LaTeX to CAS translator
This mockup demonstrates the concept of TeX to Computer Algebra System (CAS) conversion.
The demo-application converts LaTeX functions which directly translate to CAS counterparts.
Functions without explicit CAS support are available for translation via a DRMF package (under development).
The following LaTeX input ...
{\displaystyle \Gamma(x+y)}
... is translated to the CAS output ...
Semantic latex: \EulerGamma@{x + y}
Confidence: 0.61788109628084
Mathematica
Translation: Gamma[x + y]
Information
Sub Equations
- Gamma[x + y]
Free variables
- x
- y
Symbol info
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: Gamma[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Mathematica: https://reference.wolfram.com/language/ref/Gamma.html
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \EulerGamma [\EulerGamma]
Tests
Symbolic
Numeric
Maple
Translation: GAMMA(x + y)
Information
Sub Equations
- GAMMA(x + y)
Free variables
- x
- y
Symbol info
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: GAMMA($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- simple derivation of the relation
- result
- side
- product
- Emil Artin 's book The Gamma function
- page
- one
- factorial
- relation
- variable
- digamma function
- beta function
- infinite product
- infinite sum
- argument
- close relationship to the gamma function
- function
- key property of the beta function
Complete translation information:
{
"id" : "FORMULA_b5b0b2c1b74fcdb61b57699fe820eadb",
"formula" : "\\Gamma(x+y)",
"semanticFormula" : "\\EulerGamma@{x + y}",
"confidence" : 0.6178810962808362,
"translations" : {
"Mathematica" : {
"translation" : "Gamma[x + y]",
"translationInformation" : {
"subEquations" : [ "Gamma[x + y]" ],
"freeVariables" : [ "x", "y" ],
"tokenTranslations" : {
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: Gamma[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMathematica: https://reference.wolfram.com/language/ref/Gamma.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\EulerGamma [\\EulerGamma]"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"Maple" : {
"translation" : "GAMMA(x + y)",
"translationInformation" : {
"subEquations" : [ "GAMMA(x + y)" ],
"freeVariables" : [ "x", "y" ],
"tokenTranslations" : {
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: GAMMA($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
}
},
"positions" : [ {
"section" : 2,
"sentence" : 1,
"word" : 25
} ],
"includes" : [ "y", "x", "\\Gamma" ],
"isPartOf" : [ "\\Beta(x,y)=\\frac{\\Gamma(x)\\,\\Gamma(y)}{\\Gamma(x+y)}", "\\begin{align}\\Gamma(x)\\Gamma(y) &= \\int_{z=0}^\\infty\\int_{t=0}^1 e^{-z} (zt)^{x-1}(z(1-t))^{y-1}z\\,dt \\,dz \\\\[6pt] &= \\int_{z=0}^\\infty e^{-z}z^{x+y-1} \\,dz\\cdot\\int_{t=0}^1 t^{x-1}(1-t)^{y-1}\\,dt\\\\ &=\\Gamma(x+y) \\cdot \\Beta(x,y).\\end{align}", "\\Gamma(x) \\Gamma(y) = \\int_{\\R}f(u)\\,du\\cdot \\int_{\\R} g(u) \\,du = \\int_{\\R}(f*g)(u)\\,du =\\Beta(x, y)\\,\\Gamma(x+y)", "\\frac{\\partial}{\\partial x} \\mathrm{B}(x, y) = \\mathrm{B}(x, y) \\left( \\frac{\\Gamma'(x)}{\\Gamma(x)} - \\frac{\\Gamma'(x + y)}{\\Gamma(x + y)} \\right) = \\mathrm{B}(x, y) \\big(\\psi(x) - \\psi(x + y)\\big)", "\\Beta(x,y) = \\frac{x+y}{x y} \\prod_{n=1}^\\infty \\left( 1+ \\dfrac{x y}{n (x+y+n)}\\right)^{-1}", "\\Beta(\\alpha_1,\\alpha_2,\\ldots\\alpha_n) = \\frac{\\Gamma(\\alpha_1)\\,\\Gamma(\\alpha_2) \\cdots \\Gamma(\\alpha_n)}{\\Gamma(\\alpha_1 + \\alpha_2 + \\cdots + \\alpha_n)}" ],
"definiens" : [ {
"definition" : "simple derivation of the relation",
"score" : 0.6699230544300447
}, {
"definition" : "result",
"score" : 0.6687181434333315
}, {
"definition" : "side",
"score" : 0.6687181434333315
}, {
"definition" : "product",
"score" : 0.5816270233429564
}, {
"definition" : "Emil Artin 's book The Gamma function",
"score" : 0.5561420434722057
}, {
"definition" : "page",
"score" : 0.5561420434722057
}, {
"definition" : "one",
"score" : 0.5377290372506534
}, {
"definition" : "factorial",
"score" : 0.5329047619047619
}, {
"definition" : "relation",
"score" : 0.5329047619047619
}, {
"definition" : "variable",
"score" : 0.5329047619047619
}, {
"definition" : "digamma function",
"score" : 0.451864458892933
}, {
"definition" : "beta function",
"score" : 0.3719881238007382
}, {
"definition" : "infinite product",
"score" : 0.3616715029761905
}, {
"definition" : "infinite sum",
"score" : 0.3522700134674619
}, {
"definition" : "argument",
"score" : 0.35159851049127144
}, {
"definition" : "close relationship to the gamma function",
"score" : 0.3065627745308957
}, {
"definition" : "function",
"score" : 0.28507467929280045
}, {
"definition" : "key property of the beta function",
"score" : 0.2593055947715278
} ]
}