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)}
... is translated to the CAS output ...
Semantic latex: \JacobipolyP{\alpha}{\beta}{n}@{z}
Confidence: 0.66074870781611
Mathematica
Translation: JacobiP[n, \[Alpha], \[Beta], z]
Information
Sub Equations
- JacobiP[n, \[Alpha], \[Beta], z]
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.
Tests
Symbolic
Numeric
SymPy
Translation: jacobi(n, Symbol('alpha'), Symbol('beta'), z)
Information
Sub Equations
- jacobi(n, Symbol('alpha'), Symbol('beta'), z)
Free variables
- Symbol('alpha')
- Symbol('beta')
- n
- 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(n, alpha, beta, z)
Information
Sub Equations
- JacobiP(n, alpha, beta, z)
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.
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- equation
- article
- other MOI
- dependency graph from Jacobi polynomial
- definition
- outgoing dependency
- context of Jacobi polynomial
- part of any other MOI
- next equation in the same article
- different variant
- introduction
- Pochhammer 's symbol
- Jacobi polynomial
- counterexample
- ingoing dependency
- hypergeometric function
- Jacobi polynomial in arxiv.org
Complete translation information:
{
"id" : "FORMULA_10732488962d5582cd2744ace59c270b",
"formula" : "P_n^{(\\alpha,\\beta)}(z)",
"semanticFormula" : "\\JacobipolyP{\\alpha}{\\beta}{n}@{z}",
"confidence" : 0.660748707816107,
"translations" : {
"Mathematica" : {
"translation" : "JacobiP[n, \\[Alpha], \\[Beta], z]",
"translationInformation" : {
"subEquations" : [ "JacobiP[n, \\[Alpha], \\[Beta], z]" ],
"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"
}
},
"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" : "jacobi(n, Symbol('alpha'), Symbol('beta'), z)",
"translationInformation" : {
"subEquations" : [ "jacobi(n, Symbol('alpha'), Symbol('beta'), z)" ],
"freeVariables" : [ "Symbol('alpha')", "Symbol('beta')", "n", "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"
}
},
"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" : "JacobiP(n, alpha, beta, z)",
"translationInformation" : {
"subEquations" : [ "JacobiP(n, alpha, beta, z)" ],
"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"
}
},
"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" : [ {
"section" : 6,
"sentence" : 13,
"word" : 18
} ],
"includes" : [ "P_n^{(\\alpha,\\beta)}(x)", "\\alpha", "\\beta", "n", "z", "\\alpha, \\beta", "P_n^{(\\alpha, \\beta)}(x)", "P" ],
"isPartOf" : [ "P_n^{(\\alpha,\\beta)}(z)=\\frac{(\\alpha+1)_n}{n!}\\,{}_2F_1\\left(-n,1+\\alpha+\\beta+n;\\alpha+1;\\tfrac{1}{2}(1-z)\\right)", "P_n^{(\\alpha,\\beta)}(z)=\\frac{(\\alpha+1)_n}{n!}{}_2F_1\\left(-n,1+\\alpha+\\beta+n;\\alpha+1;\\tfrac{1}{2}(1-z)\\right)", "P_n^{(\\alpha,\\beta)} (z) = \\frac{\\Gamma (\\alpha+n+1)}{n!\\Gamma (\\alpha+\\beta+n+1)} \\sum_{m=0}^n \\binom{n}{m} \\frac{\\Gamma (\\alpha + \\beta + n + m + 1)}{\\Gamma (\\alpha + m + 1)} \\left(\\frac{z-1}{2}\\right)^m", "P_n^{(\\alpha,\\beta)}(x)", "P_n^{(\\alpha, \\beta)}(x)" ],
"definiens" : [ {
"definition" : "equation",
"score" : 0.8855802092325457
}, {
"definition" : "article",
"score" : 0.7560800417889251
}, {
"definition" : "other MOI",
"score" : 0.6629879847031728
}, {
"definition" : "dependency graph from Jacobi polynomial",
"score" : 0.6231540443721655
}, {
"definition" : "definition",
"score" : 0.5758968646127977
}, {
"definition" : "outgoing dependency",
"score" : 0.5758968646127977
}, {
"definition" : "context of Jacobi polynomial",
"score" : 0.5718328188515018
}, {
"definition" : "part of any other MOI",
"score" : 0.5271746031746032
}, {
"definition" : "next equation in the same article",
"score" : 0.34602378366733294
}, {
"definition" : "different variant",
"score" : 0.34586835176111275
}, {
"definition" : "introduction",
"score" : 0.3191837070106504
}, {
"definition" : "Pochhammer 's symbol",
"score" : 0.31917846089364893
}, {
"definition" : "Jacobi polynomial",
"score" : 0.299185307454904
}, {
"definition" : "counterexample",
"score" : 0.27949995246886183
}, {
"definition" : "ingoing dependency",
"score" : 0.23209258692027535
}, {
"definition" : "hypergeometric function",
"score" : 0.23208734080327384
}, {
"definition" : "Jacobi polynomial in arxiv.org",
"score" : 0.18336507936507934
} ]
}