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 \frac{1}{\big(\lambda(\tau)\big)^{1/4}}-\big(\lambda(\tau)\big)^{1/4} = \frac{1}{2}\left(\frac{\eta(\tfrac{\tau}{4})}{\eta(\tau)}\right)^4 = 2\,\frac{\theta_4^2(0,\tfrac{\tau}{2})}{\theta_2^2(0,\tfrac{\tau}{2})}}
... is translated to the CAS output ...
Semantic latex: \frac{1}{(\modularlambdatau@{\tau})^{1/4}} -(\modularlambdatau@{\tau})^{1/4} = \frac{1}{2}(\frac{\Dedekindeta@{\tfrac{\tau}{4}}}{\Dedekindeta@{\tau}})^4 = 2 \frac{\theta_4^2(0,\tfrac{\tau}{2})}{\theta_2^2(0,\tfrac{\tau}{2})}
Confidence: 0.67932481381141
Mathematica
Translation: Divide[1,(ModularLambda[\[Tau]])^(1/4)]-(ModularLambda[\[Tau]])^(1/4) == Divide[1,2]*(Divide[DedekindEta[Divide[\[Tau],4]],DedekindEta[\[Tau]]])^(4) == 2*Divide[(Subscript[\[Theta], 4])^(2)[0 ,Divide[\[Tau],2]],(Subscript[\[Theta], 2])^(2)[0 ,Divide[\[Tau],2]]]
Information
Sub Equations
- Divide[1,(ModularLambda[\[Tau]])^(1/4)]-(ModularLambda[\[Tau]])^(1/4) = Divide[1,2]*(Divide[DedekindEta[Divide[\[Tau],4]],DedekindEta[\[Tau]]])^(4)
- Divide[1,2]*(Divide[DedekindEta[Divide[\[Tau],4]],DedekindEta[\[Tau]]])^(4) = 2*Divide[(Subscript[\[Theta], 4])^(2)[0 ,Divide[\[Tau],2]],(Subscript[\[Theta], 2])^(2)[0 ,Divide[\[Tau],2]]]
Free variables
- Subscript[\[Theta], 2]
- Subscript[\[Theta], 4]
- \[Tau]
Symbol info
- Elliptic modular function; Example: \modularlambdatau@{\tau}
Will be translated to: ModularLambda[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/23.15#E6 Mathematica: https://reference.wolfram.com/language/ref/ModularLambda.html
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Dedikind's Eta function; Example: \Dedekindeta@{\tau}
Will be translated to: DedekindEta[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/23.15#E9 Mathematica: https://reference.wolfram.com/language/ref/DedekindEta.html
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \modularlambdatau [\modularlambdatau]
Tests
Symbolic
Numeric
Maple
Translation:
Information
Symbol info
- (LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \modularlambdatau [\modularlambdatau]
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_7180c6336ae80b9076a1c1e8a77d8fca",
"formula" : "\\frac{1}{(\\lambda(\\tau))^{1/4}}-(\\lambda(\\tau))^{1/4} = \\frac{1}{2}\\left(\\frac{\\eta(\\tfrac{\\tau}{4})}{\\eta(\\tau)}\\right)^4 = 2\\frac{\\theta_4^2(0,\\tfrac{\\tau}{2})}{\\theta_2^2(0,\\tfrac{\\tau}{2})}",
"semanticFormula" : "\\frac{1}{(\\modularlambdatau@{\\tau})^{1/4}} -(\\modularlambdatau@{\\tau})^{1/4} = \\frac{1}{2}(\\frac{\\Dedekindeta@{\\tfrac{\\tau}{4}}}{\\Dedekindeta@{\\tau}})^4 = 2 \\frac{\\theta_4^2(0,\\tfrac{\\tau}{2})}{\\theta_2^2(0,\\tfrac{\\tau}{2})}",
"confidence" : 0.679324813811409,
"translations" : {
"Mathematica" : {
"translation" : "Divide[1,(ModularLambda[\\[Tau]])^(1/4)]-(ModularLambda[\\[Tau]])^(1/4) == Divide[1,2]*(Divide[DedekindEta[Divide[\\[Tau],4]],DedekindEta[\\[Tau]]])^(4) == 2*Divide[(Subscript[\\[Theta], 4])^(2)[0 ,Divide[\\[Tau],2]],(Subscript[\\[Theta], 2])^(2)[0 ,Divide[\\[Tau],2]]]",
"translationInformation" : {
"subEquations" : [ "Divide[1,(ModularLambda[\\[Tau]])^(1/4)]-(ModularLambda[\\[Tau]])^(1/4) = Divide[1,2]*(Divide[DedekindEta[Divide[\\[Tau],4]],DedekindEta[\\[Tau]]])^(4)", "Divide[1,2]*(Divide[DedekindEta[Divide[\\[Tau],4]],DedekindEta[\\[Tau]]])^(4) = 2*Divide[(Subscript[\\[Theta], 4])^(2)[0 ,Divide[\\[Tau],2]],(Subscript[\\[Theta], 2])^(2)[0 ,Divide[\\[Tau],2]]]" ],
"freeVariables" : [ "Subscript[\\[Theta], 2]", "Subscript[\\[Theta], 4]", "\\[Tau]" ],
"tokenTranslations" : {
"\\modularlambdatau" : "Elliptic modular function; Example: \\modularlambdatau@{\\tau}\nWill be translated to: ModularLambda[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/23.15#E6\nMathematica: https://reference.wolfram.com/language/ref/ModularLambda.html",
"\\theta" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\Dedekindeta" : "Dedikind's Eta function; Example: \\Dedekindeta@{\\tau}\nWill be translated to: DedekindEta[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/23.15#E9\nMathematica: https://reference.wolfram.com/language/ref/DedekindEta.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"SymPy" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\modularlambdatau [\\modularlambdatau]"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"Maple" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \\modularlambdatau [\\modularlambdatau]"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
}
},
"positions" : [ ],
"includes" : [ "\\tau", "\\lambda", "\\frac{1}{\\big(\\lambda(\\tau)\\big)^{1/4}}-\\big(\\lambda(\\tau)\\big)^{1/4} = \\frac{1}{2}\\left(\\frac{\\eta(\\tfrac{\\tau}{4})}{\\eta(\\tau)}\\right)^4 = 2\\,\\frac{\\theta_4^2(0,\\tfrac{\\tau}{2})}{\\theta_2^2(0,\\tfrac{\\tau}{2})}", "\\eta(\\tau)", "\\lambda(\\tau)" ],
"isPartOf" : [ "\\frac{1}{\\big(\\lambda(\\tau)\\big)^{1/4}}-\\big(\\lambda(\\tau)\\big)^{1/4} = \\frac{1}{2}\\left(\\frac{\\eta(\\tfrac{\\tau}{4})}{\\eta(\\tau)}\\right)^4 = 2\\,\\frac{\\theta_4^2(0,\\tfrac{\\tau}{2})}{\\theta_2^2(0,\\tfrac{\\tau}{2})}" ],
"definiens" : [ ]
}