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_2^{(\alpha,\beta)}(z)= \frac{(\alpha+1)(\alpha+2)}{2} + (\alpha+2)(\alpha+\beta+3)\frac{z-1}{2} + \frac{(\alpha+\beta+3)(\alpha+\beta+4)}{2}\left(\frac{z-1}{2}\right)^2,...}
... is translated to the CAS output ...
Semantic latex: \JacobipolyP{\alpha}{\beta}{2}@{z} = \frac{(\alpha+1)(\alpha+2)}{2} +(\alpha + 2)(\alpha + \beta + 3) \frac{z-1}{2} + \frac{(\alpha+\beta+3)(\alpha+\beta+4)}{2}(\frac{z-1}{2})^2 ,
Confidence: 0.65633676869532
Mathematica
Translation: JacobiP[2, \[Alpha], \[Beta], z] == Divide[(\[Alpha]+ 1)*(\[Alpha]+ 2),2]+(\[Alpha]+ 2)*(\[Alpha]+ \[Beta]+ 3)*Divide[z - 1,2]+Divide[(\[Alpha]+ \[Beta]+ 3)*(\[Alpha]+ \[Beta]+ 4),2]*(Divide[z - 1,2])^(2)
Information
Sub Equations
- JacobiP[2, \[Alpha], \[Beta], z] = Divide[(\[Alpha]+ 1)*(\[Alpha]+ 2),2]+(\[Alpha]+ 2)*(\[Alpha]+ \[Beta]+ 3)*Divide[z - 1,2]+Divide[(\[Alpha]+ \[Beta]+ 3)*(\[Alpha]+ \[Beta]+ 4),2]*(Divide[z - 1,2])^(2)
Free variables
- \[Alpha]
- \[Beta]
- 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.
Tests
Symbolic
Test expression: (JacobiP[2, \[Alpha], \[Beta], z])-(Divide[(\[Alpha]+ 1)*(\[Alpha]+ 2),2]+(\[Alpha]+ 2)*(\[Alpha]+ \[Beta]+ 3)*Divide[z - 1,2]+Divide[(\[Alpha]+ \[Beta]+ 3)*(\[Alpha]+ \[Beta]+ 4),2]*(Divide[z - 1,2])^(2))
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: jacobi(2, Symbol('alpha'), Symbol('beta'), z) == ((Symbol('alpha')+ 1)*(Symbol('alpha')+ 2))/(2)+(Symbol('alpha')+ 2)*(Symbol('alpha')+ Symbol('beta')+ 3)*(z - 1)/(2)+((Symbol('alpha')+ Symbol('beta')+ 3)*(Symbol('alpha')+ Symbol('beta')+ 4))/(2)*((z - 1)/(2))**(2)
Information
Sub Equations
- jacobi(2, Symbol('alpha'), Symbol('beta'), z) = ((Symbol('alpha')+ 1)*(Symbol('alpha')+ 2))/(2)+(Symbol('alpha')+ 2)*(Symbol('alpha')+ Symbol('beta')+ 3)*(z - 1)/(2)+((Symbol('alpha')+ Symbol('beta')+ 3)*(Symbol('alpha')+ Symbol('beta')+ 4))/(2)*((z - 1)/(2))**(2)
Free variables
- Symbol('alpha')
- Symbol('beta')
- z
Symbol info
- Jacobi polynomial; Example: \JacobipolyP{\alpha}{\beta}{n}@{x}
Will be translated to: jacobi($2, $0, $1, $3) Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r2 SymPy: https://docs.sympy.org/latest/modules/functions/special.html#jacobi-polynomials
- 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.
Tests
Symbolic
Numeric
Maple
Translation: JacobiP(2, alpha, beta, z) = ((alpha + 1)*(alpha + 2))/(2)+(alpha + 2)*(alpha + beta + 3)*(z - 1)/(2)+((alpha + beta + 3)*(alpha + beta + 4))/(2)*((z - 1)/(2))^(2)
Information
Sub Equations
- JacobiP(2, alpha, beta, z) = ((alpha + 1)*(alpha + 2))/(2)+(alpha + 2)*(alpha + beta + 3)*(z - 1)/(2)+((alpha + beta + 3)*(alpha + beta + 4))/(2)*((z - 1)/(2))^(2)
Free variables
- alpha
- beta
- 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.
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Complete translation information:
{
"id" : "FORMULA_2456d8e10ee48d46d597e731c07db9d1",
"formula" : "P_2^{(\\alpha,\\beta)}(z)= \\frac{(\\alpha+1)(\\alpha+2)}{2}\n+ (\\alpha+2)(\\alpha+\\beta+3)\\frac{z-1}{2}\n\n+ \\frac{(\\alpha+\\beta+3)(\\alpha+\\beta+4)}{2}\\left(\\frac{z-1}{2}\\right)^2,",
"semanticFormula" : "\\JacobipolyP{\\alpha}{\\beta}{2}@{z} = \\frac{(\\alpha+1)(\\alpha+2)}{2} +(\\alpha + 2)(\\alpha + \\beta + 3) \\frac{z-1}{2} + \\frac{(\\alpha+\\beta+3)(\\alpha+\\beta+4)}{2}(\\frac{z-1}{2})^2 ,",
"confidence" : 0.6563367686953199,
"translations" : {
"Mathematica" : {
"translation" : "JacobiP[2, \\[Alpha], \\[Beta], z] == Divide[(\\[Alpha]+ 1)*(\\[Alpha]+ 2),2]+(\\[Alpha]+ 2)*(\\[Alpha]+ \\[Beta]+ 3)*Divide[z - 1,2]+Divide[(\\[Alpha]+ \\[Beta]+ 3)*(\\[Alpha]+ \\[Beta]+ 4),2]*(Divide[z - 1,2])^(2)",
"translationInformation" : {
"subEquations" : [ "JacobiP[2, \\[Alpha], \\[Beta], z] = Divide[(\\[Alpha]+ 1)*(\\[Alpha]+ 2),2]+(\\[Alpha]+ 2)*(\\[Alpha]+ \\[Beta]+ 3)*Divide[z - 1,2]+Divide[(\\[Alpha]+ \\[Beta]+ 3)*(\\[Alpha]+ \\[Beta]+ 4),2]*(Divide[z - 1,2])^(2)" ],
"freeVariables" : [ "\\[Alpha]", "\\[Beta]", "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"
}
},
"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[2, \\[Alpha], \\[Beta], z]",
"rhs" : "Divide[(\\[Alpha]+ 1)*(\\[Alpha]+ 2),2]+(\\[Alpha]+ 2)*(\\[Alpha]+ \\[Beta]+ 3)*Divide[z - 1,2]+Divide[(\\[Alpha]+ \\[Beta]+ 3)*(\\[Alpha]+ \\[Beta]+ 4),2]*(Divide[z - 1,2])^(2)",
"testExpression" : "(JacobiP[2, \\[Alpha], \\[Beta], z])-(Divide[(\\[Alpha]+ 1)*(\\[Alpha]+ 2),2]+(\\[Alpha]+ 2)*(\\[Alpha]+ \\[Beta]+ 3)*Divide[z - 1,2]+Divide[(\\[Alpha]+ \\[Beta]+ 3)*(\\[Alpha]+ \\[Beta]+ 4),2]*(Divide[z - 1,2])^(2))",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "jacobi(2, Symbol('alpha'), Symbol('beta'), z) == ((Symbol('alpha')+ 1)*(Symbol('alpha')+ 2))/(2)+(Symbol('alpha')+ 2)*(Symbol('alpha')+ Symbol('beta')+ 3)*(z - 1)/(2)+((Symbol('alpha')+ Symbol('beta')+ 3)*(Symbol('alpha')+ Symbol('beta')+ 4))/(2)*((z - 1)/(2))**(2)",
"translationInformation" : {
"subEquations" : [ "jacobi(2, Symbol('alpha'), Symbol('beta'), z) = ((Symbol('alpha')+ 1)*(Symbol('alpha')+ 2))/(2)+(Symbol('alpha')+ 2)*(Symbol('alpha')+ Symbol('beta')+ 3)*(z - 1)/(2)+((Symbol('alpha')+ Symbol('beta')+ 3)*(Symbol('alpha')+ Symbol('beta')+ 4))/(2)*((z - 1)/(2))**(2)" ],
"freeVariables" : [ "Symbol('alpha')", "Symbol('beta')", "z" ],
"tokenTranslations" : {
"\\JacobipolyP" : "Jacobi polynomial; Example: \\JacobipolyP{\\alpha}{\\beta}{n}@{x}\nWill be translated to: jacobi($2, $0, $1, $3)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r2\nSymPy: https://docs.sympy.org/latest/modules/functions/special.html#jacobi-polynomials",
"\\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"
}
}
},
"Maple" : {
"translation" : "JacobiP(2, alpha, beta, z) = ((alpha + 1)*(alpha + 2))/(2)+(alpha + 2)*(alpha + beta + 3)*(z - 1)/(2)+((alpha + beta + 3)*(alpha + beta + 4))/(2)*((z - 1)/(2))^(2)",
"translationInformation" : {
"subEquations" : [ "JacobiP(2, alpha, beta, z) = ((alpha + 1)*(alpha + 2))/(2)+(alpha + 2)*(alpha + beta + 3)*(z - 1)/(2)+((alpha + beta + 3)*(alpha + beta + 4))/(2)*((z - 1)/(2))^(2)" ],
"freeVariables" : [ "alpha", "beta", "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"
}
}
}
},
"positions" : [ ],
"includes" : [ "z", "\\alpha,\\beta", "P_{n}^{(\\alpha, \\beta)}", "P_2^{(\\alpha,\\beta)}(z)= \\frac{(\\alpha+1)(\\alpha+2)}{2}+ (\\alpha+2)(\\alpha+\\beta+3)\\frac{z-1}{2}+ \\frac{(\\alpha+\\beta+3)(\\alpha+\\beta+4)}{2}\\left(\\frac{z-1}{2}\\right)^2,..", "P_{n}^{(\\alpha, \\beta)}(x)" ],
"isPartOf" : [ ],
"definiens" : [ ]
}