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 \int_{-1}^1 \left[C_n^{(\alpha)}(x)\right]^2(1-x^2)^{\alpha-\frac{1}{2}}\,dx = \frac{\pi 2^{1-2\alpha}\Gamma(n+2\alpha)}{n!(n+\alpha)[\Gamma(\alpha)]^2}.}
... is translated to the CAS output ...
Semantic latex: \int_{-1}^1 [\ultrasphpoly{\alpha}{n}@{x}]^2(1 - x^2)^{\alpha-\frac{1}{2}} \diff{x} = \frac{\cpi 2^{1-2\alpha} \Gamma(n + 2 \alpha)}{n!(n+\alpha)[\Gamma(\alpha)]^2}
Confidence: 0.6805
Mathematica
Translation: Integrate[(GegenbauerC[n, \[Alpha], x])^(2)*(1 - (x)^(2))^(\[Alpha]-Divide[1,2]), {x, - 1, 1}, GenerateConditions->None] == Divide[Pi*(2)^(1 - 2*\[Alpha])* \[CapitalGamma][n + 2*\[Alpha]],(n)!*(n + \[Alpha])*(\[CapitalGamma][\[Alpha]])^(2)]
Information
Sub Equations
- Integrate[(GegenbauerC[n, \[Alpha], x])^(2)*(1 - (x)^(2))^(\[Alpha]-Divide[1,2]), {x, - 1, 1}, GenerateConditions->None] = Divide[Pi*(2)^(1 - 2*\[Alpha])* \[CapitalGamma][n + 2*\[Alpha]],(n)!*(n + \[Alpha])*(\[CapitalGamma][\[Alpha]])^(2)]
Free variables
- \[Alpha]
- \[CapitalGamma]
- n
Symbol info
- 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
- Pi was translated to: Pi
- 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.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Test expression: (Integrate[(GegenbauerC[n, \[Alpha], x])^(2)*(1 - (x)^(2))^(\[Alpha]-Divide[1,2]), {x, - 1, 1}, GenerateConditions->None])-(Divide[Pi*(2)^(1 - 2*\[Alpha])* \[CapitalGamma]*(n + 2*\[Alpha]),(n)!*(n + \[Alpha])*(\[CapitalGamma]*(\[Alpha]))^(2)])
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: int((GegenbauerC(n, alpha, x))^(2)*(1 - (x)^(2))^(alpha -(1)/(2)), x = - 1..1) = (Pi*(2)^(1 - 2*alpha)* Gamma(n + 2*alpha))/(factorial(n)*(n + alpha)*(Gamma(alpha))^(2))
Information
Sub Equations
- int((GegenbauerC(n, alpha, x))^(2)*(1 - (x)^(2))^(alpha -(1)/(2)), x = - 1..1) = (Pi*(2)^(1 - 2*alpha)* Gamma(n + 2*alpha))/(factorial(n)*(n + alpha)*(Gamma(alpha))^(2))
Free variables
- Gamma
- alpha
- n
Symbol info
- 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
- Pi was translated to: Pi
- 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.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_d807cf75321a8ce2d34f89336594fd7c",
"formula" : "\\int_{-1}^1 \\left[C_n^{(\\alpha)}(x)\\right]^2(1-x^2)^{\\alpha-\\frac{1}{2}}dx = \\frac{\\pi 2^{1-2\\alpha}\\Gamma(n+2\\alpha)}{n!(n+\\alpha)[\\Gamma(\\alpha)]^2}",
"semanticFormula" : "\\int_{-1}^1 [\\ultrasphpoly{\\alpha}{n}@{x}]^2(1 - x^2)^{\\alpha-\\frac{1}{2}} \\diff{x} = \\frac{\\cpi 2^{1-2\\alpha} \\Gamma(n + 2 \\alpha)}{n!(n+\\alpha)[\\Gamma(\\alpha)]^2}",
"confidence" : 0.6805,
"translations" : {
"Mathematica" : {
"translation" : "Integrate[(GegenbauerC[n, \\[Alpha], x])^(2)*(1 - (x)^(2))^(\\[Alpha]-Divide[1,2]), {x, - 1, 1}, GenerateConditions->None] == Divide[Pi*(2)^(1 - 2*\\[Alpha])* \\[CapitalGamma][n + 2*\\[Alpha]],(n)!*(n + \\[Alpha])*(\\[CapitalGamma][\\[Alpha]])^(2)]",
"translationInformation" : {
"subEquations" : [ "Integrate[(GegenbauerC[n, \\[Alpha], x])^(2)*(1 - (x)^(2))^(\\[Alpha]-Divide[1,2]), {x, - 1, 1}, GenerateConditions->None] = Divide[Pi*(2)^(1 - 2*\\[Alpha])* \\[CapitalGamma][n + 2*\\[Alpha]],(n)!*(n + \\[Alpha])*(\\[CapitalGamma][\\[Alpha]])^(2)]" ],
"freeVariables" : [ "\\[Alpha]", "\\[CapitalGamma]", "n" ],
"tokenTranslations" : {
"\\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",
"\\cpi" : "Pi was translated to: Pi",
"\\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",
"\\Gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
},
"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" : "Integrate[(GegenbauerC[n, \\[Alpha], x])^(2)*(1 - (x)^(2))^(\\[Alpha]-Divide[1,2]), {x, - 1, 1}, GenerateConditions->None]",
"rhs" : "Divide[Pi*(2)^(1 - 2*\\[Alpha])* \\[CapitalGamma]*(n + 2*\\[Alpha]),(n)!*(n + \\[Alpha])*(\\[CapitalGamma]*(\\[Alpha]))^(2)]",
"testExpression" : "(Integrate[(GegenbauerC[n, \\[Alpha], x])^(2)*(1 - (x)^(2))^(\\[Alpha]-Divide[1,2]), {x, - 1, 1}, GenerateConditions->None])-(Divide[Pi*(2)^(1 - 2*\\[Alpha])* \\[CapitalGamma]*(n + 2*\\[Alpha]),(n)!*(n + \\[Alpha])*(\\[CapitalGamma]*(\\[Alpha]))^(2)])",
"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" : "int((GegenbauerC(n, alpha, x))^(2)*(1 - (x)^(2))^(alpha -(1)/(2)), x = - 1..1) = (Pi*(2)^(1 - 2*alpha)* Gamma(n + 2*alpha))/(factorial(n)*(n + alpha)*(Gamma(alpha))^(2))",
"translationInformation" : {
"subEquations" : [ "int((GegenbauerC(n, alpha, x))^(2)*(1 - (x)^(2))^(alpha -(1)/(2)), x = - 1..1) = (Pi*(2)^(1 - 2*alpha)* Gamma(n + 2*alpha))/(factorial(n)*(n + alpha)*(Gamma(alpha))^(2))" ],
"freeVariables" : [ "Gamma", "alpha", "n" ],
"tokenTranslations" : {
"\\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",
"\\cpi" : "Pi was translated to: Pi",
"\\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",
"\\Gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
}
},
"positions" : [ ],
"includes" : [ "C_{n}^{(\\alpha)}(x)", "\\alpha", "n", "\\int_{-1}^1 \\left[C_n^{(\\alpha)}(x)\\right]^2(1-x^2)^{\\alpha-\\frac{1}{2}}\\,dx = \\frac{\\pi 2^{1-2\\alpha}\\Gamma(n+2\\alpha)}{n!(n+\\alpha)[\\Gamma(\\alpha)]^2}" ],
"isPartOf" : [ "\\int_{-1}^1 \\left[C_n^{(\\alpha)}(x)\\right]^2(1-x^2)^{\\alpha-\\frac{1}{2}}\\,dx = \\frac{\\pi 2^{1-2\\alpha}\\Gamma(n+2\\alpha)}{n!(n+\\alpha)[\\Gamma(\\alpha)]^2}" ],
"definiens" : [ ]
}