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_1^{(\alpha,\beta)}(z)= (\alpha+1) + (\alpha+\beta+2)\frac{z-1}{2},}
... is translated to the CAS output ...
Semantic latex: \JacobipolyP{\alpha}{\beta}{1}@{z} =(\alpha + 1) +(\alpha + \beta + 2) \frac{z-1}{2}
Confidence: 0.70338171203013
Mathematica
Translation: JacobiP[1, \[Alpha], \[Beta], z] == (\[Alpha]+ 1)+(\[Alpha]+ \[Beta]+ 2)*Divide[z - 1,2]
Information
Sub Equations
- JacobiP[1, \[Alpha], \[Beta], z] = (\[Alpha]+ 1)+(\[Alpha]+ \[Beta]+ 2)*Divide[z - 1,2]
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[1, \[Alpha], \[Beta], z])-((\[Alpha]+ 1)+(\[Alpha]+ \[Beta]+ 2)*Divide[z - 1,2])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: jacobi(1, Symbol('alpha'), Symbol('beta'), z) == (Symbol('alpha')+ 1)+(Symbol('alpha')+ Symbol('beta')+ 2)*(z - 1)/(2)
Information
Sub Equations
- jacobi(1, Symbol('alpha'), Symbol('beta'), z) = (Symbol('alpha')+ 1)+(Symbol('alpha')+ Symbol('beta')+ 2)*(z - 1)/(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(1, alpha, beta, z) = (alpha + 1)+(alpha + beta + 2)*(z - 1)/(2)
Information
Sub Equations
- JacobiP(1, alpha, beta, z) = (alpha + 1)+(alpha + beta + 2)*(z - 1)/(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_ca61fa237002fce94643d9197732d667",
"formula" : "P_1^{(\\alpha,\\beta)}(z)= (\\alpha+1) + (\\alpha+\\beta+2)\\frac{z-1}{2}",
"semanticFormula" : "\\JacobipolyP{\\alpha}{\\beta}{1}@{z} =(\\alpha + 1) +(\\alpha + \\beta + 2) \\frac{z-1}{2}",
"confidence" : 0.7033817120301267,
"translations" : {
"Mathematica" : {
"translation" : "JacobiP[1, \\[Alpha], \\[Beta], z] == (\\[Alpha]+ 1)+(\\[Alpha]+ \\[Beta]+ 2)*Divide[z - 1,2]",
"translationInformation" : {
"subEquations" : [ "JacobiP[1, \\[Alpha], \\[Beta], z] = (\\[Alpha]+ 1)+(\\[Alpha]+ \\[Beta]+ 2)*Divide[z - 1,2]" ],
"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[1, \\[Alpha], \\[Beta], z]",
"rhs" : "(\\[Alpha]+ 1)+(\\[Alpha]+ \\[Beta]+ 2)*Divide[z - 1,2]",
"testExpression" : "(JacobiP[1, \\[Alpha], \\[Beta], z])-((\\[Alpha]+ 1)+(\\[Alpha]+ \\[Beta]+ 2)*Divide[z - 1,2])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "jacobi(1, Symbol('alpha'), Symbol('beta'), z) == (Symbol('alpha')+ 1)+(Symbol('alpha')+ Symbol('beta')+ 2)*(z - 1)/(2)",
"translationInformation" : {
"subEquations" : [ "jacobi(1, Symbol('alpha'), Symbol('beta'), z) = (Symbol('alpha')+ 1)+(Symbol('alpha')+ Symbol('beta')+ 2)*(z - 1)/(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(1, alpha, beta, z) = (alpha + 1)+(alpha + beta + 2)*(z - 1)/(2)",
"translationInformation" : {
"subEquations" : [ "JacobiP(1, alpha, beta, z) = (alpha + 1)+(alpha + beta + 2)*(z - 1)/(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" : [ {
"section" : 4,
"sentence" : 0,
"word" : 2
} ],
"includes" : [ "P_{n}^{(\\alpha, \\beta)}(x)", "P_{n}^{(\\alpha, \\beta)}", "\\alpha,\\beta", "z" ],
"isPartOf" : [ ],
"definiens" : [ ]
}