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 D_+(x) = F(x) = \frac{\sqrt{\pi}}{2} \operatorname{Im}[ w(x) ]}
... is translated to the CAS output ...
Semantic latex: D_+(x) = F(x) = \frac{\sqrt{\cpi}}{2} \imagpart@@{[w(x)]}
Confidence: 0.61221509839463
Mathematica
Translation: Subscript[D, +][x] == F[x] == Divide[Sqrt[Pi],2]*Im[w[x]]
Information
Sub Equations
- Subscript[D, +][x] = F[x]
- F[x] = Divide[Sqrt[Pi],2]*Im[w[x]]
Free variables
- x
Symbol info
- Imaginary part of a complex num; Example: \imagpart@@{z}
Will be translated to: Im[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.9#E2 Mathematica: https://reference.wolfram.com/language/ref/Im.html
- Pi was translated to: Pi
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \imagpart [\imagpart]
Tests
Symbolic
Numeric
Maple
Translation: D[+](x) = F(x) = (sqrt(Pi))/(2)*Im(w(x))
Information
Sub Equations
- D[+](x) = F(x)
- F(x) = (sqrt(Pi))/(2)*Im(w(x))
Free variables
- x
Symbol info
- Imaginary part of a complex num; Example: \imagpart@@{z}
Will be translated to: Im($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.9#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Im
- Pi was translated to: Pi
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- entire complex plane
- Dawson function
- term
- erfi
- Faddeeva function
Complete translation information:
{
"id" : "FORMULA_fd275547ee92555872fe674fd38ec826",
"formula" : "D_+(x) = F(x) = \\frac{\\sqrt{\\pi}}{2} \\operatorname{Im}[ w(x) ]",
"semanticFormula" : "D_+(x) = F(x) = \\frac{\\sqrt{\\cpi}}{2} \\imagpart@@{[w(x)]}",
"confidence" : 0.6122150983946287,
"translations" : {
"Mathematica" : {
"translation" : "Subscript[D, +][x] == F[x] == Divide[Sqrt[Pi],2]*Im[w[x]]",
"translationInformation" : {
"subEquations" : [ "Subscript[D, +][x] = F[x]", "F[x] = Divide[Sqrt[Pi],2]*Im[w[x]]" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\imagpart" : "Imaginary part of a complex num; Example: \\imagpart@@{z}\nWill be translated to: Im[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.9#E2\nMathematica: https://reference.wolfram.com/language/ref/Im.html",
"\\cpi" : "Pi was translated to: Pi",
"D" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"F" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"w" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
},
"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: \\imagpart [\\imagpart]"
}
},
"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" : "D[+](x) = F(x) = (sqrt(Pi))/(2)*Im(w(x))",
"translationInformation" : {
"subEquations" : [ "D[+](x) = F(x)", "F(x) = (sqrt(Pi))/(2)*Im(w(x))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"\\imagpart" : "Imaginary part of a complex num; Example: \\imagpart@@{z}\nWill be translated to: Im($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.9#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Im",
"\\cpi" : "Pi was translated to: Pi",
"D" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"F" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"w" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
},
"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" : [ {
"section" : 1,
"sentence" : 4,
"word" : 28
} ],
"includes" : [ "w(z)", "F(x)", "x", "F(y)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "entire complex plane",
"score" : 0.6460746792928004
}, {
"definition" : "Dawson function",
"score" : 0.5500952380952381
}, {
"definition" : "term",
"score" : 0.5500952380952381
}, {
"definition" : "erfi",
"score" : 0.5049074255814494
}, {
"definition" : "Faddeeva function",
"score" : 0.46655930748162855
} ]
}