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 \mathbf{L}_{\nu}(z) = \left({\frac{z}{2}}\right)^{\nu+1} \sum_{k=0}^\infty \frac{1}{\Gamma \left (\frac{3}{2}+k \right ) \Gamma \left (\frac{3}{2}+k+\nu \right )} \left(\frac{z}{2}\right)^{2k}.}
... is translated to the CAS output ...
Semantic latex: \modStruveL{\nu}@{z} =({\frac{z}{2}})^{\nu+1} \sum_{k=0}^\infty \frac{1}{\EulerGamma@{\frac{3}{2} + k} \EulerGamma@{\frac{3}{2} + k + \nu}}(\frac{z}{2})^{2k}
Confidence: 0.73776549246697
Mathematica
Translation: StruveL[\[Nu], z] == (Divide[z,2])^(\[Nu]+ 1)* Sum[Divide[1,Gamma[Divide[3,2]+ k]*Gamma[Divide[3,2]+ k + \[Nu]]]*(Divide[z,2])^(2*k), {k, 0, Infinity}, GenerateConditions->None]
Information
Sub Equations
- StruveL[\[Nu], z] = (Divide[z,2])^(\[Nu]+ 1)* Sum[Divide[1,Gamma[Divide[3,2]+ k]*Gamma[Divide[3,2]+ k + \[Nu]]]*(Divide[z,2])^(2*k), {k, 0, Infinity}, GenerateConditions->None]
Free variables
- \[Nu]
- z
Symbol info
- Modified Struve function; Example: \modStruveL{\nu}@{z}
Will be translated to: StruveL[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E2 Mathematica: https://reference.wolfram.com/language/ref/StruveL.html
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: Gamma[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Mathematica: https://reference.wolfram.com/language/ref/Gamma.html
Tests
Symbolic
Test expression: (StruveL[\[Nu], z])-((Divide[z,2])^(\[Nu]+ 1)* Sum[Divide[1,Gamma[Divide[3,2]+ k]*Gamma[Divide[3,2]+ k + \[Nu]]]*(Divide[z,2])^(2*k), {k, 0, Infinity}, GenerateConditions->None])
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: \modStruveL [\modStruveL]
Tests
Symbolic
Numeric
Maple
Translation: StruveL(nu, z) = ((z)/(2))^(nu + 1)* sum((1)/(GAMMA((3)/(2)+ k)*GAMMA((3)/(2)+ k + nu))*((z)/(2))^(2*k), k = 0..infinity)
Information
Sub Equations
- StruveL(nu, z) = ((z)/(2))^(nu + 1)* sum((1)/(GAMMA((3)/(2)+ k)*GAMMA((3)/(2)+ k + nu))*((z)/(2))^(2*k), k = 0..infinity)
Free variables
- nu
- z
Symbol info
- Modified Struve function; Example: \modStruveL{\nu}@{z}
Will be translated to: StruveL($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveL
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: GAMMA($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- power series
- Struve function
Complete translation information:
{
"id" : "FORMULA_fcb6c30a36cf8f25e174d566272bc790",
"formula" : "\\mathbf{L}_{\\nu}(z) = \\left({\\frac{z}{2}}\\right)^{\\nu+1} \\sum_{k=0}^\\infty \\frac{1}{\\Gamma \\left (\\frac{3}{2}+k \\right ) \\Gamma \\left (\\frac{3}{2}+k+\\nu \\right )} \\left(\\frac{z}{2}\\right)^{2k}",
"semanticFormula" : "\\modStruveL{\\nu}@{z} =({\\frac{z}{2}})^{\\nu+1} \\sum_{k=0}^\\infty \\frac{1}{\\EulerGamma@{\\frac{3}{2} + k} \\EulerGamma@{\\frac{3}{2} + k + \\nu}}(\\frac{z}{2})^{2k}",
"confidence" : 0.7377654924669682,
"translations" : {
"Mathematica" : {
"translation" : "StruveL[\\[Nu], z] == (Divide[z,2])^(\\[Nu]+ 1)* Sum[Divide[1,Gamma[Divide[3,2]+ k]*Gamma[Divide[3,2]+ k + \\[Nu]]]*(Divide[z,2])^(2*k), {k, 0, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "StruveL[\\[Nu], z] = (Divide[z,2])^(\\[Nu]+ 1)* Sum[Divide[1,Gamma[Divide[3,2]+ k]*Gamma[Divide[3,2]+ k + \\[Nu]]]*(Divide[z,2])^(2*k), {k, 0, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Nu]", "z" ],
"tokenTranslations" : {
"\\modStruveL" : "Modified Struve function; Example: \\modStruveL{\\nu}@{z}\nWill be translated to: StruveL[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E2\nMathematica: https://reference.wolfram.com/language/ref/StruveL.html",
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: Gamma[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMathematica: https://reference.wolfram.com/language/ref/Gamma.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" : "StruveL[\\[Nu], z]",
"rhs" : "(Divide[z,2])^(\\[Nu]+ 1)* Sum[Divide[1,Gamma[Divide[3,2]+ k]*Gamma[Divide[3,2]+ k + \\[Nu]]]*(Divide[z,2])^(2*k), {k, 0, Infinity}, GenerateConditions->None]",
"testExpression" : "(StruveL[\\[Nu], z])-((Divide[z,2])^(\\[Nu]+ 1)* Sum[Divide[1,Gamma[Divide[3,2]+ k]*Gamma[Divide[3,2]+ k + \\[Nu]]]*(Divide[z,2])^(2*k), {k, 0, Infinity}, GenerateConditions->None])",
"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: \\modStruveL [\\modStruveL]"
}
}
},
"Maple" : {
"translation" : "StruveL(nu, z) = ((z)/(2))^(nu + 1)* sum((1)/(GAMMA((3)/(2)+ k)*GAMMA((3)/(2)+ k + nu))*((z)/(2))^(2*k), k = 0..infinity)",
"translationInformation" : {
"subEquations" : [ "StruveL(nu, z) = ((z)/(2))^(nu + 1)* sum((1)/(GAMMA((3)/(2)+ k)*GAMMA((3)/(2)+ k + nu))*((z)/(2))^(2*k), k = 0..infinity)" ],
"freeVariables" : [ "nu", "z" ],
"tokenTranslations" : {
"\\modStruveL" : "Modified Struve function; Example: \\modStruveL{\\nu}@{z}\nWill be translated to: StruveL($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveL",
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: GAMMA($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA"
}
}
}
},
"positions" : [ {
"section" : 2,
"sentence" : 1,
"word" : 14
} ],
"includes" : [ "\\mathbf{L}_{\\nu}(z)", "\\Gamma(z)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "power series",
"score" : 0.6859086196238077
}, {
"definition" : "Struve function",
"score" : 0.5988174995334326
} ]
}