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{J}_\nu(z)=\frac{1}{\pi} \int_0^\pi \cos (\nu\theta-z\sin\theta) \,d\theta}
... is translated to the CAS output ...
Semantic latex: \AngerJ{\nu}@{z} = \frac{1}{\cpi} \int_0^{\cpi} \cos(\nu \theta - z \sin \theta) \diff{\theta}
Confidence: 0.70910057604668
Mathematica
Translation: AngerJ[\[Nu], z] == Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]
Information
Sub Equations
- AngerJ[\[Nu], z] = Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, GenerateConditions->None]
Free variables
- \[Nu]
- z
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: Cos[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Mathematica: https://reference.wolfram.com/language/ref/Cos.html
- Anger function; Example: \AngerJ{v}@{z}
Will be translated to: AngerJ[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.10#E1 Mathematica: https://reference.wolfram.com/language/ref/AngerJ.html
- Pi was translated to: Pi
- Sine; Example: \sin@@{z}
Will be translated to: Sin[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Mathematica: https://reference.wolfram.com/language/ref/Sin.html
Tests
Symbolic
Test expression: (AngerJ[\[Nu], z])-(Divide[1,Pi]*Integrate[Cos[\[Nu]*\[Theta]- z*Sin[\[Theta]]], {\[Theta], 0, Pi}, 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: \AngerJ [\AngerJ]
Tests
Symbolic
Numeric
Maple
Translation: AngerJ(nu, z) = (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi)
Information
Sub Equations
- AngerJ(nu, z) = (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi)
Free variables
- nu
- z
Symbol info
- Cosine; Example: \cos@@{z}
Will be translated to: cos($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos
- Anger function; Example: \AngerJ{v}@{z}
Will be translated to: AngerJ($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.10#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=AngerJ
- Pi was translated to: Pi
- Sine; Example: \sin@@{z}
Will be translated to: sin($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_450922890270147d90f3cfc35d21d320",
"formula" : "\\mathbf{J}_\\nu(z)=\\frac{1}{\\pi} \\int_0^\\pi \\cos (\\nu\\theta-z\\sin\\theta) d\\theta",
"semanticFormula" : "\\AngerJ{\\nu}@{z} = \\frac{1}{\\cpi} \\int_0^{\\cpi} \\cos(\\nu \\theta - z \\sin \\theta) \\diff{\\theta}",
"confidence" : 0.709100576046682,
"translations" : {
"Mathematica" : {
"translation" : "AngerJ[\\[Nu], z] == Divide[1,Pi]*Integrate[Cos[\\[Nu]*\\[Theta]- z*Sin[\\[Theta]]], {\\[Theta], 0, Pi}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "AngerJ[\\[Nu], z] = Divide[1,Pi]*Integrate[Cos[\\[Nu]*\\[Theta]- z*Sin[\\[Theta]]], {\\[Theta], 0, Pi}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Nu]", "z" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: Cos[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nMathematica: https://reference.wolfram.com/language/ref/Cos.html",
"\\AngerJ" : "Anger function; Example: \\AngerJ{v}@{z}\nWill be translated to: AngerJ[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.10#E1\nMathematica: https://reference.wolfram.com/language/ref/AngerJ.html",
"\\cpi" : "Pi was translated to: Pi",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: Sin[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nMathematica: https://reference.wolfram.com/language/ref/Sin.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" : "AngerJ[\\[Nu], z]",
"rhs" : "Divide[1,Pi]*Integrate[Cos[\\[Nu]*\\[Theta]- z*Sin[\\[Theta]]], {\\[Theta], 0, Pi}, GenerateConditions->None]",
"testExpression" : "(AngerJ[\\[Nu], z])-(Divide[1,Pi]*Integrate[Cos[\\[Nu]*\\[Theta]- z*Sin[\\[Theta]]], {\\[Theta], 0, Pi}, 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: \\AngerJ [\\AngerJ]"
}
}
},
"Maple" : {
"translation" : "AngerJ(nu, z) = (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi)",
"translationInformation" : {
"subEquations" : [ "AngerJ(nu, z) = (1)/(Pi)*int(cos(nu*theta - z*sin(theta)), theta = 0..Pi)" ],
"freeVariables" : [ "nu", "z" ],
"tokenTranslations" : {
"\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: cos($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos",
"\\AngerJ" : "Anger function; Example: \\AngerJ{v}@{z}\nWill be translated to: AngerJ($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.10#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=AngerJ",
"\\cpi" : "Pi was translated to: Pi",
"\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: sin($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/4.14#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin"
}
}
}
},
"positions" : [ ],
"includes" : [ "\\mathbf{J}_{\\nu}", "\\mathbf{J}_\\nu(z)=\\frac{1}{\\pi} \\int_0^\\pi \\cos (\\nu\\theta-z\\sin\\theta) \\,d\\theta", "J_{\\nu}", "\\nu" ],
"isPartOf" : [ "\\mathbf{J}_\\nu(z)=\\frac{1}{\\pi} \\int_0^\\pi \\cos (\\nu\\theta-z\\sin\\theta) \\,d\\theta" ],
"definiens" : [ ]
}