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{K}_\alpha(x)=\mathbf{H}_\alpha(x)-Y_\alpha(x)}
... is translated to the CAS output ...
Semantic latex: \StruveK{\alpha}@{x} = \StruveH{\alpha}@{x} - \BesselY{\alpha}@{x}
Confidence: 0.81134869108681
Mathematica
Translation: StruveH[\[Alpha], x] - BesselY[\[Alpha], x] == StruveH[\[Alpha], x]- BesselY[\[Alpha], x]
Information
Sub Equations
- StruveH[\[Alpha], x] - BesselY[\[Alpha], x] = StruveH[\[Alpha], x]- BesselY[\[Alpha], x]
Free variables
- \[Alpha]
- x
Symbol info
- Bessel function second kind; Example: \BesselY{v}@{z}
Will be translated to: BesselY[$0, $1] Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/10.2#E3 Mathematica: https://reference.wolfram.com/language/ref/BesselY.html
- Struve function; Example: \StruveH{\nu}@{z}
Will be translated to: StruveH[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E1 Mathematica: https://reference.wolfram.com/language/ref/StruveH.html
- Associated Struve funtion; Example: \StruveK{\nu}@{z}
Will be translated to: StruveH[$0, $1] - BesselY[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E5 Mathematica: https://reference.wolfram.com/language/ref/StruveH.html
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Test expression: (StruveH[\[Alpha], x] - BesselY[\[Alpha], x])-(StruveH[\[Alpha], x]- BesselY[\[Alpha], x])
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: \StruveK [\StruveK]
Tests
Symbolic
Numeric
Maple
Translation: StruveH(alpha, x) - BesselY(alpha, x) = StruveH(alpha, x)- BesselY(alpha, x)
Information
Sub Equations
- StruveH(alpha, x) - BesselY(alpha, x) = StruveH(alpha, x)- BesselY(alpha, x)
Free variables
- alpha
- x
Symbol info
- Bessel function second kind; Example: \BesselY{v}@{z}
Will be translated to: BesselY($0, $1) Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/10.2#E3 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Bessel
- Struve function; Example: \StruveH{\nu}@{z}
Will be translated to: StruveH($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveH
- Associated Struve funtion; Example: \StruveK{\nu}@{z}
Will be translated to: StruveH($0, $1) - BesselY($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/11.2#E5 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveH
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- second-kind version
- solution
- modified Struve function
- non-homogeneous Bessel 's differential equation
Complete translation information:
{
"id" : "FORMULA_33505baab24ec94930d2671275d06c33",
"formula" : "\\mathbf{K}_\\alpha(x)=\\mathbf{H}_\\alpha(x)-Y_\\alpha(x)",
"semanticFormula" : "\\StruveK{\\alpha}@{x} = \\StruveH{\\alpha}@{x} - \\BesselY{\\alpha}@{x}",
"confidence" : 0.8113486910868101,
"translations" : {
"Mathematica" : {
"translation" : "StruveH[\\[Alpha], x] - BesselY[\\[Alpha], x] == StruveH[\\[Alpha], x]- BesselY[\\[Alpha], x]",
"translationInformation" : {
"subEquations" : [ "StruveH[\\[Alpha], x] - BesselY[\\[Alpha], x] = StruveH[\\[Alpha], x]- BesselY[\\[Alpha], x]" ],
"freeVariables" : [ "\\[Alpha]", "x" ],
"tokenTranslations" : {
"\\BesselY" : "Bessel function second kind; Example: \\BesselY{v}@{z}\nWill be translated to: BesselY[$0, $1]\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/10.2#E3\nMathematica: https://reference.wolfram.com/language/ref/BesselY.html",
"\\StruveH" : "Struve function; Example: \\StruveH{\\nu}@{z}\nWill be translated to: StruveH[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E1\nMathematica: https://reference.wolfram.com/language/ref/StruveH.html",
"\\StruveK" : "Associated Struve funtion; Example: \\StruveK{\\nu}@{z}\nWill be translated to: StruveH[$0, $1] - BesselY[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E5\nMathematica: https://reference.wolfram.com/language/ref/StruveH.html",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : "StruveH[\\[Alpha], x] - BesselY[\\[Alpha], x]",
"rhs" : "StruveH[\\[Alpha], x]- BesselY[\\[Alpha], x]",
"testExpression" : "(StruveH[\\[Alpha], x] - BesselY[\\[Alpha], x])-(StruveH[\\[Alpha], x]- BesselY[\\[Alpha], x])",
"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: \\StruveK [\\StruveK]"
}
}
},
"Maple" : {
"translation" : "StruveH(alpha, x) - BesselY(alpha, x) = StruveH(alpha, x)- BesselY(alpha, x)",
"translationInformation" : {
"subEquations" : [ "StruveH(alpha, x) - BesselY(alpha, x) = StruveH(alpha, x)- BesselY(alpha, x)" ],
"freeVariables" : [ "alpha", "x" ],
"tokenTranslations" : {
"\\BesselY" : "Bessel function second kind; Example: \\BesselY{v}@{z}\nWill be translated to: BesselY($0, $1)\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/10.2#E3\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Bessel",
"\\StruveH" : "Struve function; Example: \\StruveH{\\nu}@{z}\nWill be translated to: StruveH($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveH",
"\\StruveK" : "Associated Struve funtion; Example: \\StruveK{\\nu}@{z}\nWill be translated to: StruveH($0, $1) - BesselY($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/11.2#E5\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=StruveH",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
}
}
},
"positions" : [ {
"section" : 0,
"sentence" : 2,
"word" : 8
} ],
"includes" : [ "\\mathbf{K}_\\alpha(x)", "\\alpha", "\\mathbf{H}_{\\alpha}(x)", "\\mathbf{L}_{\\alpha}(x)", "\\mathbf{M}_\\alpha(x)", "\\mathbf{M}_\\alpha(x)=\\mathbf{L}_\\alpha(x)-I_\\alpha(x)", "\\mathbf{H}_{\\alpha}(z)", "x", "Y_{\\alpha}(x)" ],
"isPartOf" : [ "\\mathbf{M}_\\alpha(x)=\\mathbf{L}_\\alpha(x)-I_\\alpha(x)" ],
"definiens" : [ {
"definition" : "second-kind version",
"score" : 0.8080172426403338
}, {
"definition" : "solution",
"score" : 0.6033992232315736
}, {
"definition" : "modified Struve function",
"score" : 0.5074197820340112
}, {
"definition" : "non-homogeneous Bessel 's differential equation",
"score" : 0.5074197820340112
} ]
}