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(x)=\frac{n!}{1\cdot3\cdots(2n+1)}\left(x^{-(n+1)}+\frac{(n+1)(n+2)}{2(2n+3)}x^{-(n+3)}+\frac{(n+1)(n+2)(n+3)(n+4)}{2\cdot4(2n+3)(2n+5)}x^{-(n+5)}+\cdots\right)}
... is translated to the CAS output ...
Semantic latex: \assLegendreQ{n}@{x} = \frac{n!}{1\cdot3\cdots(2n+1)}(x^{-(n+1)} + \frac{(n+1)(n+2)}{2(2n+3)} x^{-(n+3)} + \frac{(n+1)(n+2)(n+3)(n+4)}{2\cdot4(2n+3)(2n+5)} x^{-(n+5)} + \cdots)
Confidence: 0.5398725926064
Mathematica
Translation: LegendreQ[n, 0, 3, x] == Divide[(n)!,1 * 3 \[Ellipsis](2*n + 1)]*((x)^(-(n + 1))+Divide[(n + 1)*(n + 2),2*(2*n + 3)]*(x)^(-(n + 3))+Divide[(n + 1)*(n + 2)*(n + 3)*(n + 4),2 * 4*(2*n + 3)*(2*n + 5)]*(x)^(-(n + 5))+ \[Ellipsis])
Information
Sub Equations
- LegendreQ[n, 0, 3, x] = Divide[(n)!,1 * 3 \[Ellipsis](2*n + 1)]*((x)^(-(n + 1))+Divide[(n + 1)*(n + 2),2*(2*n + 3)]*(x)^(-(n + 3))+Divide[(n + 1)*(n + 2)*(n + 3)*(n + 4),2 * 4*(2*n + 3)*(2*n + 5)]*(x)^(-(n + 5))+ \[Ellipsis])
Free variables
- n
- x
Symbol info
- was translated to: *
- 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
Tests
Symbolic
Test expression: (LegendreQ[n, 0, 3, x])-(Divide[(n)!,1 * 3 \[Ellipsis](2*n + 1)]*((x)^(-(n + 1))+Divide[(n + 1)*(n + 2),2*(2*n + 3)]*(x)^(-(n + 3))+Divide[(n + 1)*(n + 2)*(n + 3)*(n + 4),2 * 4*(2*n + 3)*(2*n + 5)]*(x)^(-(n + 5))+ \[Ellipsis]))
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: \assLegendreQ [\assLegendreQ]
Tests
Symbolic
Numeric
Maple
Translation: LegendreQ(n, x) = (factorial(n))/(1 * 3 .. (2*n + 1))*((x)^(-(n + 1))+((n + 1)*(n + 2))/(2*(2*n + 3))*(x)^(-(n + 3))+((n + 1)*(n + 2)*(n + 3)*(n + 4))/(2 * 4*(2*n + 3)*(2*n + 5))*(x)^(-(n + 5))+ ..)
Information
Sub Equations
- LegendreQ(n, x) = (factorial(n))/(1 * 3 .. (2*n + 1))*((x)^(-(n + 1))+((n + 1)*(n + 2))/(2*(2*n + 3))*(x)^(-(n + 3))+((n + 1)*(n + 2)*(n + 3)*(n + 4))/(2 * 4*(2*n + 3)*(2*n + 5))*(x)^(-(n + 5))+ ..)
Free variables
- n
- x
Symbol info
- was translated to: *
- 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
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- solution
Complete translation information:
{
"id" : "FORMULA_964717a264b28b551e0186224fe79528",
"formula" : "Q_n(x)=\\frac{n!}{1\\cdot3\\cdots(2n+1)}\\left(x^{-(n+1)}+\\frac{(n+1)(n+2)}{2(2n+3)}x^{-(n+3)}+\\frac{(n+1)(n+2)(n+3)(n+4)}{2\\cdot4(2n+3)(2n+5)}x^{-(n+5)}+\\cdots\\right)",
"semanticFormula" : "\\assLegendreQ{n}@{x} = \\frac{n!}{1\\cdot3\\cdots(2n+1)}(x^{-(n+1)} + \\frac{(n+1)(n+2)}{2(2n+3)} x^{-(n+3)} + \\frac{(n+1)(n+2)(n+3)(n+4)}{2\\cdot4(2n+3)(2n+5)} x^{-(n+5)} + \\cdots)",
"confidence" : 0.5398725926063954,
"translations" : {
"Mathematica" : {
"translation" : "LegendreQ[n, 0, 3, x] == Divide[(n)!,1 * 3 \\[Ellipsis](2*n + 1)]*((x)^(-(n + 1))+Divide[(n + 1)*(n + 2),2*(2*n + 3)]*(x)^(-(n + 3))+Divide[(n + 1)*(n + 2)*(n + 3)*(n + 4),2 * 4*(2*n + 3)*(2*n + 5)]*(x)^(-(n + 5))+ \\[Ellipsis])",
"translationInformation" : {
"subEquations" : [ "LegendreQ[n, 0, 3, x] = Divide[(n)!,1 * 3 \\[Ellipsis](2*n + 1)]*((x)^(-(n + 1))+Divide[(n + 1)*(n + 2),2*(2*n + 3)]*(x)^(-(n + 3))+Divide[(n + 1)*(n + 2)*(n + 3)*(n + 4),2 * 4*(2*n + 3)*(2*n + 5)]*(x)^(-(n + 5))+ \\[Ellipsis])" ],
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"\\cdot" : "was translated to: *",
"\\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"
}
},
"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" : "LegendreQ[n, 0, 3, x]",
"rhs" : "Divide[(n)!,1 * 3 \\[Ellipsis](2*n + 1)]*((x)^(-(n + 1))+Divide[(n + 1)*(n + 2),2*(2*n + 3)]*(x)^(-(n + 3))+Divide[(n + 1)*(n + 2)*(n + 3)*(n + 4),2 * 4*(2*n + 3)*(2*n + 5)]*(x)^(-(n + 5))+ \\[Ellipsis])",
"testExpression" : "(LegendreQ[n, 0, 3, x])-(Divide[(n)!,1 * 3 \\[Ellipsis](2*n + 1)]*((x)^(-(n + 1))+Divide[(n + 1)*(n + 2),2*(2*n + 3)]*(x)^(-(n + 3))+Divide[(n + 1)*(n + 2)*(n + 3)*(n + 4),2 * 4*(2*n + 3)*(2*n + 5)]*(x)^(-(n + 5))+ \\[Ellipsis]))",
"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: \\assLegendreQ [\\assLegendreQ]"
}
}
},
"Maple" : {
"translation" : "LegendreQ(n, x) = (factorial(n))/(1 * 3 .. (2*n + 1))*((x)^(-(n + 1))+((n + 1)*(n + 2))/(2*(2*n + 3))*(x)^(-(n + 3))+((n + 1)*(n + 2)*(n + 3)*(n + 4))/(2 * 4*(2*n + 3)*(2*n + 5))*(x)^(-(n + 5))+ ..)",
"translationInformation" : {
"subEquations" : [ "LegendreQ(n, x) = (factorial(n))/(1 * 3 .. (2*n + 1))*((x)^(-(n + 1))+((n + 1)*(n + 2))/(2*(2*n + 3))*(x)^(-(n + 3))+((n + 1)*(n + 2)*(n + 3)*(n + 4))/(2 * 4*(2*n + 3)*(2*n + 5))*(x)^(-(n + 5))+ ..)" ],
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"\\cdot" : "was translated to: *",
"\\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"
}
}
}
},
"positions" : [ {
"section" : 3,
"sentence" : 1,
"word" : 4
} ],
"includes" : [ "P_{n}", "Q", "Q_{n}" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "solution",
"score" : 0.722
} ]
}