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 Q_n^{m}(x) = (-1)^m (1-x^2)^\frac{m}{2} \frac{\mathrm{d}^m}{\mathrm{d}x^m}Q_n(x)\,. }
... is translated to the CAS output ...
Semantic latex: \assLegendreOlverQ[m]{n}@{x} =(- 1)^m(1 - x^2)^\frac{m}{2} \deriv [m]{ }{x} \assLegendreQ{n}@{x}
Confidence: 0.56076556462412
Mathematica
Translation: Exp[-(m) Pi I] LegendreQ[n, m, 3, x]/Gamma[n + m + 1] == (- 1)^(m)*(1 - (x)^(2))^(Divide[m,2])* D[LegendreQ[n, 0, 3, x], {x, m}]
Information
Sub Equations
- Exp[-(m) Pi I] LegendreQ[n, m, 3, x]/Gamma[n + m + 1] = (- 1)^(m)*(1 - (x)^(2))^(Divide[m,2])* D[LegendreQ[n, 0, 3, x], {x, m}]
Free variables
- m
- n
- x
Symbol info
- 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
- Legendre function of second kind; Example: \assLegendreQ{\nu}@{z}
Will be translated to: LegendreQ[$0, 0, 3, $1] Branch Cuts: (-\infty, 1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.2#i Mathematica: https://reference.wolfram.com/language/ref/LegendreQ.html
- Olver's associated Legendre function; Example: \assLegendreOlverQ[\mu]{\nu}@{z}
Will be translated to: Alternative translations: [Exp[-($0) Pi I] LegendreQ[$1, $0, 3, $2]/Gamma[$1 + $0 + 1]]Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.3#E10 Mathematica:
Tests
Symbolic
Test expression: (Exp[-(m) Pi I] LegendreQ[n, m, 3, x]/Gamma[n + m + 1])-((- 1)^(m)*(1 - (x)^(2))^(Divide[m,2])* D[LegendreQ[n, 0, 3, x], {x, m}])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \assLegendreOlverQ [\assLegendreOlverQ]
Tests
Symbolic
Numeric
Maple
Translation: exp(-(m)*Pi*I)*LegendreQ(n,m,x)/GAMMA(n+m+1) = (- 1)^(m)*(1 - (x)^(2))^((m)/(2))* diff(LegendreQ(n, x), [x$(m)])
Information
Sub Equations
- exp(-(m)*Pi*I)*LegendreQ(n,m,x)/GAMMA(n+m+1) = (- 1)^(m)*(1 - (x)^(2))^((m)/(2))* diff(LegendreQ(n, x), [x$(m)])
Free variables
- m
- n
- x
Symbol info
- 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
- Legendre function of second kind; Example: \assLegendreQ{\nu}@{z}
Will be translated to: LegendreQ($0, $1) Branch Cuts: (-\infty, 1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.2#i Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreQ
- Olver's associated Legendre function; Example: \assLegendreOlverQ[\mu]{\nu}@{z}
Will be translated to: exp(-($0)*Pi*I)*LegendreQ($1,$0,$2)/GAMMA($1+$0+1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.3#E10 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreQ
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_431033c7865a2b7913591f6f89fda419",
"formula" : "Q_n^{m}(x)\n=\n(-1)^m (1-x^2)^\\frac{m}{2} \\frac{\\mathrm{d}^m}{\\mathrm{d}x^m}Q_n(x)",
"semanticFormula" : "\\assLegendreOlverQ[m]{n}@{x} =(- 1)^m(1 - x^2)^\\frac{m}{2} \\deriv [m]{ }{x} \\assLegendreQ{n}@{x}",
"confidence" : 0.5607655646241182,
"translations" : {
"Mathematica" : {
"translation" : "Exp[-(m) Pi I] LegendreQ[n, m, 3, x]/Gamma[n + m + 1] == (- 1)^(m)*(1 - (x)^(2))^(Divide[m,2])* D[LegendreQ[n, 0, 3, x], {x, m}]",
"translationInformation" : {
"subEquations" : [ "Exp[-(m) Pi I] LegendreQ[n, m, 3, x]/Gamma[n + m + 1] = (- 1)^(m)*(1 - (x)^(2))^(Divide[m,2])* D[LegendreQ[n, 0, 3, x], {x, m}]" ],
"freeVariables" : [ "m", "n", "x" ],
"tokenTranslations" : {
"\\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",
"\\assLegendreQ" : "Legendre function of second kind; Example: \\assLegendreQ{\\nu}@{z}\nWill be translated to: LegendreQ[$0, 0, 3, $1]\nBranch Cuts: (-\\infty, 1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.2#i\nMathematica: https://reference.wolfram.com/language/ref/LegendreQ.html",
"\\assLegendreOlverQ1" : "Olver's associated Legendre function; Example: \\assLegendreOlverQ[\\mu]{\\nu}@{z}\nWill be translated to: \nAlternative translations: [Exp[-($0) Pi I] LegendreQ[$1, $0, 3, $2]/Gamma[$1 + $0 + 1]]Relevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.3#E10\nMathematica: "
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "Exp[-(m) Pi I] LegendreQ[n, m, 3, x]/Gamma[n + m + 1]",
"rhs" : "(- 1)^(m)*(1 - (x)^(2))^(Divide[m,2])* D[LegendreQ[n, 0, 3, x], {x, m}]",
"testExpression" : "(Exp[-(m) Pi I] LegendreQ[n, m, 3, x]/Gamma[n + m + 1])-((- 1)^(m)*(1 - (x)^(2))^(Divide[m,2])* D[LegendreQ[n, 0, 3, x], {x, m}])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\assLegendreOlverQ [\\assLegendreOlverQ]"
}
}
},
"Maple" : {
"translation" : "exp(-(m)*Pi*I)*LegendreQ(n,m,x)/GAMMA(n+m+1) = (- 1)^(m)*(1 - (x)^(2))^((m)/(2))* diff(LegendreQ(n, x), [x$(m)])",
"translationInformation" : {
"subEquations" : [ "exp(-(m)*Pi*I)*LegendreQ(n,m,x)/GAMMA(n+m+1) = (- 1)^(m)*(1 - (x)^(2))^((m)/(2))* diff(LegendreQ(n, x), [x$(m)])" ],
"freeVariables" : [ "m", "n", "x" ],
"tokenTranslations" : {
"\\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",
"\\assLegendreQ" : "Legendre function of second kind; Example: \\assLegendreQ{\\nu}@{z}\nWill be translated to: LegendreQ($0, $1)\nBranch Cuts: (-\\infty, 1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.2#i\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreQ",
"\\assLegendreOlverQ1" : "Olver's associated Legendre function; Example: \\assLegendreOlverQ[\\mu]{\\nu}@{z}\nWill be translated to: exp(-($0)*Pi*I)*LegendreQ($1,$0,$2)/GAMMA($1+$0+1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/14.3#E10\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreQ"
}
}
}
},
"positions" : [ ],
"includes" : [ "P_{n}", "Q", "Q_n^{m}(x)=(-1)^m (1-x^2)^\\frac{m}{2} \\frac{\\mathrm{d}^m}{\\mathrm{d}x^m}Q_n(x)\\,", "Q_{n}", "-1" ],
"isPartOf" : [ "Q_n^{m}(x)=(-1)^m (1-x^2)^\\frac{m}{2} \\frac{\\mathrm{d}^m}{\\mathrm{d}x^m}Q_n(x)\\," ],
"definiens" : [ ]
}