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 z\mathbf{E}_{\nu-1}(z)+z\mathbf{E}_{\nu+1}(z)=2\nu\mathbf{E}_\nu(z)-\frac{2(1-\cos\pi\nu)}{\pi}}
... is translated to the CAS output ...
Semantic latex: z \WeberE{\nu-1}@{z} + z \WeberE{\nu+1}@{z} = 2 \nu \WeberE{\nu}@{z} - \frac{2(1 - \cos \cpi \nu)}{\cpi}
Confidence: 0.87629473436744
Mathematica
Translation: z*WeberE[\[Nu]- 1, z]+ z*WeberE[\[Nu]+ 1, z] == 2*\[Nu]*WeberE[\[Nu], z]-Divide[2*(1 - Cos[Pi]*\[Nu]),Pi]
Information
Sub Equations
- z*WeberE[\[Nu]- 1, z]+ z*WeberE[\[Nu]+ 1, z] = 2*\[Nu]*WeberE[\[Nu], z]-Divide[2*(1 - Cos[Pi]*\[Nu]),Pi]
Free variables
- \[Nu]
- z
Symbol info
- Weber function; Example: \WeberE{v}@{z}
Will be translated to: WeberE[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.10#E2 Mathematica: https://reference.wolfram.com/language/ref/WeberE.html
- 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
- Pi was translated to: Pi
Tests
Symbolic
Test expression: (z*WeberE[\[Nu]- 1, z]+ z*WeberE[\[Nu]+ 1, z])-(2*\[Nu]*WeberE[\[Nu], z]-Divide[2*(1 - Cos[Pi]*\[Nu]),Pi])
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: \WeberE [\WeberE]
Tests
Symbolic
Numeric
Maple
Translation: z*WeberE(nu - 1, z)+ z*WeberE(nu + 1, z) = 2*nu*WeberE(nu, z)-(2*(1 - cos(Pi)*nu))/(Pi)
Information
Sub Equations
- z*WeberE(nu - 1, z)+ z*WeberE(nu + 1, z) = 2*nu*WeberE(nu, z)-(2*(1 - cos(Pi)*nu))/(Pi)
Free variables
- nu
- z
Symbol info
- Weber function; Example: \WeberE{v}@{z}
Will be translated to: WeberE($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.10#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=AngerJ
- 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
- Pi was translated to: Pi
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- inhomogeneous form of recurrence relation
- Weber function
- Anger function
Complete translation information:
{
"id" : "FORMULA_8a261214ed88171f69105f81baa1a6c2",
"formula" : "z\\mathbf{E}_{\\nu-1}(z)+z\\mathbf{E}_{\\nu+1}(z)=2\\nu\\mathbf{E}_\\nu(z)-\\frac{2(1-\\cos\\pi\\nu)}{\\pi}",
"semanticFormula" : "z \\WeberE{\\nu-1}@{z} + z \\WeberE{\\nu+1}@{z} = 2 \\nu \\WeberE{\\nu}@{z} - \\frac{2(1 - \\cos \\cpi \\nu)}{\\cpi}",
"confidence" : 0.8762947343674413,
"translations" : {
"Mathematica" : {
"translation" : "z*WeberE[\\[Nu]- 1, z]+ z*WeberE[\\[Nu]+ 1, z] == 2*\\[Nu]*WeberE[\\[Nu], z]-Divide[2*(1 - Cos[Pi]*\\[Nu]),Pi]",
"translationInformation" : {
"subEquations" : [ "z*WeberE[\\[Nu]- 1, z]+ z*WeberE[\\[Nu]+ 1, z] = 2*\\[Nu]*WeberE[\\[Nu], z]-Divide[2*(1 - Cos[Pi]*\\[Nu]),Pi]" ],
"freeVariables" : [ "\\[Nu]", "z" ],
"tokenTranslations" : {
"\\WeberE" : "Weber function; Example: \\WeberE{v}@{z}\nWill be translated to: WeberE[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.10#E2\nMathematica: https://reference.wolfram.com/language/ref/WeberE.html",
"\\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",
"\\cpi" : "Pi was translated to: Pi"
}
},
"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" : "z*WeberE[\\[Nu]- 1, z]+ z*WeberE[\\[Nu]+ 1, z]",
"rhs" : "2*\\[Nu]*WeberE[\\[Nu], z]-Divide[2*(1 - Cos[Pi]*\\[Nu]),Pi]",
"testExpression" : "(z*WeberE[\\[Nu]- 1, z]+ z*WeberE[\\[Nu]+ 1, z])-(2*\\[Nu]*WeberE[\\[Nu], z]-Divide[2*(1 - Cos[Pi]*\\[Nu]),Pi])",
"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: \\WeberE [\\WeberE]"
}
}
},
"Maple" : {
"translation" : "z*WeberE(nu - 1, z)+ z*WeberE(nu + 1, z) = 2*nu*WeberE(nu, z)-(2*(1 - cos(Pi)*nu))/(Pi)",
"translationInformation" : {
"subEquations" : [ "z*WeberE(nu - 1, z)+ z*WeberE(nu + 1, z) = 2*nu*WeberE(nu, z)-(2*(1 - cos(Pi)*nu))/(Pi)" ],
"freeVariables" : [ "nu", "z" ],
"tokenTranslations" : {
"\\WeberE" : "Weber function; Example: \\WeberE{v}@{z}\nWill be translated to: WeberE($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.10#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=AngerJ",
"\\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",
"\\cpi" : "Pi was translated to: Pi"
}
}
}
},
"positions" : [ {
"section" : 4,
"sentence" : 0,
"word" : 22
} ],
"includes" : [ "J_{\\nu}", "\\mathbf{J}_{\\nu}", "\\nu" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "inhomogeneous form of recurrence relation",
"score" : 0.8869384888466118
}, {
"definition" : "Weber function",
"score" : 0.6288842031023242
}, {
"definition" : "Anger function",
"score" : 0.5329047619047619
} ]
}