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 C_n^{(\alpha)}(x) = \frac{(2\alpha)_n}{(\alpha+\frac{1}{2})_{n}}P_n^{(\alpha-1/2,\alpha-1/2)}(x).}
... is translated to the CAS output ...
Semantic latex: \ultrasphpoly{\alpha}{n}@{x} = \frac{\Pochhammersym{2 \alpha}{n}}{\Pochhammersym{\alpha + \frac{1}{2}}{n}} \JacobipolyP{\alpha - 1 / 2}{\alpha - 1 / 2}{n}@{x}
Confidence: 0.74750232869021
Mathematica
Translation: GegenbauerC[n, \[Alpha], x] == Divide[Pochhammer[2*\[Alpha], n],Pochhammer[\[Alpha]+Divide[1,2], n]]*JacobiP[n, \[Alpha]- 1/2, \[Alpha]- 1/2, x]
Information
Sub Equations
- GegenbauerC[n, \[Alpha], x] = Divide[Pochhammer[2*\[Alpha], n],Pochhammer[\[Alpha]+Divide[1,2], n]]*JacobiP[n, \[Alpha]- 1/2, \[Alpha]- 1/2, x]
Free variables
- \[Alpha]
- n
- x
Symbol info
- Jacobi polynomial; Example: \JacobipolyP{\alpha}{\beta}{n}@{x}
Will be translated to: JacobiP[$2, $0, $1, $3] Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r2 Mathematica: https://reference.wolfram.com/language/ref/JacobiP.html?q=JacobiP
- Ultraspherical Gegenbauer polynomial; Example: \ultrasphpoly{\lambda}{n}@{x}
Will be translated to: GegenbauerC[$1, $0, $2] Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r3 Mathematica: https://reference.wolfram.com/language/ref/GegenbauerC.html
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- Pochhammer symbol; Example: \Pochhammersym{a}{n}
Will be translated to: Pochhammer[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#iii Mathematica: https://reference.wolfram.com/language/ref/Pochhammer.html
Tests
Symbolic
Test expression: (GegenbauerC[n, \[Alpha], x])-(Divide[Pochhammer[2*\[Alpha], n],Pochhammer[\[Alpha]+Divide[1,2], n]]*JacobiP[n, \[Alpha]- 1/2, \[Alpha]- 1/2, x])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \ultrasphpoly [\ultrasphpoly]
Tests
Symbolic
Numeric
Maple
Translation: GegenbauerC(n, alpha, x) = (pochhammer(2*alpha, n))/(pochhammer(alpha +(1)/(2), n))*JacobiP(n, alpha - 1/2, alpha - 1/2, x)
Information
Sub Equations
- GegenbauerC(n, alpha, x) = (pochhammer(2*alpha, n))/(pochhammer(alpha +(1)/(2), n))*JacobiP(n, alpha - 1/2, alpha - 1/2, x)
Free variables
- alpha
- n
- x
Symbol info
- Jacobi polynomial; Example: \JacobipolyP{\alpha}{\beta}{n}@{x}
Will be translated to: JacobiP($2, $0, $1, $3) Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=JacobiP
- Ultraspherical Gegenbauer polynomial; Example: \ultrasphpoly{\lambda}{n}@{x}
Will be translated to: GegenbauerC($1, $0, $2) Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r3 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GegenbauerC
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- Pochhammer symbol; Example: \Pochhammersym{a}{n}
Will be translated to: pochhammer($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#iii Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=pochhammer
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- special case of the Jacobi polynomial
Complete translation information:
{
"id" : "FORMULA_987c5c425e1be53500b40f2724d8e681",
"formula" : "C_n^{(\\alpha)}(x) = \\frac{(2\\alpha)_n}{(\\alpha+\\frac{1}{2})_{n}}P_n^{(\\alpha-1/2,\\alpha-1/2)}(x)",
"semanticFormula" : "\\ultrasphpoly{\\alpha}{n}@{x} = \\frac{\\Pochhammersym{2 \\alpha}{n}}{\\Pochhammersym{\\alpha + \\frac{1}{2}}{n}} \\JacobipolyP{\\alpha - 1 / 2}{\\alpha - 1 / 2}{n}@{x}",
"confidence" : 0.7475023286902113,
"translations" : {
"Mathematica" : {
"translation" : "GegenbauerC[n, \\[Alpha], x] == Divide[Pochhammer[2*\\[Alpha], n],Pochhammer[\\[Alpha]+Divide[1,2], n]]*JacobiP[n, \\[Alpha]- 1/2, \\[Alpha]- 1/2, x]",
"translationInformation" : {
"subEquations" : [ "GegenbauerC[n, \\[Alpha], x] = Divide[Pochhammer[2*\\[Alpha], n],Pochhammer[\\[Alpha]+Divide[1,2], n]]*JacobiP[n, \\[Alpha]- 1/2, \\[Alpha]- 1/2, x]" ],
"freeVariables" : [ "\\[Alpha]", "n", "x" ],
"tokenTranslations" : {
"\\JacobipolyP" : "Jacobi polynomial; Example: \\JacobipolyP{\\alpha}{\\beta}{n}@{x}\nWill be translated to: JacobiP[$2, $0, $1, $3]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r2\nMathematica: https://reference.wolfram.com/language/ref/JacobiP.html?q=JacobiP",
"\\ultrasphpoly" : "Ultraspherical Gegenbauer polynomial; Example: \\ultrasphpoly{\\lambda}{n}@{x}\nWill be translated to: GegenbauerC[$1, $0, $2]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r3\nMathematica: https://reference.wolfram.com/language/ref/GegenbauerC.html",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\Pochhammersym" : "Pochhammer symbol; Example: \\Pochhammersym{a}{n}\nWill be translated to: Pochhammer[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#iii\nMathematica: https://reference.wolfram.com/language/ref/Pochhammer.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "GegenbauerC[n, \\[Alpha], x]",
"rhs" : "Divide[Pochhammer[2*\\[Alpha], n],Pochhammer[\\[Alpha]+Divide[1,2], n]]*JacobiP[n, \\[Alpha]- 1/2, \\[Alpha]- 1/2, x]",
"testExpression" : "(GegenbauerC[n, \\[Alpha], x])-(Divide[Pochhammer[2*\\[Alpha], n],Pochhammer[\\[Alpha]+Divide[1,2], n]]*JacobiP[n, \\[Alpha]- 1/2, \\[Alpha]- 1/2, x])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\ultrasphpoly [\\ultrasphpoly]"
}
}
},
"Maple" : {
"translation" : "GegenbauerC(n, alpha, x) = (pochhammer(2*alpha, n))/(pochhammer(alpha +(1)/(2), n))*JacobiP(n, alpha - 1/2, alpha - 1/2, x)",
"translationInformation" : {
"subEquations" : [ "GegenbauerC(n, alpha, x) = (pochhammer(2*alpha, n))/(pochhammer(alpha +(1)/(2), n))*JacobiP(n, alpha - 1/2, alpha - 1/2, x)" ],
"freeVariables" : [ "alpha", "n", "x" ],
"tokenTranslations" : {
"\\JacobipolyP" : "Jacobi polynomial; Example: \\JacobipolyP{\\alpha}{\\beta}{n}@{x}\nWill be translated to: JacobiP($2, $0, $1, $3)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=JacobiP",
"\\ultrasphpoly" : "Ultraspherical Gegenbauer polynomial; Example: \\ultrasphpoly{\\lambda}{n}@{x}\nWill be translated to: GegenbauerC($1, $0, $2)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r3\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GegenbauerC",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\Pochhammersym" : "Pochhammer symbol; Example: \\Pochhammersym{a}{n}\nWill be translated to: pochhammer($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#iii\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=pochhammer"
}
}
}
},
"positions" : [ {
"section" : 1,
"sentence" : 9,
"word" : 9
} ],
"includes" : [ "C_{n}^{(\\alpha)}(x)", "(2\\alpha)_{n}", "\\alpha", "n", "(\\theta)_n" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "special case of the Jacobi polynomial",
"score" : 0.7125985104912714
} ]
}