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 P_n^{(\alpha,\beta)} (z) = \frac{\Gamma (\alpha+n+1)}{n!\,\Gamma (\alpha+\beta+n+1)} \sum_{m=0}^n {n\choose m} \frac{\Gamma (\alpha + \beta + n + m + 1)}{\Gamma (\alpha + m + 1)} \left(\frac{z-1}{2}\right)^m.}
... is translated to the CAS output ...
Semantic latex: \JacobipolyP{\alpha}{\beta}{n}@{z} = \frac{\EulerGamma@{\alpha + n + 1}}{n! \EulerGamma@{\alpha + \beta + n + 1}} \sum_{m=0}^n{n\choose m} \frac{\EulerGamma@{\alpha + \beta + n + m + 1}}{\EulerGamma@{\alpha + m + 1}}(\frac{z-1}{2})^m
Confidence: 0.64259245941821
Mathematica
Translation: JacobiP[n, \[Alpha], \[Beta], z] == Divide[Gamma[\[Alpha]+ n + 1],(n)!*Gamma[\[Alpha]+ \[Beta]+ n + 1]]*Sum[Binomial[n,m]*Divide[Gamma[\[Alpha]+ \[Beta]+ n + m + 1],Gamma[\[Alpha]+ m + 1]]*(Divide[z - 1,2])^(m), {m, 0, n}, GenerateConditions->None]
Information
Sub Equations
- JacobiP[n, \[Alpha], \[Beta], z] = Divide[Gamma[\[Alpha]+ n + 1],(n)!*Gamma[\[Alpha]+ \[Beta]+ n + 1]]*Sum[Binomial[n,m]*Divide[Gamma[\[Alpha]+ \[Beta]+ n + m + 1],Gamma[\[Alpha]+ m + 1]]*(Divide[z - 1,2])^(m), {m, 0, n}, GenerateConditions->None]
Free variables
- \[Alpha]
- \[Beta]
- n
- z
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
- 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.
- 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
Test expression: (JacobiP[n, \[Alpha], \[Beta], z])-(Divide[Gamma[\[Alpha]+ n + 1],(n)!*Gamma[\[Alpha]+ \[Beta]+ n + 1]]*Sum[Binomial[n,m]*Divide[Gamma[\[Alpha]+ \[Beta]+ n + m + 1],Gamma[\[Alpha]+ m + 1]]*(Divide[z - 1,2])^(m), {m, 0, n}, GenerateConditions->None])
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: \EulerGamma [\EulerGamma]
Tests
Symbolic
Numeric
Maple
Translation: JacobiP(n, alpha, beta, z) = (GAMMA(alpha + n + 1))/(factorial(n)*GAMMA(alpha + beta + n + 1))*sum(binomial(n,m)*(GAMMA(alpha + beta + n + m + 1))/(GAMMA(alpha + m + 1))*((z - 1)/(2))^(m), m = 0..n)
Information
Sub Equations
- JacobiP(n, alpha, beta, z) = (GAMMA(alpha + n + 1))/(factorial(n)*GAMMA(alpha + beta + n + 1))*sum(binomial(n,m)*(GAMMA(alpha + beta + n + m + 1))/(GAMMA(alpha + m + 1))*((z - 1)/(2))^(m), m = 0..n)
Free variables
- alpha
- beta
- n
- z
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
- 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.
- 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
Complete translation information:
{
"id" : "FORMULA_d1b07572345f7ab922eac9f7afa8e29d",
"formula" : "P_n^{(\\alpha,\\beta)} (z) = \\frac{\\Gamma (\\alpha+n+1)}{n!\\Gamma (\\alpha+\\beta+n+1)} \\sum_{m=0}^n {n\\choose m} \\frac{\\Gamma (\\alpha + \\beta + n + m + 1)}{\\Gamma (\\alpha + m + 1)} \\left(\\frac{z-1}{2}\\right)^m",
"semanticFormula" : "\\JacobipolyP{\\alpha}{\\beta}{n}@{z} = \\frac{\\EulerGamma@{\\alpha + n + 1}}{n! \\EulerGamma@{\\alpha + \\beta + n + 1}} \\sum_{m=0}^n{n\\choose m} \\frac{\\EulerGamma@{\\alpha + \\beta + n + m + 1}}{\\EulerGamma@{\\alpha + m + 1}}(\\frac{z-1}{2})^m",
"confidence" : 0.6425924594182052,
"translations" : {
"Mathematica" : {
"translation" : "JacobiP[n, \\[Alpha], \\[Beta], z] == Divide[Gamma[\\[Alpha]+ n + 1],(n)!*Gamma[\\[Alpha]+ \\[Beta]+ n + 1]]*Sum[Binomial[n,m]*Divide[Gamma[\\[Alpha]+ \\[Beta]+ n + m + 1],Gamma[\\[Alpha]+ m + 1]]*(Divide[z - 1,2])^(m), {m, 0, n}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "JacobiP[n, \\[Alpha], \\[Beta], z] = Divide[Gamma[\\[Alpha]+ n + 1],(n)!*Gamma[\\[Alpha]+ \\[Beta]+ n + 1]]*Sum[Binomial[n,m]*Divide[Gamma[\\[Alpha]+ \\[Beta]+ n + m + 1],Gamma[\\[Alpha]+ m + 1]]*(Divide[z - 1,2])^(m), {m, 0, n}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Alpha]", "\\[Beta]", "n", "z" ],
"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",
"\\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",
"\\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" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "JacobiP[n, \\[Alpha], \\[Beta], z]",
"rhs" : "Divide[Gamma[\\[Alpha]+ n + 1],(n)!*Gamma[\\[Alpha]+ \\[Beta]+ n + 1]]*Sum[Binomial[n,m]*Divide[Gamma[\\[Alpha]+ \\[Beta]+ n + m + 1],Gamma[\\[Alpha]+ m + 1]]*(Divide[z - 1,2])^(m), {m, 0, n}, GenerateConditions->None]",
"testExpression" : "(JacobiP[n, \\[Alpha], \\[Beta], z])-(Divide[Gamma[\\[Alpha]+ n + 1],(n)!*Gamma[\\[Alpha]+ \\[Beta]+ n + 1]]*Sum[Binomial[n,m]*Divide[Gamma[\\[Alpha]+ \\[Beta]+ n + m + 1],Gamma[\\[Alpha]+ m + 1]]*(Divide[z - 1,2])^(m), {m, 0, n}, GenerateConditions->None])",
"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: \\EulerGamma [\\EulerGamma]"
}
}
},
"Maple" : {
"translation" : "JacobiP(n, alpha, beta, z) = (GAMMA(alpha + n + 1))/(factorial(n)*GAMMA(alpha + beta + n + 1))*sum(binomial(n,m)*(GAMMA(alpha + beta + n + m + 1))/(GAMMA(alpha + m + 1))*((z - 1)/(2))^(m), m = 0..n)",
"translationInformation" : {
"subEquations" : [ "JacobiP(n, alpha, beta, z) = (GAMMA(alpha + n + 1))/(factorial(n)*GAMMA(alpha + beta + n + 1))*sum(binomial(n,m)*(GAMMA(alpha + beta + n + m + 1))/(GAMMA(alpha + m + 1))*((z - 1)/(2))^(m), m = 0..n)" ],
"freeVariables" : [ "alpha", "beta", "n", "z" ],
"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",
"\\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",
"\\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"
}
}
}
},
"positions" : [ ],
"includes" : [ "z", "n + \\alpha + \\beta", "\\alpha,\\beta", "\\Gamma(z)", "n", "P_{n}^{(\\alpha, \\beta)}", "P_n^{(\\alpha,\\beta)} (z) = \\frac{\\Gamma (\\alpha+n+1)}{n!\\,\\Gamma (\\alpha+\\beta+n+1)} \\sum_{m=0}^n {n\\choose m} \\frac{\\Gamma (\\alpha + \\beta + n + m + 1)}{\\Gamma (\\alpha + m + 1)} \\left(\\frac{z-1}{2}\\right)^m", "P_{n}^{(\\alpha, \\beta)}(x)" ],
"isPartOf" : [ "P_n^{(\\alpha,\\beta)} (z) = \\frac{\\Gamma (\\alpha+n+1)}{n!\\,\\Gamma (\\alpha+\\beta+n+1)} \\sum_{m=0}^n {n\\choose m} \\frac{\\Gamma (\\alpha + \\beta + n + m + 1)}{\\Gamma (\\alpha + m + 1)} \\left(\\frac{z-1}{2}\\right)^m" ],
"definiens" : [ ]
}