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_{3}^{2}(x)=15x(1-x^2)}
... is translated to the CAS output ...
Semantic latex: \assLegendreP[2]{3}@{x} = 15 x(1 - x^2)
Confidence: 0.77035532448677
Mathematica
Translation: LegendreP[3, 2, 3, x] == 15*x*(1 - (x)^(2))
Information
Sub Equations
- LegendreP[3, 2, 3, x] = 15*x*(1 - (x)^(2))
Free variables
- x
Symbol info
- associated Legendre polynomial of the first kind; Example: \assLegendreP[mu]{nu}@{z}
Will be translated to: LegendreP[$1, $0, 3, $2] Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.21#Ex1 Mathematica: https://reference.wolfram.com/language/ref/LegendreP.html
Tests
Symbolic
Test expression: (LegendreP[3, 2, 3, x])-(15*x*(1 - (x)^(2)))
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: \assLegendreP [\assLegendreP]
Tests
Symbolic
Numeric
Maple
Translation: LegendreP(3, 2, x) = 15*x*(1 - (x)^(2))
Information
Sub Equations
- LegendreP(3, 2, x) = 15*x*(1 - (x)^(2))
Free variables
- x
Symbol info
- associated Legendre polynomial of the first kind; Example: \assLegendreP[mu]{nu}@{z}
Will be translated to: LegendreP($1, $0, $2) Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.21#Ex1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreP
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- Legendre function
- negative value
Complete translation information:
{
"id" : "FORMULA_0691eac040cc0adf81be5ce568096d79",
"formula" : "P_{3}^{2}(x)=15x(1-x^2)",
"semanticFormula" : "\\assLegendreP[2]{3}@{x} = 15 x(1 - x^2)",
"confidence" : 0.7703553244867746,
"translations" : {
"Mathematica" : {
"translation" : "LegendreP[3, 2, 3, x] == 15*x*(1 - (x)^(2))",
"translationInformation" : {
"subEquations" : [ "LegendreP[3, 2, 3, x] = 15*x*(1 - (x)^(2))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\assLegendreP1" : "associated Legendre polynomial of the first kind; Example: \\assLegendreP[mu]{nu}@{z}\nWill be translated to: LegendreP[$1, $0, 3, $2]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.21#Ex1\nMathematica: https://reference.wolfram.com/language/ref/LegendreP.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" : "LegendreP[3, 2, 3, x]",
"rhs" : "15*x*(1 - (x)^(2))",
"testExpression" : "(LegendreP[3, 2, 3, x])-(15*x*(1 - (x)^(2)))",
"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: \\assLegendreP [\\assLegendreP]"
}
}
},
"Maple" : {
"translation" : "LegendreP(3, 2, x) = 15*x*(1 - (x)^(2))",
"translationInformation" : {
"subEquations" : [ "LegendreP(3, 2, x) = 15*x*(1 - (x)^(2))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\assLegendreP1" : "associated Legendre polynomial of the first kind; Example: \\assLegendreP[mu]{nu}@{z}\nWill be translated to: LegendreP($1, $0, $2)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.21#Ex1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreP"
}
}
}
},
"positions" : [ {
"section" : 7,
"sentence" : 0,
"word" : 31
} ],
"includes" : [ "P_{\\ell}^{m}", "P_\\ell^{m}(x)", "P", "P_\\lambda^{\\mu}(z)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "Legendre function",
"score" : 0.6859086196238077
}, {
"definition" : "negative value",
"score" : 0.5988174995334326
} ]
}