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 (1-x)^{\alpha} (1+x)^{\beta} P_m^{(\alpha,\beta)} (x)P_n^{(\alpha,\beta)} (x)\,dx =\frac{2^{\alpha+\beta+1}}{2n+\alpha+\beta+1} \frac{\Gamma(n+\alpha+1)\Gamma(n+\beta+1)}{\Gamma(n+\alpha+\beta+1)n!} \delta_{nm}, \qquad \alpha,\ \beta > -1.}
... is translated to the CAS output ...
Semantic latex: \int_{-1}^1(1 - x)^{\alpha}(1 + x)^{\beta} \JacobipolyP{\alpha}{\beta}{m}@{x} \JacobipolyP{\alpha}{\beta}{n}@{x} \diff{x} = \frac{2^{\alpha+\beta+1}}{2n+\alpha+\beta+1} \frac{\EulerGamma@{n + \alpha + 1} \EulerGamma@{n + \beta + 1}}{\EulerGamma@{n + \alpha + \beta + 1} n!} \delta_{nm} , \qquad \alpha , \beta > - 1
Confidence: 0.64544110844472
Mathematica
Translation: Integrate[(1 - x)^\[Alpha]*(1 + x)^\[Beta]* JacobiP[m, \[Alpha], \[Beta], x]*JacobiP[n, \[Alpha], \[Beta], x], {x, - 1, 1}, GenerateConditions->None] == Divide[(2)^(\[Alpha]+ \[Beta]+ 1),2*n + \[Alpha]+ \[Beta]+ 1]*Divide[Gamma[n + \[Alpha]+ 1]*Gamma[n + \[Beta]+ 1],Gamma[n + \[Alpha]+ \[Beta]+ 1]*(n)!]*Subscript[\[Delta], n, m]
Information
Sub Equations
- Integrate[(1 - x)^\[Alpha]*(1 + x)^\[Beta]* JacobiP[m, \[Alpha], \[Beta], x]*JacobiP[n, \[Alpha], \[Beta], x], {x, - 1, 1}, GenerateConditions->None] = Divide[(2)^(\[Alpha]+ \[Beta]+ 1),2*n + \[Alpha]+ \[Beta]+ 1]*Divide[Gamma[n + \[Alpha]+ 1]*Gamma[n + \[Beta]+ 1],Gamma[n + \[Alpha]+ \[Beta]+ 1]*(n)!]*Subscript[\[Delta], n, m]
Free variables
- Subscript[\[Delta], n, m]
- \[Alpha]
- \[Beta]
- m
- n
Constraints
- \[Alpha], \[Beta] > - 1
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 first Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- 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
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: int((1 - x)^(alpha)*(1 + x)^(beta)* JacobiP(m, alpha, beta, x)*JacobiP(n, alpha, beta, x), x = - 1..1) = ((2)^(alpha + beta + 1))/(2*n + alpha + beta + 1)*(GAMMA(n + alpha + 1)*GAMMA(n + beta + 1))/(GAMMA(n + alpha + beta + 1)*factorial(n))*delta[n, m]
Information
Sub Equations
- int((1 - x)^(alpha)*(1 + x)^(beta)* JacobiP(m, alpha, beta, x)*JacobiP(n, alpha, beta, x), x = - 1..1) = ((2)^(alpha + beta + 1))/(2*n + alpha + beta + 1)*(GAMMA(n + alpha + 1)*GAMMA(n + beta + 1))/(GAMMA(n + alpha + beta + 1)*factorial(n))*delta[n, m]
Free variables
- alpha
- beta
- delta[n, m]
- m
- n
Constraints
- alpha , beta > - 1
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 first Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- 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_a6fdf6dd3eab666e22ab2f03ae3740ca",
"formula" : "\\int_{-1}^1 (1-x)^{\\alpha} (1+x)^{\\beta} P_m^{(\\alpha,\\beta)} (x)P_n^{(\\alpha,\\beta)} (x)dx =\\frac{2^{\\alpha+\\beta+1}}{2n+\\alpha+\\beta+1} \\frac{\\Gamma(n+\\alpha+1)\\Gamma(n+\\beta+1)}{\\Gamma(n+\\alpha+\\beta+1)n!} \\delta_{nm}, \\qquad \\alpha,\\beta > -1",
"semanticFormula" : "\\int_{-1}^1(1 - x)^{\\alpha}(1 + x)^{\\beta} \\JacobipolyP{\\alpha}{\\beta}{m}@{x} \\JacobipolyP{\\alpha}{\\beta}{n}@{x} \\diff{x} = \\frac{2^{\\alpha+\\beta+1}}{2n+\\alpha+\\beta+1} \\frac{\\EulerGamma@{n + \\alpha + 1} \\EulerGamma@{n + \\beta + 1}}{\\EulerGamma@{n + \\alpha + \\beta + 1} n!} \\delta_{nm} , \\qquad \\alpha , \\beta > - 1",
"confidence" : 0.6454411084447216,
"translations" : {
"Mathematica" : {
"translation" : "Integrate[(1 - x)^\\[Alpha]*(1 + x)^\\[Beta]* JacobiP[m, \\[Alpha], \\[Beta], x]*JacobiP[n, \\[Alpha], \\[Beta], x], {x, - 1, 1}, GenerateConditions->None] == Divide[(2)^(\\[Alpha]+ \\[Beta]+ 1),2*n + \\[Alpha]+ \\[Beta]+ 1]*Divide[Gamma[n + \\[Alpha]+ 1]*Gamma[n + \\[Beta]+ 1],Gamma[n + \\[Alpha]+ \\[Beta]+ 1]*(n)!]*Subscript[\\[Delta], n, m]",
"translationInformation" : {
"subEquations" : [ "Integrate[(1 - x)^\\[Alpha]*(1 + x)^\\[Beta]* JacobiP[m, \\[Alpha], \\[Beta], x]*JacobiP[n, \\[Alpha], \\[Beta], x], {x, - 1, 1}, GenerateConditions->None] = Divide[(2)^(\\[Alpha]+ \\[Beta]+ 1),2*n + \\[Alpha]+ \\[Beta]+ 1]*Divide[Gamma[n + \\[Alpha]+ 1]*Gamma[n + \\[Beta]+ 1],Gamma[n + \\[Alpha]+ \\[Beta]+ 1]*(n)!]*Subscript[\\[Delta], n, m]" ],
"freeVariables" : [ "Subscript[\\[Delta], n, m]", "\\[Alpha]", "\\[Beta]", "m", "n" ],
"constraints" : [ "\\[Alpha], \\[Beta] > - 1" ],
"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",
"\\delta" : "Could be the first Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\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" : "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" : "int((1 - x)^(alpha)*(1 + x)^(beta)* JacobiP(m, alpha, beta, x)*JacobiP(n, alpha, beta, x), x = - 1..1) = ((2)^(alpha + beta + 1))/(2*n + alpha + beta + 1)*(GAMMA(n + alpha + 1)*GAMMA(n + beta + 1))/(GAMMA(n + alpha + beta + 1)*factorial(n))*delta[n, m]",
"translationInformation" : {
"subEquations" : [ "int((1 - x)^(alpha)*(1 + x)^(beta)* JacobiP(m, alpha, beta, x)*JacobiP(n, alpha, beta, x), x = - 1..1) = ((2)^(alpha + beta + 1))/(2*n + alpha + beta + 1)*(GAMMA(n + alpha + 1)*GAMMA(n + beta + 1))/(GAMMA(n + alpha + beta + 1)*factorial(n))*delta[n, m]" ],
"freeVariables" : [ "alpha", "beta", "delta[n, m]", "m", "n" ],
"constraints" : [ "alpha , beta > - 1" ],
"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",
"\\delta" : "Could be the first Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\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"
}
},
"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" : [ ],
"includes" : [ "n + \\alpha + \\beta", "\\int_{-1}^1 (1-x)^{\\alpha} (1+x)^{\\beta} P_m^{(\\alpha,\\beta)} (x)P_n^{(\\alpha,\\beta)} (x)\\,dx =\\frac{2^{\\alpha+\\beta+1}}{2n+\\alpha+\\beta+1} \\frac{\\Gamma(n+\\alpha+1)\\Gamma(n+\\beta+1)}{\\Gamma(n+\\alpha+\\beta+1)n!} \\delta_{nm}, \\qquad \\alpha,\\ \\beta > -1", "\\alpha,\\beta", "\\Gamma(z)", "n", "P_{n}^{(\\alpha, \\beta)}", "x", "(1 - x)^{\\alpha}(1 + x)^{\\beta}", "P_{n}^{(\\alpha, \\beta)}(x)" ],
"isPartOf" : [ "\\int_{-1}^1 (1-x)^{\\alpha} (1+x)^{\\beta} P_m^{(\\alpha,\\beta)} (x)P_n^{(\\alpha,\\beta)} (x)\\,dx =\\frac{2^{\\alpha+\\beta+1}}{2n+\\alpha+\\beta+1} \\frac{\\Gamma(n+\\alpha+1)\\Gamma(n+\\beta+1)}{\\Gamma(n+\\alpha+\\beta+1)n!} \\delta_{nm}, \\qquad \\alpha,\\ \\beta > -1" ],
"definiens" : [ ]
}