function subject-area: "abstract algebra" mathml: @@ -5421,9 +5421,9 @@ concepts: - concept: gamma-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: gamma function of a1 + en: gamma function of $a1 property: operator subject-area: "special functions" mathml: @@ -5440,9 +5440,9 @@ concepts: - concept: gateaux-derivative arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: gateaux derivative of a1 at a2 ; £3 + en: gateaux derivative of $a1 at $a2 ; £3 property: mixfix subject-area: "differential calculus" mathml: @@ -5456,9 +5456,9 @@ concepts: - concept: gauss arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: gauss of a1 + en: gauss of $a1 property: unit subject-area: "physics" mathml: @@ -5484,9 +5484,9 @@ concepts: - concept: gaussian-curvature arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: gaussian curvature of a1 + en: gaussian curvature of $a1 property: function subject-area: "differential geometry" mathml: @@ -5512,14 +5512,14 @@ concepts: - concept: gegenbauer-polynomial arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: gegenbauer polynomial property: "indexed function" subject-area: "orthogonal polynomials" mathml: - "Cn(α)(x)" - notation: "msubsup C a1 (a2" + notation: "msubsup C $a1 ($a2" urls: - "https://mathworld.wolfram.com/GegenbauerPolynomial.html" - "https://en.wikipedia.org/wiki/Gegenbauer_polynomials" @@ -5528,9 +5528,9 @@ concepts: - concept: gelfand-triple arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: gelfand triple of a1, a2 and a3 + en: gelfand triple of $a1, $a2 and $a3 property: fenced subject-area: "functional analysis" mathml: @@ -5580,9 +5580,9 @@ concepts: - concept: general-linear-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: general linear group of a1 + en: general linear group of $a1 property: function subject-area: "group theory" mathml: @@ -5597,9 +5597,9 @@ concepts: - concept: generalized-hypergeometric-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: generalized hypergeometric function a1 a2 + en: generalized hypergeometric function $a1 $a2 property: mmultiscripts subject-area: "special functions" mathml: @@ -5619,9 +5619,9 @@ concepts: - concept: generalized-mean arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: generalized mean of a1 + en: generalized mean of $a1 property: function subject-area: "means" mathml: @@ -5636,7 +5636,7 @@ concepts: - concept: genocchi-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: genocchi number property: symbol @@ -5665,9 +5665,9 @@ concepts: - concept: geodesic-distance arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: geodesic distance of a1 + en: geodesic distance of $a1 property: function subject-area: "graph theory" mathml: @@ -5682,9 +5682,9 @@ concepts: - concept: geometric-genus arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: geometric genus of a1 + en: geometric genus of $a1 property: function subject-area: "algebraic geometry" mathml: @@ -5696,21 +5696,21 @@ concepts: - concept: geometric-integral arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: geometric integral over a1 a2 + en: geometric integral over $a1 $a2 property: indexed subject-area: "calculus" mathml: - - "Πab" + - "Πab" urls: - "https://en.wikipedia.org/wiki/Product_integral" - concept: geometric-mean arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: geometric mean of a1 + en: geometric mean of $a1 property: function subject-area: "means" mathml: @@ -5722,9 +5722,9 @@ concepts: - concept: geometric-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 geometric product a2 + en: $a1 geometric product $a2 property: infix subject-area: "geometric algebra" mathml: @@ -5734,9 +5734,9 @@ concepts: - concept: germ arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: germ of a1 at a2 + en: germ of $a1 at $a2 property: mixfix subject-area: "topology" mathml: @@ -5764,9 +5764,9 @@ concepts: - concept: global-dimension arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: global dimension of a1 + en: global dimension of $a1 property: function subject-area: "ring theory" mathml: @@ -5817,9 +5817,9 @@ concepts: - concept: gram-determinant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: gram determinant of a1 + en: gram determinant of $a1 property: function subject-area: "linear algebra" mathml: @@ -5848,9 +5848,9 @@ concepts: - concept: grassmannian arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: grassmannian of a1 + en: grassmannian of $a1 property: function subject-area: "differential geometry" mathml: @@ -5862,9 +5862,9 @@ concepts: - concept: green-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: green function of a1 + en: green function of $a1 property: function subject-area: "mathematical physics" mathml: @@ -5892,9 +5892,9 @@ concepts: - concept: group-algebra arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: group algebra a2 over a1 + en: group algebra $a2 over $a1 property: mixfix subject-area: "ring theory" mathml: @@ -5908,9 +5908,9 @@ concepts: - concept: group-of-units arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: group of units of a1 + en: group of units of $a1 property: msup, function subject-area: "ring theory" mathml: @@ -5923,9 +5923,9 @@ concepts: - concept: group-ring arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: group ring a2 over a1 + en: group ring $a2 over $a1 property: mixfix, infix subject-area: "ring theory" mathml: @@ -5937,9 +5937,9 @@ concepts: - concept: gudermannian-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: gudermannian function of a1 + en: gudermannian function of $a1 property: function subject-area: "trigonometry" mathml: @@ -5953,9 +5953,9 @@ concepts: - concept: hadamard-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 hadamard product a2 + en: $a1 hadamard product $a2 property: infix subject-area: "algebra" mathml: @@ -5971,9 +5971,9 @@ concepts: - concept: hahn-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hahn polynomial of a1 + en: hahn polynomial of $a1 property: function subject-area: "orthogonal polynomials" mathml: @@ -5985,9 +5985,9 @@ concepts: - concept: hamiltonian arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hamiltonian of a1 + en: hamiltonian of $a1 property: operator subject-area: "quantum mechanics" mathml: @@ -6004,9 +6004,9 @@ concepts: - concept: hankel-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hankel function of a1 + en: hankel function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -6018,9 +6018,9 @@ concepts: - concept: hardy-class arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hardy class of a1 + en: hardy class of $a1 property: "indexed symbol" subject-area: "complex analysis" mathml: @@ -6033,9 +6033,9 @@ concepts: - concept: hardy-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hardy space of a1 + en: hardy space of $a1 property: mixfix subject-area: "complex analysis" mathml: @@ -6047,9 +6047,9 @@ concepts: - concept: hardy-littlewood-maximal-operator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hardy littlewood maximal operator of a1 + en: hardy littlewood maximal operator of $a1 property: operator subject-area: "real analysis" mathml: @@ -6061,9 +6061,9 @@ concepts: - concept: harmonic-mean arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: harmonic mean of a1 + en: harmonic mean of $a1 property: function subject-area: "means" mathml: @@ -6077,9 +6077,9 @@ concepts: - concept: hausdorff-measure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hausdorff measure of a1 + en: hausdorff measure of $a1 property: "indexed function" subject-area: "metric geometry" mathml: @@ -6090,9 +6090,9 @@ concepts: - concept: hausdorff-metric arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: hausdorff distance a1 a2 + en: hausdorff distance $a1 $a2 property: function subject-area: "metric geometry" mathml: @@ -6117,9 +6117,9 @@ concepts: - concept: hazard-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hazard function of a1 + en: hazard function of $a1 property: function subject-area: "engineering" mathml: @@ -6131,9 +6131,9 @@ concepts: - concept: heaviside-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: heaviside function of a1 + en: heaviside function of $a1 property: function subject-area: "special functions" mathml: @@ -6147,9 +6147,9 @@ concepts: - concept: heawood-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: heawood number of a1 + en: heawood number of $a1 property: function subject-area: "topological graph theory" mathml: @@ -6159,9 +6159,9 @@ concepts: - concept: hecke-operator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hecke operator of a1 + en: hecke operator of $a1 property: operator subject-area: "modular forms" mathml: @@ -6172,9 +6172,9 @@ concepts: - concept: height-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: height function of a1 + en: height function of $a1 property: function subject-area: "algebra" mathml: @@ -6185,9 +6185,9 @@ concepts: - concept: height-of-abelian-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: height of abelian group of a1 + en: height of abelian group of $a1 property: function subject-area: "group theory" mathml: @@ -6197,9 +6197,9 @@ concepts: - concept: height-of-prime-ideal arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: height of prime ideal of a1 + en: height of prime ideal of $a1 property: function subject-area: "commutative algebra" mathml: @@ -6213,7 +6213,7 @@ concepts: - concept: heisenberg-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: heisenberg group property: symbol @@ -6227,9 +6227,9 @@ concepts: - concept: hermite-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hermite polynomial of a1 + en: hermite polynomial of $a1 property: function subject-area: "special functions" mathml: @@ -6244,9 +6244,9 @@ concepts: - concept: hermitian-adjoint arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hermitian adjoint of a1 + en: hermitian adjoint of $a1 property: msup subject-area: "functional analysis" mathml: @@ -6259,9 +6259,9 @@ concepts: - concept: hermitian-conjugate arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hermitian conjugate of a1 + en: hermitian conjugate of $a1 property: msup subject-area: "linear algebra" mathml: @@ -6274,9 +6274,9 @@ concepts: - concept: heronian-mean arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: heronian mean of a1 + en: heronian mean of $a1 property: function subject-area: "means" mathml: @@ -6287,9 +6287,9 @@ concepts: - concept: hessian arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hessian of a1 + en: hessian of $a1 property: operator subject-area: "differential operators" mathml: @@ -6303,9 +6303,9 @@ concepts: - concept: heun-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: heun function of a1 + en: heun function of $a1 property: function subject-area: "special functions" mathml: @@ -6319,9 +6319,9 @@ concepts: - concept: heun-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: heun polynomial of a1 + en: heun polynomial of $a1 property: function subject-area: "special functions" mathml: @@ -6333,22 +6333,22 @@ concepts: - concept: hexadecimal arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hexadecimal of a1 + en: hexadecimal of $a1 property: unit subject-area: "arithmetic" mathml: - "hexX" - notationb: "msub a1 hex" - notationa: "msub a1 16" + notationb: "msub $a1 hex" + notationa: "msub $a1 16" urls: - "https://mathworld.wolfram.com/Hexadecimal.html" - "https://en.wikipedia.org/wiki/Hexadecimal" - concept: hilbert-symbol arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: hilbert symbol property: fenced @@ -6361,14 +6361,14 @@ concepts: - concept: hilbert-schmidt-norm arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hilbert schmidt norm of a1 + en: hilbert schmidt norm of $a1 property: fenced subject-area: "matrix norms" mathml: - "|X|HS" - notation: "msub mrow | a1 | HS" + notation: "msub mrow | $a1 | HS" urls: - "https://mathworld.wolfram.com/Hilbert-SchmidtNorm.html" - "https://en.wikipedia.org/wiki/Hilbert%E2%80%93Schmidt_operator" @@ -6376,9 +6376,9 @@ concepts: - concept: hit-or-miss-transform arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 hit or miss transform a2 + en: $a1 hit or miss transform $a2 property: infix subject-area: "mathematical morphology" mathml: @@ -6388,9 +6388,9 @@ concepts: - concept: hodge-star-operator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hodge star operator of a1 + en: hodge star operator of $a1 property: prefix subject-area: "differential geometry" mathml: @@ -6401,9 +6401,9 @@ concepts: - concept: holomorph arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: holomorph of a1 + en: holomorph of $a1 property: function subject-area: "group theory" mathml: @@ -6414,9 +6414,9 @@ concepts: - concept: holonomy-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: holonomy group of a1 + en: holonomy group of $a1 property: "indexed symbol" subject-area: "differential geometry" mathml: @@ -6428,9 +6428,9 @@ concepts: - concept: home-prime arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: home prime of a1 + en: home prime of $a1 property: function subject-area: "number theory" mathml: @@ -6441,9 +6441,9 @@ concepts: - concept: homology-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: homology group of a1 + en: homology group of $a1 property: function subject-area: "homology theory" mathml: @@ -6454,9 +6454,9 @@ concepts: - concept: homomorphic-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 homomorphic product a2 + en: $a1 homomorphic product $a2 property: infix subject-area: "graph theory" mathml: @@ -6467,9 +6467,9 @@ concepts: - concept: homotopy-category arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: homotopy category of a1 + en: homotopy category of $a1 property: function subject-area: "category theory" mathml: @@ -6479,9 +6479,9 @@ concepts: - concept: horsepower-mechanical arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 horsepower + en: $a1 horsepower property: unit subject-area: "imperial unit" mathml: @@ -6493,9 +6493,9 @@ concepts: - concept: horsepower-metric arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: horsepower metric of a1 + en: horsepower metric of $a1 property: unit subject-area: "metric unit" mathml: @@ -6512,9 +6512,9 @@ concepts: - concept: hurwitz-zeta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hurwitz zeta function of a1 + en: hurwitz zeta function of $a1 property: function subject-area: "special functions" mathml: @@ -6527,9 +6527,9 @@ concepts: - concept: hvat arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hvat of a1 + en: hvat of $a1 property: unit subject-area: "customary units" mathml: @@ -6542,9 +6542,9 @@ concepts: - concept: hydrated-compound arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 hydrated compound a2 + en: $a1 hydrated compound $a2 property: infix subject-area: "chemistry" mathml: @@ -6557,9 +6557,9 @@ concepts: - concept: hyperbolic-cosine-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hyperbolic cosine integral of a1 + en: hyperbolic cosine integral of $a1 property: function subject-area: "special functions" mathml: @@ -6583,9 +6583,9 @@ concepts: - concept: hyperbolic-sine-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hyperbolic sine integral of a1 + en: hyperbolic sine integral of $a1 property: function subject-area: "special functions" mathml: @@ -6596,22 +6596,22 @@ concepts: - concept: hyperbolic-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: hyperbolic space property: symbol subject-area: "non-euclidean geometry" mathml: - - "Hn" + - "Hn" urls: - "https://mathworld.wolfram.com/HyperbolicSpace.html" - "https://en.wikipedia.org/wiki/Hyperbolic_space" - concept: hyperbolic-umbilic-canonical-integral-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hyperbolic umbilic canonical integral function of a1 + en: hyperbolic umbilic canonical integral function of $a1 property: function subject-area: "special functions" mathml: @@ -6623,9 +6623,9 @@ concepts: - concept: hyperdeterminant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: hyperdeterminant of a1 + en: hyperdeterminant of $a1 property: "function, fenced" subject-area: "multilinear algebra" mathml: @@ -6638,9 +6638,9 @@ concepts: - concept: hypertorus arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th hypertorus + en: $a1th hypertorus property: "indexed symbol" subject-area: "topology" mathml: @@ -6673,9 +6673,9 @@ concepts: - concept: identity-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: identity function of a1 + en: identity function of $a1 property: function subject-area: "algebra" mathml: @@ -6693,9 +6693,9 @@ concepts: - concept: identity-functor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: identity functor of a1 + en: identity functor of $a1 property: function subject-area: "category theory" mathml: @@ -6723,9 +6723,9 @@ concepts: - concept: image arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: image a1 + en: image $a1 property: mixfix subject-area: "set theory" mathml: @@ -6757,9 +6757,9 @@ concepts: - concept: incidence-relation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 incidence relation a2 + en: $a1 incidence relation $a2 property: infix subject-area: "projective geometry" mathml: @@ -6771,9 +6771,9 @@ concepts: - concept: incidence-structure arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: incidence structure of a1, a2 and a3 + en: incidence structure of $a1, $a2 and $a3 property: fenced subject-area: "incidence geometry" mathml: @@ -6783,9 +6783,9 @@ concepts: - concept: inclusion-map arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: inclusion map of a1 + en: inclusion map of $a1 property: function subject-area: "set theory" mathml: @@ -6799,9 +6799,9 @@ concepts: - concept: incomparability arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 incomparable to a2 + en: $a1 incomparable to $a2 property: infix subject-area: "order theory" mathml: @@ -6813,9 +6813,9 @@ concepts: - concept: incomplete-beta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: incomplete beta function of a1 + en: incomplete beta function of $a1 property: function subject-area: "special functions" mathml: @@ -6828,9 +6828,9 @@ concepts: - concept: incomplete-elliptic-integral-of-the-first-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: incomplete elliptic integral of the first kind of a1 + en: incomplete elliptic integral of the first kind of $a1 property: function subject-area: "elliptic functions" mathml: @@ -6842,9 +6842,9 @@ concepts: - concept: incomplete-elliptic-integral-of-the-second-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: incomplete elliptic integral of the second kind of a1 + en: incomplete elliptic integral of the second kind of $a1 property: function subject-area: "elliptic functions" mathml: @@ -6856,9 +6856,9 @@ concepts: - concept: incomplete-gamma-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: incomplete gamma function of a1 + en: incomplete gamma function of $a1 property: function subject-area: "special functions" mathml: @@ -6874,9 +6874,9 @@ concepts: - concept: increase arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: increase of a1 + en: increase of $a1 property: postfix subject-area: "physics" mathml: @@ -6886,9 +6886,9 @@ concepts: - concept: increase-tends-to arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 increase tends to a2 + en: $a1 increase tends to $a2 property: infix subject-area: "calculus" mathml: @@ -6899,9 +6899,9 @@ concepts: - concept: independent arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 independent a2 + en: $a1 independent $a2 property: infix subject-area: "probability theory" mathml: @@ -6914,7 +6914,7 @@ concepts: - concept: index-of-subgroup arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: index of subgroup property: fenced @@ -6928,9 +6928,9 @@ concepts: - concept: index-of-lie-algebra arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: index of lie algebra of a1 + en: index of lie algebra of $a1 property: function subject-area: "lie algebra" mathml: @@ -6940,9 +6940,9 @@ concepts: - concept: infimum arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: infimum of a1 + en: infimum of $a1 property: "function, largeop" subject-area: "order theory" mathml: @@ -6957,9 +6957,9 @@ concepts: - concept: infimum-limit arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: infimum limit of a1 + en: infimum limit of $a1 property: indexed subject-area: "limits" mathml: @@ -6978,9 +6978,9 @@ concepts: - concept: infinite-product arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: infinite product of a1 + en: infinite product of $a1 property: indexed subject-area: "mathematical analysis" mathml: @@ -6992,9 +6992,9 @@ concepts: - concept: infinitely-many-concurrently-active-copies arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: infinitely many concurrently active copies of a1 + en: infinitely many concurrently active copies of $a1 property: prefix subject-area: "formal languages" mathml: @@ -7004,9 +7004,9 @@ concepts: - concept: injection arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: injection a1, from a2 to a3 + en: injection $a1, from $a2 to $a3 property: mixfix, subject-area: "set theory" mathml: @@ -7016,9 +7016,9 @@ concepts: - concept: inner-automorphism-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: inner automorphism group of a1 + en: inner automorphism group of $a1 property: function subject-area: "abstract algebra" mathml: @@ -7033,9 +7033,9 @@ concepts: - concept: inner-jordan-measure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: inner jordan measure of a1 + en: inner jordan measure of $a1 property: function subject-area: "measure theory" mathml: @@ -7047,9 +7047,9 @@ concepts: - concept: inner-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 inner product a2 + en: $a1 inner product $a2 property: infix, fenced subject-area: "linear algebra" mathml: @@ -7064,9 +7064,9 @@ concepts: - concept: instantaneous-activity arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: instantaneous activity of a1 at a2 + en: instantaneous activity of $a1 at $a2 property: mixfix subject-area: "chemistry" mathml: @@ -7076,23 +7076,23 @@ concepts: - concept: integer-part arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: integer part of a1 + en: integer part of $a1 property: "function, fenced" subject-area: "number theory" mathml: - "intX" - notationa: "[ a1 ]" + notationa: "[ $a1 ]" urls: - "https://mathworld.wolfram.com/IntegerPart.html" - "https://en.wikipedia.org/wiki/Floor_and_ceiling_functions" - concept: interior arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: interior of a1 + en: interior of $a1 property: msup subject-area: "topology" mathml: @@ -7106,9 +7106,9 @@ concepts: - concept: interior-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: interior product of a1 a2 + en: interior product of $a1 $a2 property: "infix, indexed function" subject-area: "differential forms" mathml: @@ -7120,9 +7120,9 @@ concepts: - concept: intersection-number arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 intersection number a2 + en: $a1 intersection number $a2 property: infix subject-area: "algebraic geometry" mathml: @@ -7132,9 +7132,9 @@ concepts: - concept: inverse-image arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: inverse image a1 a2 + en: inverse image $a1 $a2 property: mixfix subject-area: "set theory" mathml: @@ -7147,9 +7147,9 @@ concepts: - concept: inverse-limit arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: inverse limit of a1 + en: inverse limit of $a1 property: prefix subject-area: "category theory" mathml: @@ -7163,9 +7163,9 @@ concepts: - concept: inverse-moment-of-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a2th inverse moment of function a1 + en: $a2th inverse moment of function $a1 property: "msub, mixfix" subject-area: "mathematics" mathml: @@ -7177,9 +7177,9 @@ concepts: - concept: inverse-tangent-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: inverse tangent integral of a1 + en: inverse tangent integral of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -7203,7 +7203,7 @@ concepts: - concept: ionic-charge arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: ionic charge property: msup @@ -7215,9 +7215,9 @@ concepts: - concept: isogonal-conjugate arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: isogonal conjugate of a1 + en: isogonal conjugate of $a1 property: msup subject-area: "geometry" mathml: @@ -7228,9 +7228,9 @@ concepts: - concept: isomorphism arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 isomorphism a2 + en: $a1 isomorphism $a2 property: infix subject-area: "set theory" mathml: @@ -7246,7 +7246,7 @@ concepts: - concept: isotropy-group arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: isotropy group property: msub @@ -7262,9 +7262,9 @@ concepts: - concept: iverson-bracket arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: iverson bracket of a1 + en: iverson bracket of $a1 property: fenced subject-area: "set theory" mathml: @@ -7274,9 +7274,9 @@ concepts: - concept: j-invariant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: j invariant of a1 + en: j invariant of $a1 property: function subject-area: "number theory" mathml: @@ -7287,9 +7287,9 @@ concepts: - concept: jacobi-matrix arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: jacobi matrix of a1 + en: jacobi matrix of $a1 property: function subject-area: "operator theory" mathml: @@ -7303,13 +7303,13 @@ concepts: - concept: jacobi-polynomial arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1thjacobi polynomial of a2 + en: $a1thjacobi polynomial of $a2 property: function subject-area: "orthogonal polynomials" mathml: - - "Pnα,β(x)" + - "Pnα,β(x)" notation: "msubsup P" urls: - "https://mathworld.wolfram.com/JacobiPolynomial.html" @@ -7321,7 +7321,7 @@ concepts: - concept: jacobi-symbol arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: jacobi symbol property: mixfix @@ -7336,9 +7336,9 @@ concepts: - concept: jacobi-theta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: jacobi theta function of a1 + en: jacobi theta function of $a1 property: function subject-area: "special-functions" mathml: @@ -7349,7 +7349,7 @@ concepts: - concept: jacobi-zeta-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: jacobi zeta function property: function @@ -7364,9 +7364,9 @@ concepts: - concept: jacobian-elliptic-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: jacobian elliptic function of a1 + en: jacobian elliptic function of $a1 property: function subject-area: "special-functions" mathml: @@ -7387,9 +7387,9 @@ concepts: - concept: jacobson-radical arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: jacobson radical of a1 + en: jacobson radical of $a1 property: function subject-area: "ring theory" mathml: @@ -7432,9 +7432,9 @@ concepts: - concept: jet arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: a1 jet of a3 at a2 + en: $a1 jet of $a3 at $a2 property: function subject-area: "differential geometry" mathml: @@ -7445,9 +7445,9 @@ concepts: - concept: join arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: join of a1 + en: join of $a1 property: indexed subject-area: "measure theory" mathml: @@ -7461,9 +7461,9 @@ concepts: - concept: jone-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: jone polynomial of a1 + en: jone polynomial of $a1 property: function subject-area: "knot theory" mathml: @@ -7475,7 +7475,7 @@ concepts: - concept: jordan-block arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: jordan block property: "indexed symbol" @@ -7490,9 +7490,9 @@ concepts: - concept: jordan-measure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: jordan measure of a1 + en: jordan measure of $a1 property: function subject-area: "measure theory" mathml: @@ -7504,9 +7504,9 @@ concepts: - concept: jordan-totient-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: jordan totient function of a1 + en: jordan totient function of $a1 property: function subject-area: "number theory" mathml: @@ -7516,9 +7516,9 @@ concepts: - concept: julia-set arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: julia set of a1 + en: julia set of $a1 property: function subject-area: "complex dynamics" mathml: @@ -7545,9 +7545,9 @@ concepts: - concept: kauffman-bracket arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kauffman bracket of a1 + en: kauffman bracket of $a1 property: fenced subject-area: "knot theory" mathml: @@ -7559,9 +7559,9 @@ concepts: - concept: kelvin-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th order kelvin function + en: $a1th order kelvin function property: function subject-area: "special functions" mathml: @@ -7579,9 +7579,9 @@ concepts: - concept: kernel arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kernel of a1 + en: kernel of $a1 property: function subject-area: "linear algebra" mathml: @@ -7616,9 +7616,9 @@ concepts: - concept: killing-form arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: killing form of a1 + en: killing form of $a1 property: function subject-area: "lie algebra" mathml: @@ -7631,9 +7631,9 @@ concepts: - concept: kleene-star arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kleene star of a1 + en: kleene star of $a1 property: msup subject-area: "formal languages" mathml: @@ -7643,9 +7643,9 @@ concepts: - concept: kleene-plus arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kleene plus of a1 + en: kleene plus of $a1 property: msup subject-area: "formal languages" mathml: @@ -7669,9 +7669,9 @@ concepts: - concept: kloosterman-sum arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kloosterman sum of a1 + en: kloosterman sum of $a1 property: function subject-area: "analytic number theory" mathml: @@ -7683,9 +7683,9 @@ concepts: - concept: kneser-graph arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: kneser graph a1 a2 + en: kneser graph $a1 $a2 property: "indexed symbol" subject-area: "graph theory" mathml: @@ -7697,9 +7697,9 @@ concepts: - concept: knodel-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: knodel number of a1 + en: knodel number of $a1 property: "indexed symbol" subject-area: "number theory" mathml: @@ -7710,9 +7710,9 @@ concepts: - concept: kodaira-dimension arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kodaira dimension of a1 + en: kodaira dimension of $a1 property: function subject-area: "algebraic geometry" mathml: @@ -7723,9 +7723,9 @@ concepts: - concept: kolmogorov-complexity arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kolmogorov complexity of a1 + en: kolmogorov complexity of $a1 property: function subject-area: "information theory" mathml: @@ -7748,9 +7748,9 @@ concepts: - concept: kontsevich-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kontsevich integral of a1 + en: kontsevich integral of $a1 property: function subject-area: "knot theory" mathml: @@ -7763,9 +7763,9 @@ concepts: - concept: krawtchouk-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: krawtchouk polynomial of a1 + en: krawtchouk polynomial of $a1 property: function subject-area: "orthogonal polynomials" mathml: @@ -7778,7 +7778,7 @@ concepts: - concept: kripke-frame arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: kripke frame property: fenced @@ -7790,7 +7790,7 @@ concepts: - concept: kronecker-delta arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: kronecker delta property: "indexed function" @@ -7805,9 +7805,9 @@ concepts: - concept: kronecker-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 kronecker product a2 + en: $a1 kronecker product $a2 property: infix subject-area: "matrix theory" mathml: @@ -7821,7 +7821,7 @@ concepts: - concept: kronecker-symbol arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: kronecker symbol property: fenced, fenced stacked @@ -7836,9 +7836,9 @@ concepts: - concept: krull-dimension arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: krull dimension of a1 + en: krull dimension of $a1 property: function subject-area: "commutative algebra" mathml: @@ -7850,9 +7850,9 @@ concepts: - concept: kulkarni-nomizu-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: kulkarni nomizu product of a1 and a2 + en: kulkarni nomizu product of $a1 and $a2 property: embellished infix subject-area: "differential geometry" mathml: @@ -7862,9 +7862,9 @@ concepts: - concept: kullback-leibler-distance arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: kullback leibler distance of a1 + en: kullback leibler distance of $a1 property: function subject-area: "mathematical statistics" mathml: @@ -7881,13 +7881,13 @@ concepts: - concept: lagrange-bracket arity: 4 - arguments: [a1, a2, a3, a4] + arguments: [$a1, $a2, $a3, $a4] speech: - en: "lagrange bracket of a1, a2, canonical coordinates a3, a4" + en: "lagrange bracket of $a1, $a2, canonical coordinates $a3, $a4" property: indexed fenced subject-area: "classical mechanics" mathml: - - "[u,v]p,q" + - "[u,v]p,q" urls: - "https://mathworld.wolfram.com/LagrangeBracket.html" - "https://en.wikipedia.org/wiki/Lagrange_bracket" @@ -7932,9 +7932,9 @@ concepts: - concept: laguerre-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: laguerre polynomial of a1 + en: laguerre polynomial of $a1 property: "indexed function" subject-area: "orthogonal polynomials" mathml: @@ -7964,9 +7964,9 @@ concepts: - concept: laplace-operator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: laplace operator of a1 + en: laplace operator of $a1 property: "embellished operator" subject-area: "differential operators" mathml: @@ -7980,9 +7980,9 @@ concepts: - concept: laplace-transform arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: laplace transform of a1 + en: laplace transform of $a1 property: operator subject-area: "integral transforms" mathml: @@ -8008,9 +8008,9 @@ concepts: - concept: latin-rectangle arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: latin rectangle a1 + en: latin rectangle $a1 property: mtable subject-area: "combinatorial mathematics" mathml: @@ -8023,9 +8023,9 @@ concepts: - concept: latin-square arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: latin square a1 + en: latin square $a1 property: mtable subject-area: "combinatorial mathematics" mathml: @@ -8039,9 +8039,9 @@ concepts: - concept: least-prime-factor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: least prime factor of a1 + en: least prime factor of $a1 property: function subject-area: "number theory" mathml: @@ -8051,9 +8051,9 @@ concepts: - concept: lebesgue-constant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lebesgue constant of a1 + en: lebesgue constant of $a1 property: indexed constant subject-area: "fourier series" mathml: @@ -8066,9 +8066,9 @@ concepts: - concept: lebesgue-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lebesgue integral of a1 + en: lebesgue integral of $a1 property: indexed subject-area: "measure theory" mathml: @@ -8093,9 +8093,9 @@ concepts: - concept: left-adjoint arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 left adjoint a2 + en: $a1 left adjoint $a2 property: infix subject-area: "category theory" mathml: @@ -8105,9 +8105,9 @@ concepts: - concept: left-composition arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 left composition a2 + en: $a1 left composition $a2 property: infix subject-area: "algebra" mathml: @@ -8119,9 +8119,9 @@ concepts: - concept: left-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: left derivative of a1 + en: left derivative of $a1 property: operator subject-area: "calculus" mathml: @@ -8131,9 +8131,9 @@ concepts: - concept: legendre-chi-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: legendre chi function of a1 + en: legendre chi function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -8144,9 +8144,9 @@ concepts: - concept: legendre-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: legendre polynomial of a1 + en: legendre polynomial of $a1 property: function subject-area: "orthogonal polynomials" mathml: @@ -8160,7 +8160,7 @@ concepts: - concept: legendre-symbol arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: legendre symbol property: fenced, fenced stacked @@ -8175,9 +8175,9 @@ concepts: - concept: lehmer-mean arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lehmer mean of a1 + en: lehmer mean of $a1 property: "indexed function" subject-area: "means" mathml: @@ -8188,9 +8188,9 @@ concepts: - concept: lehmer-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lehmer number of a1 + en: lehmer number of $a1 property: "indexed function" subject-area: "number theory" mathml: @@ -8202,9 +8202,9 @@ concepts: - concept: level arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: level of a1 + en: level of $a1 property: function subject-area: "scales of measurement" mathml: @@ -8216,13 +8216,13 @@ concepts: - concept: levi-civita-symbol arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: levi civita symbol of a1, a2 and a3 + en: levi civita symbol of $a1, $a2 and $a3 property: "indexed symbol" subject-area: "combinatorics" mathml: - - "ϵijk" + - "ϵijk" urls: - "https://mathworld.wolfram.com/Levi-CivitaSymbol.html" - "https://en.wikipedia.org/wiki/Levi-Civita_symbol" @@ -8232,9 +8232,9 @@ concepts: - concept: levy-prokhorov-metric arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: levy prokhorov metric of a1 + en: levy prokhorov metric of $a1 property: function subject-area: "measure theory" mathml: @@ -8245,9 +8245,9 @@ concepts: - concept: lexicographic-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 lexicographic product a2 + en: $a1 lexicographic product $a2 property: infix, mixfix subject-area: "graph theory" mathml: @@ -8259,9 +8259,9 @@ concepts: - concept: lexicographic-order arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 lexicographic order a2 + en: $a1 lexicographic order $a2 property: infix subject-area: "discrete mathematics" mathml: @@ -8275,9 +8275,9 @@ concepts: - concept: lie-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lie derivative of a1 + en: lie derivative of $a1 property: "indexed operator" subject-area: "lie algebra" mathml: @@ -8289,7 +8289,7 @@ concepts: - concept: lie-superbracket arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: lie superbracket property: fenced @@ -8303,9 +8303,9 @@ concepts: - concept: like-charge arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 like charge a2 + en: $a1 like charge $a2 property: infix subject-area: "physics" mathml: @@ -8315,9 +8315,9 @@ concepts: - concept: line-graph arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: line graph of a1 + en: line graph of $a1 property: function subject-area: "graph theory" mathml: @@ -8328,9 +8328,9 @@ concepts: - concept: line-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: line integral of a1 + en: line integral of $a1 property: indexed subject-area: "analysis" mathml: @@ -8347,9 +8347,9 @@ concepts: - concept: linear-span arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: linear span of a1 + en: linear span of $a1 property: function subject-area: "linear algebra" mathml: @@ -8363,9 +8363,9 @@ concepts: - concept: link arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: link of a1 + en: link of $a1 property: function subject-area: "graph theory" mathml: @@ -8375,9 +8375,9 @@ concepts: - concept: gunter-link arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: gunter link of a1 + en: gunter link of $a1 property: unit subject-area: "units" mathml: @@ -8403,9 +8403,9 @@ concepts: - concept: liouville-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: liouville function of a1 + en: liouville function of $a1 property: function subject-area: "number theory" mathml: @@ -8417,9 +8417,9 @@ concepts: - concept: localization arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: localization of a2 by a1 + en: localization of $a2 by $a1 property: mixfix subject-area: "module theory" mathml: @@ -8433,9 +8433,9 @@ concepts: - concept: logarithmic-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: logarithmic integral of a1 + en: logarithmic integral of $a1 property: function subject-area: "special functions" mathml: @@ -8447,14 +8447,14 @@ concepts: - concept: logarithmic-moment-of-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1th logarithmic moment of a2 + en: $a1th logarithmic moment of $a2 property: "mixfix" subject-area: "mathematics" mathml: - "E[lnn(X)]" - notation: "E [ msup ln a1 /msup ( a2 ) ]" + notation: "E [ msup ln $a1 /msup ( $a2 ) ]" urls: - "https://en.wikipedia.org/wiki/Moment_(mathematics)" alias: @@ -8462,9 +8462,9 @@ concepts: - concept: logit arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: logit of a1 + en: logit of $a1 property: function subject-area: "statistics" mathml: @@ -8474,9 +8474,9 @@ concepts: - concept: lommel-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 ,a2 lommel function + en: $a1 ,$a2 lommel function property: "indexed function" subject-area: "special functions" mathml: @@ -8490,9 +8490,9 @@ concepts: - concept: long-division arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: long division of a1 by a2 + en: long division of $a1 by $a2 property: mfrac subject-area: "arithmetic" comments: @@ -8503,9 +8503,9 @@ concepts: - concept: loop-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: loop space of a1 + en: loop space of $a1 property: function subject-area: "topology" mathml: @@ -8517,9 +8517,9 @@ concepts: - concept: lower-closure-poset arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lower closure poset of a1 + en: lower closure poset of $a1 property: prefix subject-area: "order theory" mathml: @@ -8529,9 +8529,9 @@ concepts: - concept: lower-darboux-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lower darboux integral of a1 + en: lower darboux integral of $a1 property: indexed subject-area: "real analysis" mathml: @@ -8544,9 +8544,9 @@ concepts: - concept: lower-dini-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lower dini derivative of a1 + en: lower dini derivative of $a1 property: decorated function subject-area: "analysis" mathml: @@ -8558,9 +8558,9 @@ concepts: - concept: lower-shadow arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lower shadow of a1 + en: lower shadow of $a1 property: function subject-area: "combinatorics" mathml: @@ -8573,9 +8573,9 @@ concepts: - concept: lucas-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lucas number of a1 + en: lucas number of $a1 property: "indexed symbol" subject-area: "integer sequences" mathml: @@ -8587,9 +8587,9 @@ concepts: - concept: lucas-sequence arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lucas sequence of a1 + en: lucas sequence of $a1 property: "indexed function" subject-area: "integer sequences" mathml: @@ -8601,9 +8601,9 @@ concepts: - concept: lyapunov-candidate-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: lyapunov candidate function of a1 + en: lyapunov candidate function of $a1 property: function subject-area: "stability theory" mathml: @@ -8617,9 +8617,9 @@ concepts: - concept: macdonald-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: macdonald polynomial of a1 + en: macdonald polynomial of $a1 property: function subject-area: "orthogonal polynomials" mathml: @@ -8630,9 +8630,9 @@ concepts: - concept: mahler-measure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mahler measure of a1 + en: mahler measure of $a1 property: function subject-area: "number theory" mathml: @@ -8644,9 +8644,9 @@ concepts: - concept: mangoldt-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mangoldt function of a1 + en: mangoldt function of $a1 property: function subject-area: "special functions" mathml: @@ -8660,9 +8660,9 @@ concepts: - concept: mapping-class-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mapping class group of a1 + en: mapping class group of $a1 property: function subject-area: "geometric topology" mathml: @@ -8673,14 +8673,14 @@ concepts: - concept: mapping-cone arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mapping cone of a1 + en: mapping cone of $a1 property: "indexed symbol" subject-area: "homotopy theory" mathml: - "Cx" - notationa: "mrow C a1" + notationa: "mrow C $a1" urls: - "https://en.wikipedia.org/wiki/Mapping_cone_(topology)" - "https://en.wikipedia.org/wiki/Mapping_cone_(homological_algebra)" @@ -8690,9 +8690,9 @@ concepts: - concept: matching-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: matching polynomial of a1 + en: matching polynomial of $a1 property: "indexed function" subject-area: "graph theory" mathml: @@ -8704,9 +8704,9 @@ concepts: - concept: mathieu-function-of-first-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mathieu function of first kind of a1 + en: mathieu function of first kind of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -8731,9 +8731,9 @@ concepts: - concept: mathieu-function-of-second-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mathieu function of second kind of a1 + en: mathieu function of second kind of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -8758,9 +8758,9 @@ concepts: - concept: mathieu-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mathieu group a1 + en: mathieu group $a1 property: "indexed symbol" subject-area: "group theory" mathml: @@ -8783,9 +8783,9 @@ concepts: - concept: matrix arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: matrix a1 + en: matrix $a1 property: mtable, fenced subject-area: "algebra" mathml: @@ -8804,9 +8804,9 @@ concepts: - concept: matrix-ring arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: matrix ring of a1 + en: matrix ring of $a1 property: function subject-area: "abstract algebra" mathml: @@ -8817,9 +8817,9 @@ concepts: - concept: maximum-degree arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: maximum degree of a1 + en: maximum degree of $a1 property: function subject-area: "graph theory" mathml: @@ -8831,9 +8831,9 @@ concepts: - concept: mean-curvature arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mean curvature of a1 + en: mean curvature of $a1 property: function subject-area: "differential geometry" mathml: @@ -8845,9 +8845,9 @@ concepts: - concept: mean-squared-error arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mean squared error of a1 + en: mean squared error of $a1 property: function subject-area: "statistics" mathml: @@ -8857,9 +8857,9 @@ concepts: - concept: meixner-pollaczek-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: meixner pollaczek polynomial of a1 + en: meixner pollaczek polynomial of $a1 property: "indexed function" subject-area: "orthogonal polynomials" mathml: @@ -8871,9 +8871,9 @@ concepts: - concept: mellin-transform arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mellin transform of a1 + en: mellin transform of $a1 property: operator subject-area: "integral transforms" mathml: @@ -8886,9 +8886,9 @@ concepts: - concept: meridian-radius-of-curvature arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: meridian radius of curvature of a1 + en: meridian radius of curvature of $a1 property: function subject-area: "geodesy" mathml: @@ -8899,9 +8899,9 @@ concepts: - concept: meridian-distance arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: meridian distance of a1 + en: meridian distance of $a1 property: function subject-area: "geodesy" mathml: @@ -8911,9 +8911,9 @@ concepts: - concept: mersenne-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mersenne number of a1 + en: mersenne number of $a1 property: "indexed symbol" subject-area: "number theory" mathml: @@ -8924,9 +8924,9 @@ concepts: - concept: mersenne-prime arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mersenne prime of a1 + en: mersenne prime of $a1 property: "indexed symbol" subject-area: "number theory" mathml: @@ -8938,9 +8938,9 @@ concepts: - concept: merten-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: merten function of a1 + en: merten function of $a1 property: function subject-area: "number theory" mathml: @@ -8951,9 +8951,9 @@ concepts: - concept: meson arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: meson of a1 + en: meson of $a1 property: urls: - "https://en.wikipedia.org/wiki/Meson" @@ -8962,7 +8962,7 @@ concepts: - concept: metaplectic-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: metaplectic group property: symbol @@ -8990,9 +8990,9 @@ concepts: - concept: mills-ratio arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mills ratio of a1 + en: mills ratio of $a1 property: function subject-area: "probability theory" mathml: @@ -9005,9 +9005,9 @@ concepts: - concept: minimum-degree arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: minimum degree of a1 + en: minimum degree of $a1 property: function subject-area: "graph theory" mathml: @@ -9019,9 +9019,9 @@ concepts: - concept: minkowski-difference arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 minkowski difference a2 + en: $a1 minkowski difference $a2 property: infix subject-area: "geometry" mathml: @@ -9033,9 +9033,9 @@ concepts: - concept: minkowski-sum arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 minkowski sum a2 + en: $a1 minkowski sum $a2 property: infix subject-area: "geometry" mathml: @@ -9048,9 +9048,9 @@ concepts: - concept: mittag-leffler-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mittag leffler function of a1 + en: mittag leffler function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -9063,9 +9063,9 @@ concepts: - concept: mobius-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mobius function of a1 + en: mobius function of $a1 property: function subject-area: "number theory" mathml: @@ -9079,9 +9079,9 @@ concepts: - concept: modified-bessel-function-of-first-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: modified bessel function of first kind of a1 + en: modified bessel function of first kind of $a1 property: function subject-area: "special functions" mathml: @@ -9093,9 +9093,9 @@ concepts: - concept: modified-bessel-function-of-second-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: modified bessel function of second kind of a1 + en: modified bessel function of second kind of $a1 property: function subject-area: "special functions" mathml: @@ -9107,9 +9107,9 @@ concepts: - concept: modified-mathieu-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: modified mathieu function of a1 + en: modified mathieu function of $a1 property: function subject-area: "special functions" mathml: @@ -9133,9 +9133,9 @@ concepts: - concept: modified-spherical-bessel-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: modified spherical bessel function of a1 + en: modified spherical bessel function of $a1 property: function subject-area: "special functions" mathml: @@ -9150,9 +9150,9 @@ concepts: - concept: modified-struve-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: modified struve function of a1 + en: modified struve function of $a1 property: function subject-area: "special functions" mathml: @@ -9164,9 +9164,9 @@ concepts: - concept: modular-discriminant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: modular discriminant of a1 + en: modular discriminant of $a1 property: operator subject-area: "special functions" mathml: @@ -9177,9 +9177,9 @@ concepts: - concept: modulo arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 modulo a2 + en: $a1 modulo $a2 property: infix, mixfix subject-area: "modular arithmetic" mathml: @@ -9194,9 +9194,9 @@ concepts: - concept: moebius-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: moebius function of a1 + en: moebius function of $a1 property: function subject-area: "number theory" mathml: @@ -9207,14 +9207,14 @@ concepts: - concept: moment-of-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1th moment + en: $a1th moment property: "msub, mixfix" subject-area: "mathematics" mathml: - "μn" - notationa: "mrow E [ msup a1 a2 ]" + notationa: "mrow E [ msup $a1 $a2 ]" urls: - "https://en.wikipedia.org/wiki/Moment_(mathematics)" alias: @@ -9289,9 +9289,9 @@ concepts: - concept: moore-penrose-inverse arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: moore penrose inverse of a1 + en: moore penrose inverse of $a1 property: msup subject-area: "linear algebra" mathml: @@ -9303,9 +9303,9 @@ concepts: - concept: moore-smith-sequence arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: moore smith sequence of a1 + en: moore smith sequence of $a1 property: fenced subject-area: "topology" mathml: @@ -9318,9 +9318,9 @@ concepts: - concept: motzkin-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: motzkin number of a1 + en: motzkin number of $a1 property: "indexed symbol" subject-area: "combinatorial analysis" mathml: @@ -9334,9 +9334,9 @@ concepts: - concept: multiple-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: multiple integral of a1 + en: multiple integral of $a1 property: indexed subject-area: "multivariable calculus" mathml: @@ -9349,9 +9349,9 @@ concepts: - concept: multiplicative-inverse arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: multiplicative inverse of a1 + en: multiplicative inverse of $a1 property: msup, mixfix subject-area: "abstract algebra" mathml: @@ -9369,9 +9369,9 @@ concepts: - concept: multiplicative-order arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: multiplicative order of a1 + en: multiplicative order of $a1 property: "indexed function" subject-area: "modular arithmetic" mathml: @@ -9383,9 +9383,9 @@ concepts: - concept: multiplier-algebra arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: multiplier algebra of a1 + en: multiplier algebra of $a1 property: function subject-area: "functional analysis" mathml: @@ -9397,7 +9397,7 @@ concepts: - concept: multichoose arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: multichoose property: fenced-stacked @@ -9409,7 +9409,7 @@ concepts: - concept: multiset-coefficient arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: multiset coefficient property: fenced-stacked @@ -9423,7 +9423,7 @@ concepts: - concept: multivariate-gaussian-distribution arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: multivariate gaussian distribution property: symbol @@ -9438,14 +9438,14 @@ concepts: - concept: mutation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: mutation property: msup subject-area: "abstract algebra" mathml: - "Ay" - notation: "msup a1 a2" + notation: "msup $a1 $a2" urls: - "https://mathworld.wolfram.com/Mutation.html" - "https://en.wikipedia.org/wiki/Mutation_(knot_theory)" @@ -9458,9 +9458,9 @@ concepts: - concept: mutual-information arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: mutual information of a1 + en: mutual information of $a1 property: function subject-area: "information theory" mathml: @@ -9471,7 +9471,7 @@ concepts: - concept: narayana-number arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: narayana number property: function @@ -9485,9 +9485,9 @@ concepts: - concept: narrow-denjoy-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: narrow denjoy integral of a1 + en: narrow denjoy integral of $a1 property: indexed subject-area: "calculus" mathml: @@ -9517,9 +9517,9 @@ concepts: - concept: negative-hypergeometric-distribution arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: negative hypergeometric distribution of a1 + en: negative hypergeometric distribution of $a1 property: "indexed symbol" subject-area: "probability theory" mathml: @@ -9530,15 +9530,15 @@ concepts: - concept: neighbourhood arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: neighbourhood of a2 in a1 + en: neighbourhood of $a2 in $a1 property: "indexed function, function" subject-area: "graph theory" mathml: - "Nv(G)" - notation: "msub N a1 ( a2 )" - notationa: "mrow N ( a1" + notation: "msub N $a1 ( $a2 )" + notationa: "mrow N ( $a1" urls: - "https://en.wikipedia.org/wiki/Neighbourhood_(graph_theory)" alias: @@ -9546,9 +9546,9 @@ concepts: - concept: neighbourhood-filter arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: neighbourhood filter of a1 + en: neighbourhood filter of $a1 property: function subject-area: "topology" mathml: @@ -9561,9 +9561,9 @@ concepts: - concept: neron-severi-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: neron severi group of a1 + en: neron severi group of $a1 property: function subject-area: "group theory" mathml: @@ -9588,9 +9588,9 @@ concepts: - concept: nerve arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: nerve of a1 + en: nerve of $a1 property: function subject-area: "category theory" mathml: @@ -9602,9 +9602,9 @@ concepts: - concept: nome arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: nome of a1 + en: nome of $a1 property: function subject-area: "special functions" mathml: @@ -9615,9 +9615,9 @@ concepts: - concept: non-oriented-angle arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: non oriented angle of a1 + en: non oriented angle of $a1 property: prefix subject-area: "geometry" mathml: @@ -9630,9 +9630,9 @@ concepts: - concept: nor arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 nor a2 + en: $a1 nor $a2 property: infix subject-area: "logic" mathml: @@ -9645,14 +9645,14 @@ concepts: - concept: norm arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: norm of a1 + en: norm of $a1 property: fenced subject-area: "linear algebra" mathml: - "‖x‖" - notationa: "mrow | a1" + notationa: "mrow | $a1" urls: - "https://mathworld.wolfram.com/Norm.html" - "https://en.wikipedia.org/wiki/Norm_(mathematics)" @@ -9662,9 +9662,9 @@ concepts: - concept: normalizer arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: normalizer of a1 + en: normalizer of $a1 property: function subject-area: "group theory" mathml: @@ -9676,9 +9676,9 @@ concepts: - concept: not-divisible-by arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 not divisible by a2 + en: $a1 not divisible by $a2 property: infix subject-area: "number theory" mathml: @@ -9688,9 +9688,9 @@ concepts: - concept: null-graph arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: null graph of order a1 + en: null graph of order $a1 property: symbol subject-area: "graph theory" mathml: @@ -9704,9 +9704,9 @@ concepts: - concept: numerical-part arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: numerical part of a1 + en: numerical part of $a1 property: fenced subject-area: "SI units" mathml: @@ -9716,9 +9716,9 @@ concepts: - concept: object arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: object of a1 + en: object of $a1 property: prefix subject-area: "category theory" mathml: @@ -9730,9 +9730,9 @@ concepts: - concept: octant arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: octant of a1, a2 and a3 + en: octant of $a1, $a2 and $a3 property: fenced subject-area: "euclidean solid geometry" mathml: @@ -9775,9 +9775,9 @@ concepts: - concept: onsager-machlup-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: onsager machlup function of a1 + en: onsager machlup function of $a1 property: function subject-area: "functional analysis" mathml: @@ -9789,9 +9789,9 @@ concepts: - concept: open-ball arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: open ball a1 a2 + en: open ball $a1 $a2 property: mixfix subject-area: "topology" mathml: @@ -9804,7 +9804,7 @@ concepts: - concept: open-interval arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: open interval property: fenced @@ -9818,9 +9818,9 @@ concepts: - concept: open-real-interval arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: open real interval a1 to a2 + en: open real interval $a1 to $a2 property: fenced subject-area: "algebra" mathml: @@ -9830,9 +9830,9 @@ concepts: - concept: opposite arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: opposite of a1 + en: opposite of $a1 property: msup subject-area: "category theory,, group theory" mathml: @@ -9847,9 +9847,9 @@ concepts: - concept: opposite-charge arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 opposite charge a2 + en: $a1 opposite charge $a2 property: infix subject-area: "physics" mathml: @@ -9859,9 +9859,9 @@ concepts: - concept: or-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 or product a2 + en: $a1 or product $a2 property: infix subject-area: "graph theory" mathml: @@ -9874,9 +9874,9 @@ concepts: - concept: order-of-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: order of group of a1 + en: order of group of $a1 property: "function, fenced" subject-area: "group theory" mathml: @@ -9887,9 +9887,9 @@ concepts: - concept: orthocomplement arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: orthocomplement of a1 + en: orthocomplement of $a1 property: msup subject-area: "lattice theory" mathml: @@ -9899,9 +9899,9 @@ concepts: - concept: orthogonal arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 orthogonal a2 + en: $a1 orthogonal $a2 property: infix subject-area: "geometry,, algebra" mathml: @@ -9918,9 +9918,9 @@ concepts: - concept: orthogonal-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: orthogonal group of a1 + en: orthogonal group of $a1 property: function subject-area: "group theory" mathml: @@ -9934,9 +9934,9 @@ concepts: - concept: outer-automorphism-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: outer automorphism group of a1 + en: outer automorphism group of $a1 property: function subject-area: "abstract algebra" mathml: @@ -9949,9 +9949,9 @@ concepts: - concept: outer-jordan-measure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: outer jordan measure of a1 + en: outer jordan measure of $a1 property: function subject-area: "measure theory" mathml: @@ -9963,9 +9963,9 @@ concepts: - concept: outer-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 outer product a2 + en: $a1 outer product $a2 property: infix subject-area: "linear algebra" mathml: @@ -9977,9 +9977,9 @@ concepts: - concept: p-core arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: p core of a1 + en: p core of $a1 property: function subject-area: "group theory" mathml: @@ -9992,9 +9992,9 @@ concepts: - concept: pade-approximant arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: pade approximant of a1, a2 and a3 + en: pade approximant of $a1, $a2 and $a3 property: mixfix subject-area: "numerical analysis" mathml: @@ -10006,9 +10006,9 @@ concepts: - concept: padovan-sequence arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: padovan sequence of a1 + en: padovan sequence of $a1 property: function subject-area: "number theory" mathml: @@ -10019,9 +10019,9 @@ concepts: - concept: paraboloidal-coordinate arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: paraboloidal coordinate of a1, a2 and a3 + en: paraboloidal coordinate of $a1, $a2 and $a3 property: fenced subject-area: "geometry" mathml: @@ -10033,9 +10033,9 @@ concepts: - concept: parallel arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 parallel a2 + en: $a1 parallel $a2 property: infix subject-area: "geometry" mathml: @@ -10047,7 +10047,7 @@ concepts: - concept: parallel-morphism arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: parallel morphism property: embellished infix @@ -10059,7 +10059,7 @@ concepts: - concept: partial-charge arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: partial charge property: symbol @@ -10075,9 +10075,9 @@ concepts: - concept: partition arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 partition a2 + en: $a1 partition $a2 property: infix subject-area: "number theory" mathml: @@ -10091,7 +10091,7 @@ concepts: - concept: partition-frequency-representation arity: ">=0" speech: - en: "partition a1 sup a2, a2 sup a3, ..." + en: "partition $a1 sup $a2, $a2 sup $a3, ..." property: mixfix subject-area: "number theory" mathml: @@ -10101,9 +10101,9 @@ concepts: - concept: partition-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: partition function of a1 + en: partition function of $a1 property: function subject-area: "number theory" mathml: @@ -10113,9 +10113,9 @@ concepts: - concept: pauli-matrix arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: pauli matrix of a1 + en: pauli matrix of $a1 property: "indexed symbol" subject-area: "mathematical physics" mathml: @@ -10128,9 +10128,9 @@ concepts: - concept: peclet-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: peclet number of a1 + en: peclet number of $a1 property: "indexed symbol" subject-area: "fluid dynamics" mathml: @@ -10142,9 +10142,9 @@ concepts: - concept: peirce-arrow arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 peirce arrow a2 + en: $a1 peirce arrow $a2 property: infix subject-area: "logic" mathml: @@ -10154,7 +10154,7 @@ concepts: - concept: pell-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: pell number property: symbol @@ -10167,7 +10167,7 @@ concepts: - concept: pell-luca-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: pell luca number property: symbol @@ -10180,9 +10180,9 @@ concepts: - concept: periodic-continued-fraction arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: periodic continued fraction a1 + en: periodic continued fraction $a1 property: mfrac subject-area: "mathematical analysis" mathml: @@ -10193,9 +10193,9 @@ concepts: - concept: permanent arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: permanent of a1 + en: permanent of $a1 property: function subject-area: "linear algebra" mathml: @@ -10207,9 +10207,9 @@ concepts: - concept: permutation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: permutation a1 + en: permutation $a1 property: fenced, mtable, mixfix subject-area: "combinatorics" mathml: @@ -10224,9 +10224,9 @@ concepts: - concept: perpendicular arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 perpendicular a2 + en: $a1 perpendicular $a2 property: infix subject-area: "geometry" mathml: @@ -10237,9 +10237,9 @@ concepts: - concept: perrin-sequence arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: perrin sequence of a1 + en: perrin sequence of $a1 property: function subject-area: "number theory" mathml: @@ -10250,9 +10250,9 @@ concepts: - concept: pfaffian arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: pfaffian of a1 + en: pfaffian of $a1 property: function subject-area: "multilinear algebra" mathml: @@ -10282,9 +10282,9 @@ concepts: - concept: phase arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: phase of a1 + en: phase of $a1 property: function subject-area: "physics" mathml: @@ -10313,9 +10313,9 @@ concepts: - concept: picard-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: picard group of a1 + en: picard group of $a1 property: function subject-area: "group theory" mathml: @@ -10364,7 +10364,7 @@ concepts: - concept: playing-card-suit arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: playing card suit property: unit @@ -10381,9 +10381,9 @@ concepts: - concept: plethysm arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: plethysm a1 a2 + en: plethysm $a1 $a2 property: mixfix subject-area: "algebra" mathml: @@ -10395,7 +10395,7 @@ concepts: - concept: plucker-coordinate arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: plucker coordinate property: fenced @@ -10409,9 +10409,9 @@ concepts: - concept: pointwise-convergent arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 converges pointwise + en: $a1 converges pointwise property: postfix subject-area: "convergence" mathml: @@ -10423,7 +10423,7 @@ concepts: - concept: poisson-bracket arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: poisson bracket property: fenced @@ -10452,9 +10452,9 @@ concepts: - concept: polar-set arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: polar set of a1 + en: polar set of $a1 property: msup subject-area: "functional analysis" mathml: @@ -10466,9 +10466,9 @@ concepts: - concept: pollaczek-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th pollaczek polynomial + en: $a1th pollaczek polynomial property: "indexed function" subject-area: "orthogonal polynomials" mathml: @@ -10480,9 +10480,9 @@ concepts: - concept: polygamma-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: polygamma function of a1 + en: polygamma function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -10495,9 +10495,9 @@ concepts: - concept: polynomial-ring arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: polynomial ring a1 a2 + en: polynomial ring $a1 $a2 property: mixfix subject-area: "ring theory" mathml: @@ -10509,9 +10509,9 @@ concepts: - concept: polylogarithm arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: polylogarithm of a1 + en: polylogarithm of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -10525,9 +10525,9 @@ concepts: - concept: pontrjagin-dual arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: pontrjagin dual of a1 + en: pontrjagin dual of $a1 property: mover subject-area: "harmonic analysis" mathml: @@ -10538,9 +10538,9 @@ concepts: - concept: pontryagin-class arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: pontryagin class of a1 + en: pontryagin class of $a1 property: "indexed symbol" subject-area: "differential topology" mathml: @@ -10553,14 +10553,14 @@ concepts: - concept: positive-part arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: positive part of a1 + en: positive part of $a1 property: msup, msub subject-area: "elementary mathematics" mathml: - "X+" - notationa: "msub a1 +" + notationa: "msub $a1 +" urls: - "https://mathworld.wolfram.com/PositiveElement.html" - "https://en.wikipedia.org/wiki/Positive_and_negative_parts" @@ -10568,9 +10568,9 @@ concepts: - concept: positivitiy-predicate arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: positivitiy predicate of a1 + en: positivitiy predicate of $a1 property: prefix subject-area: "predicative mathematics" mathml: @@ -10580,9 +10580,9 @@ concepts: - concept: post-canonical-system arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: post canonical system a1 a2 a3 + en: post canonical system $a1 $a2 $a3 property: fenced subject-area: "formal languages" mathml: @@ -10594,9 +10594,9 @@ concepts: - concept: power-set arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: power set of a1 + en: power set of $a1 property: "function, msup" subject-area: "set theory" mathml: @@ -10605,7 +10605,7 @@ concepts: - "ℙX" - "℘X" - "2X" - notationa: "msup 2 a1" + notationa: "msup 2 $a1" urls: - "https://mathworld.wolfram.com/PowerSet.html" - "https://en.wikipedia.org/wiki/Power_set" @@ -10655,9 +10655,9 @@ concepts: - concept: prime-counting-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: prime counting function of a1 + en: prime counting function of $a1 property: function subject-area: "number theory" mathml: @@ -10667,9 +10667,9 @@ concepts: - concept: prime-difference-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: prime difference function of a1 + en: prime difference function of $a1 property: "indexed function" subject-area: "number theory" mathml: @@ -10679,9 +10679,9 @@ concepts: - concept: prime-gap arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: prime gap of a1 + en: prime gap of $a1 property: "indexed function" subject-area: "number theory" mathml: @@ -10693,9 +10693,9 @@ concepts: - concept: primorial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: primorial of a1 + en: primorial of $a1 property: postfix subject-area: "number theory" mathml: @@ -10706,9 +10706,9 @@ concepts: - concept: principal-value arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: principal value of a1 + en: principal value of $a1 property: function subject-area: "complex analysis" mathml: @@ -10718,9 +10718,9 @@ concepts: - concept: probability-limit arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: probability limit of a1 + en: probability limit of $a1 property: "indexed function" subject-area: "probability theory" mathml: @@ -10732,9 +10732,9 @@ concepts: - concept: product-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: product integral of a1 + en: product integral of $a1 property: indexed subject-area: "calculus" mathml: @@ -10746,7 +10746,7 @@ concepts: - concept: product-measure arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: product measure property: function @@ -10759,9 +10759,9 @@ concepts: - concept: projective-line arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: projective line of a1 + en: projective line of $a1 property: function subject-area: "projective geometry" mathml: @@ -10791,9 +10791,9 @@ concepts: - concept: proper-subgroup arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 proper subgroup a2 + en: $a1 proper subgroup $a2 property: infix subject-area: "group theory" mathml: @@ -10803,9 +10803,9 @@ concepts: - concept: proportional arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 proportional a2 + en: $a1 proportional $a2 property: infix subject-area: "arithmetic" mathml: @@ -10832,14 +10832,14 @@ concepts: - concept: prufer-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: prufer group of a1 + en: prufer group of $a1 property: mixfix subject-area: "group theory" mathml: - "𝐙(p∞)" - notation: "mrow Z ( msup a1 ∞ /msup" + notation: "mrow Z ( msup $a1 ∞ /msup" urls: - "https://en.wikipedia.org/wiki/Pr%C3%BCfer_group" alias: @@ -10847,9 +10847,9 @@ concepts: - concept: pseudovector arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: pseudovector a1 + en: pseudovector $a1 property: mixfix subject-area: "vector calculus" mathml: @@ -10862,7 +10862,7 @@ concepts: - concept: pseudo-inner-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: pseudo inner product property: fenced @@ -10886,9 +10886,9 @@ concepts: - concept: pushforward arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 pushforward a2 + en: $a1 pushforward $a2 property: infix subject-area: "differential geometry" mathml: @@ -10916,9 +10916,9 @@ concepts: - concept: pythagorean-triple arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: pythagorean triple a1, a2 and a3 + en: pythagorean triple $a1, $a2 and $a3 property: fenced subject-area: "geometry" mathml: @@ -10929,9 +10929,9 @@ concepts: - concept: q-binomial-coefficient arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: a3 q binomial coefficient of a1, a2 + en: $a3 q binomial coefficient of $a1, $a2 property: fenced-stacked subject-area: "combinatorics" mathml: @@ -10957,14 +10957,14 @@ concepts: - concept: quadratic-differential arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: quadratic differential of a1 + en: quadratic differential of $a1 property: mixfix subject-area: "complex manifolds" mathml: - "f(z)dz⊗dz" - notation: "mrow d a1 d a1" + notation: "mrow d $a1 d $a1" urls: - "https://en.wikipedia.org/wiki/Quadratic_differential" - "https://ncatlab.org/nlab/show/quadratic+differential" @@ -10972,22 +10972,22 @@ concepts: - concept: quadratic-variation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: quadratic variation a1 a2 + en: quadratic variation $a1 $a2 property: indexed fenced subject-area: "stochastic processes" mathml: - "[X]t" - notation: "msub mrow [ a1 ] /mrow a2" + notation: "msub mrow [ $a1 ] /mrow $a2" urls: - "https://en.wikipedia.org/wiki/Quadratic_variation" - concept: quadrilateral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: quadrilateral of a1 + en: quadrilateral of $a1 property: prefix subject-area: "geometry" mathml: @@ -11001,9 +11001,9 @@ concepts: - concept: quotient-group arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 quotient group a2 + en: $a1 quotient group $a2 property: infix subject-area: "group theory" mathml: @@ -11015,9 +11015,9 @@ concepts: - concept: quotient-space arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 quotient space a2 + en: $a1 quotient space $a2 property: infix subject-area: "topology" mathml: @@ -11047,9 +11047,9 @@ concepts: - concept: racah-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: racah polynomial of a1 + en: racah polynomial of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -11061,9 +11061,9 @@ concepts: - concept: radial-mathieu-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: radial mathieu function of a1 + en: radial mathieu function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -11076,9 +11076,9 @@ concepts: - concept: radical arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: radical of a1 + en: radical of $a1 property: function subject-area: "number theory" mathml: @@ -11113,9 +11113,9 @@ concepts: - concept: ramanujan-sum arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: ramanujan sum of a1 + en: ramanujan sum of $a1 property: "indexed function" subject-area: "number theory" mathml: @@ -11127,9 +11127,9 @@ concepts: - concept: ramanujan-tau-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: ramanujan tau function of a1 + en: ramanujan tau function of $a1 property: function subject-area: "number theory" mathml: @@ -11157,9 +11157,9 @@ concepts: - concept: ramification-index arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: ramification index of a1 + en: ramification index of $a1 property: msub subject-area: "algebraic number theory" mathml: @@ -11170,9 +11170,9 @@ concepts: - concept: ramsey-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: ramsey number of a1 + en: ramsey number of $a1 property: function subject-area: "graph theory" mathml: @@ -11183,9 +11183,9 @@ concepts: - concept: rank arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: rank of a1 + en: rank of $a1 property: function subject-area: "graph theory, linear algebra, " mathml: @@ -11202,9 +11202,9 @@ concepts: - concept: real-bipolar arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: real bipolar of a1 + en: real bipolar of $a1 property: msup subject-area: "functional analysis" mathml: @@ -11216,9 +11216,9 @@ concepts: - concept: real-part arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: real part of a1 + en: real part of $a1 property: function subject-area: "complex analysis" mathml: @@ -11232,9 +11232,9 @@ concepts: - concept: real-prepolar arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: real prepolar of a1 + en: real prepolar of $a1 property: prescript subject-area: "functional analysis" mathml: @@ -11246,9 +11246,9 @@ concepts: - concept: real-polar arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: real polar of a1 + en: real polar of $a1 property: msup subject-area: "functional analysis" mathml: @@ -11260,9 +11260,9 @@ concepts: - concept: recession-cone arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: recession cone of a1 + en: recession cone of $a1 property: function subject-area: "convex analysis" mathml: @@ -11272,9 +11272,9 @@ concepts: - concept: reciprocal-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: reciprocal polynomial of a1 + en: reciprocal polynomial of $a1 property: msup subject-area: "algebra" mathml: @@ -11288,9 +11288,9 @@ concepts: - concept: rectification arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: rectification of a1 + en: rectification of $a1 property: function subject-area: "euclidean geometry" mathml: @@ -11302,9 +11302,9 @@ concepts: - concept: reduced-suspension arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: reduced suspension of a1 + en: reduced suspension of $a1 property: function subject-area: "topology" mathml: @@ -11314,9 +11314,9 @@ concepts: - concept: relative-homology arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: relative homology of a1 + en: relative homology of $a1 property: "indexed function" subject-area: "algebraic topology" mathml: @@ -11328,9 +11328,9 @@ concepts: - concept: repunit arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: repunit of a1 + en: repunit of $a1 property: "indexed symbol" subject-area: "number theory" mathml: @@ -11342,9 +11342,9 @@ concepts: - concept: residue arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: residue of a1 + en: residue of $a1 property: function subject-area: "complex analysis" mathml: @@ -11357,7 +11357,7 @@ concepts: - concept: resolvent arity: 1 - arguments: [a1] + arguments: [$a1] speech: en: resolvent property: "indexed function" @@ -11371,9 +11371,9 @@ concepts: - concept: resolvent-set arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: resolvent set of a1 + en: resolvent set of $a1 property: function subject-area: "set theory" mathml: @@ -11384,9 +11384,9 @@ concepts: - concept: restricted-quantifier arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: restricted quantifier a1 a2 + en: restricted quantifier $a1 $a2 property: mixfix subject-area: "formal logic" mathml: @@ -11398,9 +11398,9 @@ concepts: - concept: restricted-wreath-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 restricted wreath product a2 + en: $a1 restricted wreath product $a2 property: infix subject-area: "group theory" mathml: @@ -11414,7 +11414,7 @@ concepts: - concept: restriction arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: restriction property: indexed postfix @@ -11430,9 +11430,9 @@ concepts: - concept: resultant arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: resultant of a1 + en: resultant of $a1 property: function subject-area: "polynomials" mathml: @@ -11448,9 +11448,9 @@ concepts: - concept: rewrite-rule arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 rewrite rule a2 + en: $a1 rewrite rule $a2 property: infix subject-area: "logic" mathml: @@ -11491,9 +11491,9 @@ concepts: - concept: ricci-tensor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: ricci tensor of a1 + en: ricci tensor of $a1 property: "indexed symbol" subject-area: "riemannian geometry" mathml: @@ -11504,9 +11504,9 @@ concepts: - concept: riemann-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: riemann integral of a1 + en: riemann integral of $a1 property: indexed subject-area: "calculus" mathml: @@ -11540,9 +11540,9 @@ concepts: - concept: riemann-theta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: riemann theta function of a1 + en: riemann theta function of $a1 property: function subject-area: "special functions" mathml: @@ -11554,9 +11554,9 @@ concepts: - concept: riemann-zeta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: riemann zeta function of a1 + en: riemann zeta function of $a1 property: function subject-area: "special functions" mathml: @@ -11572,9 +11572,9 @@ concepts: - concept: riemann-christoffel-tensor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: riemann christoffel tensor of a1 + en: riemann christoffel tensor of $a1 property: "indexed function" subject-area: "riemannian geometry" mathml: @@ -11589,9 +11589,9 @@ concepts: - concept: riemann-stieltje-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: riemann stieltje integral of a1 + en: riemann stieltje integral of $a1 property: indexed subject-area: "measure theory" mathml: @@ -11608,9 +11608,9 @@ concepts: - concept: right-angle arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: right angle of a1 + en: right angle of $a1 property: prefix subject-area: "geometry" mathml: @@ -11624,9 +11624,9 @@ concepts: - concept: right-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: right derivative of a1 + en: right derivative of $a1 property: operator subject-area: "calculus" mathml: @@ -11636,9 +11636,9 @@ concepts: - concept: right-quotient arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 right quotient a2 + en: $a1 right quotient $a2 property: infix subject-area: "formal languages" mathml: @@ -11648,9 +11648,9 @@ concepts: - concept: ring-of-formal-power-series arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: ring of formal power series a1 a2 + en: ring of formal power series $a1 $a2 property: mixfix subject-area: "ring theory" mathml: @@ -11660,9 +11660,9 @@ concepts: - concept: rising-factorial arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a2th rising factorial of a1 + en: $a2th rising factorial of $a1 property: mixfix subject-area: "combinatorics" mathml: @@ -11704,9 +11704,9 @@ concepts: - concept: roof arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: roof of a1, a2 and a3 + en: roof of $a1, $a2 and $a3 property: mixfix subject-area: "category theory" mathml: @@ -11734,9 +11734,9 @@ concepts: - concept: root-mean-square arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: root mean square of a1 + en: root mean square of $a1 property: msub subject-area: "means" mathml: @@ -11749,9 +11749,9 @@ concepts: - concept: rooted-product-of-graphs arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 rooted product of graphs a2 + en: $a1 rooted product of graphs $a2 property: infix subject-area: "graph theory" mathml: @@ -11813,9 +11813,9 @@ concepts: - concept: sample-variance arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: sample variance of a1 + en: sample variance of $a1 property: embellished symbol subject-area: "probability theory" mathml: @@ -11827,9 +11827,9 @@ concepts: - concept: scalar-triple-product arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: scalar triple product of a1, a2 and a3 + en: scalar triple product of $a1, $a2 and $a3 property: mixfix, fenced subject-area: "vector algebra" mathml: @@ -11841,9 +11841,9 @@ concepts: - concept: scaled-riemann-theta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: scaled riemann theta function of a1 + en: scaled riemann theta function of $a1 property: mover subject-area: "special functions" mathml: @@ -11855,7 +11855,7 @@ concepts: - concept: schlaefli-symbol arity: ">=0" speech: - en: schlaefli symbol of a1, ... + en: schlaefli symbol of $a1, ... property: fenced subject-area: "geometry" mathml: @@ -11865,9 +11865,9 @@ concepts: - concept: schroder-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: schroder number of a1 + en: schroder number of $a1 property: "indexed symbol" subject-area: "combinatorics" mathml: @@ -11879,9 +11879,9 @@ concepts: - concept: schur-multiplier arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: schur multiplier of a1 + en: schur multiplier of $a1 property: function subject-area: "group theory" mathml: @@ -11910,14 +11910,14 @@ concepts: - concept: schwarzian-derivative arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: schwarzian derivative a1 a2 + en: schwarzian derivative $a1 $a2 property: fenced, mixfix subject-area: "complex analysis" mathml: - "{x,y}" - notationa: "mrow ( S a1 ) (a2" + notationa: "mrow ( S $a1 ) ($a2" urls: - "https://mathworld.wolfram.com/SchwarzianDerivative.html" - "https://en.wikipedia.org/wiki/Schwarzian_derivative" @@ -11926,9 +11926,9 @@ concepts: - concept: second-carmichael-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: second carmichael function of a1 + en: second carmichael function of $a1 property: function subject-area: "number theory" mathml: @@ -11939,9 +11939,9 @@ concepts: - concept: sectional-curvature arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: sectional curvature of a1 + en: sectional curvature of $a1 property: function subject-area: "riemannian geometry" mathml: @@ -11967,7 +11967,7 @@ concepts: - concept: selection arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: en: selection property: "indexed function" @@ -11979,9 +11979,9 @@ concepts: - concept: seminorm arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: seminorm of a1 + en: seminorm of $a1 property: fenced subject-area: "linear algebra" mathml: @@ -11995,9 +11995,9 @@ concepts: - concept: set-of-invertible-maps arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: set of invertible maps of a1 + en: set of invertible maps of $a1 property: prefix subject-area: "commutative algebra" mathml: @@ -12024,9 +12024,9 @@ concepts: - concept: shift-operator arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: shift operator of a1 + en: shift operator of $a1 property: operator subject-area: "functional analysis" mathml: @@ -12041,9 +12041,9 @@ concepts: - concept: shimura-variety arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: shimura variety of a1 + en: shimura variety of $a1 property: function subject-area: "algebraic geometry" mathml: @@ -12055,9 +12055,9 @@ concepts: - concept: short-exact-sequence arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: short exact sequence a1 a2 a3 + en: short exact sequence $a1 $a2 $a3 property: mixfix subject-area: "group theory" mathml: @@ -12098,9 +12098,9 @@ concepts: - concept: sign-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: sign function of a1 + en: sign function of $a1 property: function subject-area: "special-functions" mathml: @@ -12112,9 +12112,9 @@ concepts: - concept: signature-of-permutation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: signature of permutation of a1 + en: signature of permutation of $a1 property: function subject-area: "combinatorics" mathml: @@ -12140,9 +12140,9 @@ concepts: - concept: similar arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 similar a2 + en: $a1 similar $a2 property: infix subject-area: "geometry" mathml: @@ -12154,9 +12154,9 @@ concepts: - concept: simplex arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 simplex + en: $a1 simplex property: "indexed symbol" subject-area: "geometry" mathml: @@ -12170,9 +12170,9 @@ concepts: - concept: sinc-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: sinc function of a1 + en: sinc function of $a1 property: function subject-area: "special functions" mathml: @@ -12185,9 +12185,9 @@ concepts: - concept: sine-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: sine integral of a1 + en: sine integral of $a1 property: operator subject-area: "special functions" mathml: @@ -12212,9 +12212,9 @@ concepts: - concept: skewes-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: skewes number of a1 + en: skewes number of $a1 property: "indexed symbol" subject-area: "number theory" mathml: @@ -12225,9 +12225,9 @@ concepts: - concept: small-o arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: small o of a1 + en: small o of $a1 property: prefix subject-area: "complexity" mathml: @@ -12238,9 +12238,9 @@ concepts: - concept: smith-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: smith number of a1 + en: smith number of $a1 property: "indexed symbol" subject-area: "number theory" mathml: @@ -12251,7 +12251,7 @@ concepts: - concept: sobolev-space arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: sobolev space property: "indexed symbol" @@ -12266,9 +12266,9 @@ concepts: - concept: socle arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: socle of a1 + en: socle of $a1 property: function subject-area: "group theory" mathml: @@ -12308,9 +12308,9 @@ concepts: - concept: span arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1 span + en: $a1 span property: unit subject-area: "imperial units" mathml: @@ -12320,9 +12320,9 @@ concepts: - concept: special-linear-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: special linear group of a1 + en: special linear group of $a1 property: "indexed function" subject-area: "group theory" mathml: @@ -12335,9 +12335,9 @@ concepts: - concept: special-orthogonal-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: special orthogonal group of a1 + en: special orthogonal group of $a1 property: "indexed function" subject-area: "group theory" mathml: @@ -12348,9 +12348,9 @@ concepts: - concept: special-unitary-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: special unitary group of a1 + en: special unitary group of $a1 property: function subject-area: "lie groups" mathml: @@ -12362,9 +12362,9 @@ concepts: - concept: spectral-radius arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: spectral radius of a1 + en: spectral radius of $a1 property: function subject-area: "spectral theory" mathml: @@ -12376,9 +12376,9 @@ concepts: - concept: spectrum arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: spectrum of a1 + en: spectrum of $a1 property: function subject-area: "functional analysis" mathml: @@ -12400,9 +12400,9 @@ concepts: - concept: spectrum-of-matrix arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: spectrum of matrix of a1 + en: spectrum of matrix of $a1 property: msub subject-area: "linear algebra" mathml: @@ -12412,9 +12412,9 @@ concepts: - concept: spectrum-of-algebra arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: spectrum of algebra of a1 + en: spectrum of algebra of $a1 property: mover subject-area: "algebra" mathml: @@ -12424,9 +12424,9 @@ concepts: - concept: spectrum-of-ring arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: spectrum of ring of a1 + en: spectrum of ring of $a1 property: function subject-area: "group theory" mathml: @@ -12436,7 +12436,7 @@ concepts: - concept: spherical-bessel-function-of-third-kind arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: en: spherical bessel function of third kind property: "indexed function" @@ -12451,7 +12451,7 @@ concepts: - concept: spherical-coordinate arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: en: spherical coordinate property: fenced @@ -12503,9 +12503,9 @@ concepts: - concept: square arity: 4 - arguments: [a1, a2, a3, a4] + arguments: [$a1, $a2, $a3, $a4] speech: - en: "square a1 a2 a3 a4" + en: "square $a1 $a2 $a3 $a4" property: prefix subject-area: "geometry" mathml: @@ -12531,9 +12531,9 @@ concepts: - concept: stalk arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: stalk of a1 at a2 + en: stalk of $a1 at $a2 property: msub subject-area: "sheaf theory" mathml: @@ -12558,9 +12558,9 @@ concepts: - concept: standard-flattening arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: standard flattening of a1 + en: standard flattening of $a1 property: "indexed symbol" subject-area: "multilinear algebra" mathml: @@ -12573,9 +12573,9 @@ concepts: - concept: stanley-reisner-ring arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: stanley reisner ring a1 a2 + en: stanley reisner ring $a1 $a2 property: mixfix subject-area: "commutative algebra" mathml: @@ -12589,9 +12589,9 @@ concepts: - concept: stanley-reisner-ideal arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: stanley reisner ideal of a1 + en: stanley reisner ideal of $a1 property: msub subject-area: "commutative algebra" mathml: @@ -12618,9 +12618,9 @@ concepts: - concept: star-height arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: star height of a1 + en: star height of $a1 property: function subject-area: "formal languages" mathml: @@ -12630,9 +12630,9 @@ concepts: - concept: steinberg-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: steinberg group of a1 + en: steinberg group of $a1 property: function subject-area: "k-theory" mathml: @@ -12644,14 +12644,14 @@ concepts: - concept: stiefel-manifold arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1th stiefel manifold over a2 + en: $a1th stiefel manifold over $a2 property: mixfix subject-area: "differential geometry" mathml: - "Vk(ℝn)" - notation: "mrow msub V a1 /msub ( a2" + notation: "mrow msub V $a1 /msub ( $a2" urls: - "https://mathworld.wolfram.com/StiefelManifold.html" - "https://en.wikipedia.org/wiki/Stiefel_manifold" @@ -12659,9 +12659,9 @@ concepts: - concept: stiefel-whitney-class arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: stiefel whitney class of a1 + en: stiefel whitney class of $a1 property: function subject-area: "algebraic topology" mathml: @@ -12675,9 +12675,9 @@ concepts: - concept: stieltjes-wigert-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: stieltjes wigert polynomial of a1 + en: stieltjes wigert polynomial of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -12689,9 +12689,9 @@ concepts: - concept: stirling-number-of-first-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: stirling number of first kind of a1 + en: stirling number of first kind of $a1 property: function subject-area: "special functions" mathml: @@ -12703,9 +12703,9 @@ concepts: - concept: stirling-number-of-second-kind arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: stirling number of second kind of a1 + en: stirling number of second kind of $a1 property: function subject-area: "special functions" mathml: @@ -12717,9 +12717,9 @@ concepts: - concept: strength-of-a-graph arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: strength of a graph of a1 + en: strength of a graph of $a1 property: function subject-area: "graph theory" mathml: @@ -12731,9 +12731,9 @@ concepts: - concept: string-concatenation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 string concatenation a2 + en: $a1 string concatenation $a2 property: infix subject-area: "computer science" mathml: @@ -12745,9 +12745,9 @@ concepts: - concept: strong-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 strong product a2 + en: $a1 strong product $a2 property: infix subject-area: "graph theory" mathml: @@ -12760,9 +12760,9 @@ concepts: - concept: struve-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: struve function of a1 + en: struve function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -12776,9 +12776,9 @@ concepts: - concept: stufe arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: stufe of a1 + en: stufe of $a1 property: function subject-area: "field theory" mathml: @@ -12788,9 +12788,9 @@ concepts: - concept: subfactorial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: subfactorial of a1 + en: subfactorial of $a1 property: prefix subject-area: "combinatorics" mathml: @@ -12803,9 +12803,9 @@ concepts: - concept: subgroup arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 subgroup a2 + en: $a1 subgroup $a2 property: infix subject-area: "group theory" mathml: @@ -12818,9 +12818,9 @@ concepts: - concept: succeeds arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 succeeds a2 + en: $a1 succeeds $a2 property: infix subject-area: "set theory" mathml: @@ -12831,9 +12831,9 @@ concepts: - concept: succeeds-or-equals arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 succeeds or equals a2 + en: $a1 succeeds or equals $a2 property: infix subject-area: "set theory" mathml: @@ -12843,9 +12843,9 @@ concepts: - concept: successor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: successor of a1 + en: successor of $a1 property: "function, msup" subject-area: "number theory" mathml: @@ -12860,9 +12860,9 @@ concepts: - concept: such-that arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 such that a2 + en: $a1 such that $a2 property: infix subject-area: "set theory" mathml: @@ -12873,9 +12873,9 @@ concepts: - concept: sumset arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 sumset a2 + en: $a1 sumset $a2 property: infix subject-area: "set theory" mathml: @@ -12886,9 +12886,9 @@ concepts: - concept: superfluous-submodule arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 superfluous submodule a2 + en: $a1 superfluous submodule $a2 property: infix subject-area: "abstract algebra" mathml: @@ -12901,9 +12901,9 @@ concepts: - concept: support arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: support of a1 + en: support of $a1 property: function subject-area: "analysis" mathml: @@ -12920,9 +12920,9 @@ concepts: - concept: supremum arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: supremum of a1 + en: supremum of $a1 property: "function, largeop" subject-area: "order theory, lattice theory" mathml: @@ -12936,9 +12936,9 @@ concepts: - concept: supremum-limit arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: supremum limit of a1 + en: supremum limit of $a1 property: indexed subject-area: "limits" mathml: @@ -12957,9 +12957,9 @@ concepts: - concept: surface-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: surface integral of a1 + en: surface integral of $a1 property: indexed subject-area: "calculus" mathml: @@ -12971,9 +12971,9 @@ concepts: - concept: surjection arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: surjection a1, from a2 to a3 + en: surjection $a1, from $a2 to $a3 property: mixfix, infix subject-area: "set theory" mathml: @@ -12984,9 +12984,9 @@ concepts: - concept: suspension arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: suspension of a1 + en: suspension of $a1 property: function subject-area: "topology" mathml: @@ -12999,9 +12999,9 @@ concepts: - concept: symmetric-algebra arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: symmetric algebra of a1 + en: symmetric algebra of $a1 property: function subject-area: "algebra" mathml: @@ -13014,9 +13014,9 @@ concepts: - concept: symmetric-difference arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 symmetric difference a2 + en: $a1 symmetric difference $a2 property: infix subject-area: "set theory" mathml: @@ -13030,18 +13030,18 @@ concepts: - concept: symmetric-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: symmetric group of a1 + en: symmetric group of $a1 property: "msub, function, postfix" subject-area: "group theory" mathml: - "Sx" - "𝔖x" - "Σx" - notationd: "mrow Σ ( a1 )" - notationc: "mrow Sym ( a1 )" - notationb: "mrow a1 !" + notationd: "mrow Σ ( $a1 )" + notationc: "mrow Sym ( $a1 )" + notationb: "mrow $a1 !" notationa: "" urls: - "https://mathworld.wolfram.com/SymmetricGroup.html" @@ -13062,9 +13062,9 @@ concepts: - concept: symplectic-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: symplectic group of a1 + en: symplectic group of $a1 property: function subject-area: "group theory" mathml: @@ -13078,9 +13078,9 @@ concepts: - concept: szego-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: szego polynomial of a1 + en: szego polynomial of $a1 property: "indexed function" subject-area: "orthogonal polynomials" mathml: @@ -13092,9 +13092,9 @@ concepts: - concept: tangent-bundle arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: tangent bundle of a1 + en: tangent bundle of $a1 property: function subject-area: "differential geometry" mathml: @@ -13107,9 +13107,9 @@ concepts: - concept: tangent-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: tangent space of a1 + en: tangent space of $a1 property: "indexed function" subject-area: "topology" mathml: @@ -13135,9 +13135,9 @@ concepts: - concept: tate-module arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: tate module of a1 + en: tate module of $a1 property: "indexed function" subject-area: "group theory" mathml: @@ -13161,9 +13161,9 @@ concepts: - concept: taxicab-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: taxicab number of a1 + en: taxicab number of $a1 property: function subject-area: "number theory" mathml: @@ -13174,9 +13174,9 @@ concepts: - concept: taylor-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: taylor polynomial of a1 + en: taylor polynomial of $a1 property: function subject-area: "number theory" mathml: @@ -13188,9 +13188,9 @@ concepts: - concept: teichmuller-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: teichmuller space of a1 + en: teichmuller space of $a1 property: function subject-area: "differential geometry" mathml: @@ -13216,9 +13216,9 @@ concepts: - concept: tensor-algebra arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: tensor algebra of a1 + en: tensor algebra of $a1 property: function subject-area: "multilinear algebra" mathml: @@ -13229,9 +13229,9 @@ concepts: - concept: tensor-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 tensor product a2 + en: $a1 tensor product $a2 property: infix subject-area: "algebra" mathml: @@ -13245,9 +13245,9 @@ concepts: - concept: tensor-product-of-graphs arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 tensor product of graphs a2 + en: $a1 tensor product of graphs $a2 property: infix subject-area: "graph theory" mathml: @@ -13260,9 +13260,9 @@ concepts: - concept: therefore-sign arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: therefore a1 + en: therefore $a1 property: prefix subject-area: "logic" mathml: @@ -13274,9 +13274,9 @@ concepts: - concept: theta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: theta function of a1 + en: theta function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -13291,9 +13291,9 @@ concepts: - concept: thom-space arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: thom space of a1 + en: thom space of $a1 property: function subject-area: "algebraic topology" mathml: @@ -13319,9 +13319,9 @@ concepts: - concept: to arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 to a2 + en: $a1 to $a2 property: infix subject-area: "arithmetic" mathml: @@ -13331,9 +13331,9 @@ concepts: - concept: todd-class arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: todd class of a1 + en: todd class of $a1 property: function subject-area: "characteristic classes" mathml: @@ -13346,9 +13346,9 @@ concepts: - concept: topological-entropy arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: topological entropy of a1 + en: topological entropy of $a1 property: function subject-area: "topology" mathml: @@ -13360,9 +13360,9 @@ concepts: - concept: toroidal-coordinate arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: toroidal coordinates a1 a2 a3 + en: toroidal coordinates $a1 $a2 $a3 property: fenced subject-area: "geometry" mathml: @@ -13401,9 +13401,9 @@ concepts: - concept: torsion-submodule arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: torsion submodule of a1 + en: torsion submodule of $a1 property: function subject-area: "abstract algebra" mathml: @@ -13413,9 +13413,9 @@ concepts: - concept: torsion-subgroup arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: torsion subgroup of a1 + en: torsion subgroup of $a1 property: msub subject-area: "group theory" mathml: @@ -13426,9 +13426,9 @@ concepts: - concept: torsion-tensor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: torsion tensor of a1 + en: torsion tensor of $a1 property: function subject-area: "differential geometry" mathml: @@ -13438,9 +13438,9 @@ concepts: - concept: total-derivative arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: total derivative of a1 at a2 + en: total derivative of $a1 at $a2 property: mixfix subject-area: "differential calculus" mathml: @@ -13454,9 +13454,9 @@ concepts: - concept: total-variation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: total variation of a1 + en: total variation of $a1 property: fenced subject-area: "measure theory" mathml: @@ -13468,9 +13468,9 @@ concepts: - concept: trace arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: trace of a1 + en: trace of $a1 property: function subject-area: "linear algebra" mathml: @@ -13480,9 +13480,9 @@ concepts: - concept: transitive-closure arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: transitive closure of a1 + en: transitive closure of $a1 property: msup subject-area: "set theory" mathml: @@ -13494,7 +13494,7 @@ concepts: - concept: triangle arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: en: triangle property: prefix @@ -13509,9 +13509,9 @@ concepts: - concept: triangle-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: triangle function of a1 + en: triangle function of $a1 property: function subject-area: "special functions" mathml: @@ -13526,9 +13526,9 @@ concepts: - concept: triangular-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: triangular number a1 + en: triangular number $a1 property: "indexed symbol" subject-area: "number theory" mathml: @@ -13541,9 +13541,9 @@ concepts: - concept: trilinear-coordinates arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: trilinear coordinates a1, a2, a3 + en: trilinear coordinates $a1, $a2, $a3 property: infix subject-area: "geometry" mathml: @@ -13553,9 +13553,9 @@ concepts: - concept: trimean arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: trimean of a1 + en: trimean of $a1 property: function subject-area: "statistics" mathml: @@ -13567,9 +13567,9 @@ concepts: - concept: triple-bond arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 triple bond a2 + en: $a1 triple bond $a2 property: infix subject-area: "chemistry" mathml: @@ -13579,9 +13579,9 @@ concepts: - concept: triple-scalar-product arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: triple scalar product of a1, a2 and a3 + en: triple scalar product of $a1, $a2 and $a3 property: fenced subject-area: "algebra" mathml: @@ -13607,9 +13607,9 @@ concepts: - concept: truncation arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: truncation of a1 + en: truncation of $a1 property: function subject-area: "numerical analysis" mathml: @@ -13620,9 +13620,9 @@ concepts: - concept: tube-domain arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: tube domain of a1 + en: tube domain of $a1 property: msub subject-area: "complex analysis" mathml: @@ -13633,9 +13633,9 @@ concepts: - concept: turan-graph arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: turan graph a1 a2 + en: turan graph $a1 $a2 property: "function, indexed function" subject-area: "graph theory" mathml: @@ -13647,9 +13647,9 @@ concepts: - concept: turan-number arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: turan number of a1, a2 and a3 + en: turan number of $a1, $a2 and $a3 property: function subject-area: "graph theory" mathml: @@ -13661,9 +13661,9 @@ concepts: - concept: turn arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: turn of a1 + en: turn of $a1 property: unit subject-area: "geometry" mathml: @@ -13680,9 +13680,9 @@ concepts: - concept: twisted-tensor-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 twisted tensor product a2 + en: $a1 twisted tensor product $a2 property: infix subject-area: "topology" mathml: @@ -13708,9 +13708,9 @@ concepts: - concept: typing-judgement arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 typing judgement a2 + en: $a1 typing judgement $a2 property: infix subject-area: "type theory" mathml: @@ -13720,9 +13720,9 @@ concepts: - concept: ulam-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th ulam number + en: $a1th ulam number property: "indexed symbol" subject-area: "integer sequences" mathml: @@ -13733,9 +13733,9 @@ concepts: - concept: ultrapower arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: ultrapower a1 a2 + en: ultrapower $a1 $a2 property: mixfix subject-area: "abstract algebra" mathml: @@ -13747,9 +13747,9 @@ concepts: - concept: ultraproduct arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: ultraproduct of a1, a2 modulo a3 + en: ultraproduct of $a1, $a2 modulo $a3 property: mixfix subject-area: "abstract algebra" mathml: @@ -13761,23 +13761,23 @@ concepts: - concept: uniformly-convergent arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 uniformly convergs to a2 + en: $a1 uniformly convergs to $a2 property: infix, indexed, postfix subject-area: "convergence" mathml: - - "f⇉g" - - "f⟶unifg" - - "unif limf=g" + - "f⇉g" + - "f⟶unifg" + - "unif limf=g" urls: - "https://en.wikipedia.org/wiki/Uniform_convergence" - concept: unit-part arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: unit part of a1 + en: unit part of $a1 property: fenced subject-area: "SI units" mathml: @@ -13788,9 +13788,9 @@ concepts: - concept: unit-vector arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: unit vector of a1 + en: unit vector of $a1 property: mover subject-area: "linear algebra" mathml: @@ -13802,9 +13802,9 @@ concepts: - concept: unitary-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th unitary group + en: $a1th unitary group property: "indexed symbol" subject-area: "group theory" mathml: @@ -13865,9 +13865,9 @@ concepts: - concept: unique-existential arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: There exists unique a1 + en: There exists unique $a1 property: prefix subject-area: "logic" mathml: @@ -13878,9 +13878,9 @@ concepts: - concept: unnatural-isomorphism arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 unnatural isomorphism a2 + en: $a1 unnatural isomorphism $a2 property: infix subject-area: "set theory" mathml: @@ -13890,9 +13890,9 @@ concepts: - concept: unrestricted-wreath-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 unrestricted wreath product a2 + en: $a1 unrestricted wreath product $a2 property: infix subject-area: "group theory" mathml: @@ -13907,9 +13907,9 @@ concepts: - concept: upper-closure-poset arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: upper closure poset of a1 + en: upper closure poset of $a1 property: prefix subject-area: "order theory" mathml: @@ -13919,9 +13919,9 @@ concepts: - concept: upper-darboux-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: upper darboux integral of a1 + en: upper darboux integral of $a1 property: indexed subject-area: "real analysis" mathml: @@ -13932,9 +13932,9 @@ concepts: - concept: upper-dini-derivative arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: upper dini derivative of a1 + en: upper dini derivative of $a1 property: decorated function subject-area: "analysis" mathml: @@ -13961,9 +13961,9 @@ concepts: - concept: upper-shadow arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: upper shadow of a1 + en: upper shadow of $a1 property: function subject-area: "combinatorics" mathml: @@ -13973,9 +13973,9 @@ concepts: - concept: variance arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: variance of a1 + en: variance of $a1 property: function subject-area: "statistics" mathml: @@ -13987,9 +13987,9 @@ concepts: - concept: vect arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: vect of a1 + en: vect of $a1 property: "indexed symbol" subject-area: "category theory" mathml: @@ -13999,9 +13999,9 @@ concepts: - concept: vector-concatenation arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 vector concatenation a2 + en: $a1 vector concatenation $a2 property: infix subject-area: "machine learning" mathml: @@ -14013,9 +14013,9 @@ concepts: - concept: vector-projection arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: vector projection of a1 + en: vector projection of $a1 property: function subject-area: "linear algebra" mathml: @@ -14028,9 +14028,9 @@ concepts: - concept: vectorization arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: vectorization of a1 + en: vectorization of $a1 property: function subject-area: "linear algebra" mathml: @@ -14042,9 +14042,9 @@ concepts: - concept: versor arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: versor of a1 + en: versor of $a1 property: function subject-area: "quaternions" mathml: @@ -14071,9 +14071,9 @@ concepts: - concept: vertical-composition arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 vertical composition a2 + en: $a1 vertical composition $a2 property: infix subject-area: "category theory" mathml: @@ -14084,9 +14084,9 @@ concepts: - concept: volterra-integral arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: volterra integral of a1 + en: volterra integral of $a1 property: indexed subject-area: "calculus" mathml: @@ -14127,9 +14127,9 @@ concepts: - concept: walsh-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: walsh function of a1 + en: walsh function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -14141,14 +14141,14 @@ concepts: - concept: wavelet-transform arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: wavelet transform a1 a2 + en: wavelet transform $a1 $a2 property: "embellished function" subject-area: "functional analysis" mathml: - "Wψy" - notation: "mrow [ msub W a1 /msub a2 ]" + notation: "mrow [ msub W $a1 /msub $a2 ]" urls: - "https://mathworld.wolfram.com/WaveletTransform.html" - "https://en.wikipedia.org/wiki/Wavelet_transform" @@ -14158,9 +14158,9 @@ concepts: - concept: way-below arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 way below a2 + en: $a1 way below $a2 property: infix subject-area: "domain theory" mathml: @@ -14174,9 +14174,9 @@ concepts: - concept: weak-convergence arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 weak convergence a2 + en: $a1 weak convergence $a2 property: infix subject-area: "analysis" mathml: @@ -14188,9 +14188,9 @@ concepts: - concept: weber-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: weber function of a1 + en: weber function of $a1 property: "indexed function" subject-area: "special functions" mathml: @@ -14202,9 +14202,9 @@ concepts: - concept: weierstrass-elliptic-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: weierstrass elliptic function of a1 + en: weierstrass elliptic function of $a1 property: function subject-area: "special functions" mathml: @@ -14218,9 +14218,9 @@ concepts: - concept: weierstrass-sigma-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: weierstrass sigma function of a1 + en: weierstrass sigma function of $a1 property: function subject-area: "special functions" mathml: @@ -14233,9 +14233,9 @@ concepts: - concept: weierstrass-zeta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: weierstrass zeta function of a1 + en: weierstrass zeta function of $a1 property: function subject-area: "special functions" mathml: @@ -14248,9 +14248,9 @@ concepts: - concept: weight arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: weight of a1 + en: weight of $a1 property: function subject-area: "group theory" mathml: @@ -14263,7 +14263,7 @@ concepts: - concept: weighted-lehmer-mean arity: ">=0" speech: - en: weighted lehmer mean of a1 a2 ... + en: weighted lehmer mean of $a1 $a2 ... property: "indexed function" subject-area: "means" mathml: @@ -14274,9 +14274,9 @@ concepts: - concept: weighted-mean arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: weighted mean of a1 + en: weighted mean of $a1 property: fenced subject-area: "special functions" mathml: @@ -14290,9 +14290,9 @@ concepts: - concept: wheel-graph arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: wheel graph of a1 + en: wheel graph of $a1 property: "indexed symbol" subject-area: "graph theory" mathml: @@ -14303,9 +14303,9 @@ concepts: - concept: whitehead-group arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: whitehead group of a1 + en: whitehead group of $a1 property: function subject-area: "group theory" mathml: @@ -14317,9 +14317,9 @@ concepts: - concept: whitehead-bracket arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: whitehead bracket a1 a2 + en: whitehead bracket $a1 $a2 property: fenced subject-area: "lie algebra" mathml: @@ -14331,9 +14331,9 @@ concepts: - concept: whitehead-torsion arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: whitehead torsion of a1 + en: whitehead torsion of $a1 property: function subject-area: "geometric topology" mathml: @@ -14345,9 +14345,9 @@ concepts: - concept: whittaker-function arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: whittaker function a1 a2 + en: whittaker function $a1 $a2 property: "indexed function" subject-area: "special functions" mathml: @@ -14361,9 +14361,9 @@ concepts: - concept: whittaker-function arity: 3 - arguments: [a1, a2, a3] + arguments: [$a1, $a2, $a3] speech: - en: whittaker function a1 a2 of a3 + en: whittaker function $a1 $a2 of $a3 property: "indexed function" subject-area: "special functions" mathml: @@ -14390,9 +14390,9 @@ concepts: - concept: wiener-process arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: wiener process of a1 + en: wiener process of $a1 property: "indexed symbol" subject-area: "martingale theory" mathml: @@ -14404,9 +14404,9 @@ concepts: - concept: wiener-sausage arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: wiener sausage of radius a1 and length a2 + en: wiener sausage of radius $a1 and length $a2 property: "indexed symbol" subject-area: "mathematical physics" mathml: @@ -14418,9 +14418,9 @@ concepts: - concept: wilson-polynomial arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: a1th wilson polynomial + en: $a1th wilson polynomial property: "indexed function" subject-area: "orthogonal polynomials" mathml: @@ -14433,9 +14433,9 @@ concepts: - concept: wilson-quotient arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: wilson quotient of a1 + en: wilson quotient of $a1 property: function subject-area: "number theory" mathml: @@ -14446,9 +14446,9 @@ concepts: - concept: winding-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: winding number of a1 + en: winding number of $a1 property: "function, symbol" subject-area: "algebraic topology" mathml: @@ -14463,9 +14463,9 @@ concepts: - concept: window-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: window function of a1 + en: window function of $a1 property: function subject-area: "fourier analysis" mathml: @@ -14491,9 +14491,9 @@ concepts: - concept: witt-polynomials arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: witt polynomials of a1 + en: witt polynomials of $a1 property: "indexed function" subject-area: "ring theory" mathml: @@ -14505,7 +14505,7 @@ concepts: - concept: witt-vector arity: ">=0" speech: - en: witt vector of a1 + en: witt vector of $a1 property: fenced subject-area: "ring theory" mathml: @@ -14516,9 +14516,9 @@ concepts: - concept: woodall-number arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: woodall number of a1 + en: woodall number of $a1 property: "indexed symbol" subject-area: "number theory" mathml: @@ -14530,9 +14530,9 @@ concepts: - concept: wright-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: wright function of a1 + en: wright function of $a1 property: function subject-area: "special functions" mathml: @@ -14542,9 +14542,9 @@ concepts: - concept: wright-omega-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: wright omega function of a1 + en: wright omega function of $a1 property: function subject-area: "special functions" mathml: @@ -14556,9 +14556,9 @@ concepts: - concept: writhe arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: writhe of a1 + en: writhe of $a1 property: function subject-area: "knot theory" mathml: @@ -14570,9 +14570,9 @@ concepts: - concept: wronskian arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: wronskian of a1, a2 + en: wronskian of $a1, $a2 property: operator subject-area: "special functions" mathml: @@ -14587,9 +14587,9 @@ concepts: - concept: yang-mill-functional arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: yang mill functional of a1 + en: yang mill functional of $a1 property: function subject-area: "gauge theory" mathml: @@ -14613,9 +14613,9 @@ concepts: - concept: z-matrix-molecule arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: z matrix molecule of a1 + en: z matrix molecule of $a1 property: mtable subject-area: "chemistry" mathml: @@ -14625,9 +14625,9 @@ concepts: - concept: z-transform arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: z transform of a1 + en: z transform of $a1 property: function subject-area: "combinatorics" mathml: @@ -14640,9 +14640,9 @@ concepts: - concept: zernike-polynomial arity: 4 - arguments: [a1, a2, a3, a4] + arguments: [$a1, $a2, $a3, $a4] speech: - en: a1 a2 zernike polynomial of a3, a4 + en: $a1 $a2 zernike polynomial of $a3, $a4 property: "indexed function" subject-area: "orthogonal polynomials" mathml: @@ -14667,9 +14667,9 @@ concepts: - concept: zero-matrix arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 a2 zero matrix + en: $a1 $a2 zero matrix property: "indexed symbol" subject-area: "linear algebra" mathml: @@ -14679,9 +14679,9 @@ concepts: - concept: zero-morphism arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: zero morphism a1 a2 + en: zero morphism $a1 $a2 property: "indexed symbol" subject-area: "category theory" mathml: @@ -14732,9 +14732,9 @@ concepts: - concept: zeta-function arity: 1 - arguments: [a1] + arguments: [$a1] speech: - en: zeta function of a1 + en: zeta function of $a1 property: function subject-area: "number theory" mathml: @@ -14747,9 +14747,9 @@ concepts: - concept: zig-zag-product arity: 2 - arguments: [a1, a2] + arguments: [$a1, $a2] speech: - en: a1 zig zag product a2 + en: $a1 zig zag product $a2 property: infix subject-area: "graph theory" mathml: From 1f797fa5aa69bf68b5c57ce331e60df0948410c3 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Mon, 31 Aug 2026 20:35:19 +0100 Subject: [PATCH 31/33] prevent linebreaks in arg list --- intent-core-concepts/index.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/intent-core-concepts/index.md b/intent-core-concepts/index.md index 28e4f067..f915c239 100644 --- a/intent-core-concepts/index.md +++ b/intent-core-concepts/index.md @@ -32,6 +32,7 @@ title: Core Concept List p.langs {margin:1em; padding:1em;background-color: #EEE} tr:target >td:first-child {border-left:solid thick black} span.cb {margin-right: 2em; white-space:nowrap} +span.nw {white-space:nowrap} .markdown-body table tr.row0, .markdown-body table th.row0 {background-color:#F6F8FA} .markdown-body table tr.row1 {background-color:#FEFFFE} .markdown-body table tr.subj {background-color:beige;font-size:110%;text-align:left;} @@ -201,12 +202,12 @@ if c.link
{{c.concept}}{{arityr}}
-[ +[ {%- for arg in c.arguments -%} {{arg}} {%- unless forloop.last -%},{% endunless -%} {%- endfor -%} -]		{{c.property}}{%- unless c.default == false or c.arity == 0 -%}*{%- endunless -%} @@ -241,12 +242,12 @@ if c.link {{c.concept}} {{arityr}}
-[ +[ {%- for arg in c.arguments -%} {{arg}} {%- unless forloop.last -%},{% endunless -%} {%- endfor -%} -] +] 		{{c.property}}{%- unless c.default == false or c.arity == 0-%}*{%- endunless -%}
{{c.concept}}{{arityr}}{{arityr}}
+[ +{%- for arg in c.arguments -%} +{{arg}} +{%- unless forloop.last -%},{% endunless -%} +{%- endfor -%} +]		{{c.property}}{%- unless c.default == false or c.arity == 0 -%}*{%- endunless -%} @@ -222,7 +229,13 @@ arXiv {%- else -%}
{{c.concept}}{{arityr}}{{arityr}}
+[ +{%- for arg in c.arguments -%} +{{arg}} +{%- unless forloop.last -%},{% endunless -%} +{%- endfor -%} +]		 {{c.property}}{%- unless c.default == false or c.arity == 0-%}*{%- endunless -%} From 2d6b58ade364a1d194140624c8b34589bb170c00 Mon Sep 17 00:00:00 2001 From: David Carlisle Date: Mon, 31 Aug 2026 21:27:35 +0100 Subject: [PATCH 33/33] show args as not --- intent-open-concepts/index.md | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/intent-open-concepts/index.md b/intent-open-concepts/index.md index 1605bd63..98da64a5 100644 --- a/intent-open-concepts/index.md +++ b/intent-open-concepts/index.md @@ -42,15 +42,15 @@ a.self {color: black; font-weight:500} [arg] { background-color: #ddfafa;} [arg]:hover {display:inline;background-color: #add8e6;} [arg]:hover::after {display:inline;vertical-align: sub; font-size: 0.7em; } - [arg="a1"]:hover::after { content: " $1" ; } - [arg="a2"]:hover::after { content: " $2" ; } - [arg="a3"]:hover::after { content: " $3" ; } - [arg="a4"]:hover::after { content: " $4" ; } - [arg="a5"]:hover::after { content: " $5" ; } - [arg="a6"]:hover::after { content: " $6" ; } - [arg="a7"]:hover::after { content: " $7" ; } - [arg="a8"]:hover::after { content: " $8" ; } - [arg="a9"]:hover::after { content: " $9" ; } + [arg="a1"]:hover::after { content: " $a1" ; } + [arg="a2"]:hover::after { content: " $a2" ; } + [arg="a3"]:hover::after { content: " $a3" ; } + [arg="a4"]:hover::after { content: " $a4" ; } + [arg="a5"]:hover::after { content: " $a5" ; } + [arg="a6"]:hover::after { content: " $a6" ; } + [arg="a7"]:hover::after { content: " $a7" ; } + [arg="a8"]:hover::after { content: " $a8" ; } + [arg="a9"]:hover::after { content: " $a9" ; } math:not(:has(*[intent])) { color: red; }