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}(z) = \frac{1 }{2^n n! } \frac{d^n }{ d z^n } ( z^2 - 1 )^n \; . }
... is translated to the CAS output ...
Semantic latex: \LegendrepolyP{n}@{z} = \frac{1 }{2^n n! } \deriv [n]{ }{z}(z^2 - 1)^n
Confidence: 0.67814962762282
Mathematica
Translation: LegendreP[n, z] == Divide[1,(2)^(n)* (n)!]*D[((z)^(2)- 1)^(n), {z, n}]
Information
Sub Equations
- LegendreP[n, z] = Divide[1,(2)^(n)* (n)!]*D[((z)^(2)- 1)^(n), {z, n}]
Free variables
- n
- z
Symbol info
- Legendre polynomial; Example: \LegendrepolyP{n}@{x}
Will be translated to: LegendreP[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r10 Mathematica: https://reference.wolfram.com/language/ref/LegendreP.html
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: D[$1, {$2, $0}] Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 Mathematica: https://reference.wolfram.com/language/ref/D.html
Tests
Symbolic
Test expression: (LegendreP[n, z])-(Divide[1,(2)^(n)* (n)!]*D[((z)^(2)- 1)^(n), {z, n}])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \LegendrepolyP [\LegendrepolyP]
Tests
Symbolic
Numeric
Maple
Translation: LegendreP(n, z) = (1)/((2)^(n)* factorial(n))*diff(((z)^(2)- 1)^(n), [z$(n)])
Information
Sub Equations
- LegendreP(n, z) = (1)/((2)^(n)* factorial(n))*diff(((z)^(2)- 1)^(n), [z$(n)])
Free variables
- n
- z
Symbol info
- Legendre polynomial; Example: \LegendrepolyP{n}@{x}
Will be translated to: LegendreP($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r10 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreP
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: diff($1, [$2$($0)]) Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 Maple: https://www.maplesoft.com/support/help/Maple/view.aspx?path=diff
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_0d9e2107b86d41c929d755c9eaac3f88",
"formula" : "P_{n}(z) = \\frac{1 }{2^n n! } \\frac{d^n }{ d z^n } ( z^2 - 1 )^n",
"semanticFormula" : "\\LegendrepolyP{n}@{z} = \\frac{1 }{2^n n! } \\deriv [n]{ }{z}(z^2 - 1)^n",
"confidence" : 0.6781496276228178,
"translations" : {
"Mathematica" : {
"translation" : "LegendreP[n, z] == Divide[1,(2)^(n)* (n)!]*D[((z)^(2)- 1)^(n), {z, n}]",
"translationInformation" : {
"subEquations" : [ "LegendreP[n, z] = Divide[1,(2)^(n)* (n)!]*D[((z)^(2)- 1)^(n), {z, n}]" ],
"freeVariables" : [ "n", "z" ],
"tokenTranslations" : {
"\\LegendrepolyP" : "Legendre polynomial; Example: \\LegendrepolyP{n}@{x}\nWill be translated to: LegendreP[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r10\nMathematica: https://reference.wolfram.com/language/ref/LegendreP.html",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: D[$1, {$2, $0}]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nMathematica: https://reference.wolfram.com/language/ref/D.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "LegendreP[n, z]",
"rhs" : "Divide[1,(2)^(n)* (n)!]*D[((z)^(2)- 1)^(n), {z, n}]",
"testExpression" : "(LegendreP[n, z])-(Divide[1,(2)^(n)* (n)!]*D[((z)^(2)- 1)^(n), {z, n}])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\LegendrepolyP [\\LegendrepolyP]"
}
}
},
"Maple" : {
"translation" : "LegendreP(n, z) = (1)/((2)^(n)* factorial(n))*diff(((z)^(2)- 1)^(n), [z$(n)])",
"translationInformation" : {
"subEquations" : [ "LegendreP(n, z) = (1)/((2)^(n)* factorial(n))*diff(((z)^(2)- 1)^(n), [z$(n)])" ],
"freeVariables" : [ "n", "z" ],
"tokenTranslations" : {
"\\LegendrepolyP" : "Legendre polynomial; Example: \\LegendrepolyP{n}@{x}\nWill be translated to: LegendreP($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r10\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreP",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: diff($1, [$2$($0)])\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nMaple: https://www.maplesoft.com/support/help/Maple/view.aspx?path=diff"
}
}
}
},
"positions" : [ ],
"includes" : [ "z", "P_{n}(z) = \\frac{1 }{2^n n! } \\frac{d^n }{ d z^n } ( z^2 - 1 )^n \\;", "n" ],
"isPartOf" : [ "P_{n}(z) = \\frac{1 }{2^n n! } \\frac{d^n }{ d z^n } ( z^2 - 1 )^n \\;" ],
"definiens" : [ ]
}