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{H}_\alpha(x) - Y_\alpha(x) = \frac{\left(\frac{x}{2}\right)^{\alpha-1}}{\sqrt{\pi} \Gamma \left (\alpha+\frac{1}{2} \right )} + O\left(\left (\tfrac{x}{2}\right)^{\alpha-3}\right),}
... is translated to the CAS output ...
Semantic latex: \StruveH{\alpha}@{x} - \BesselY{\alpha}@{x} = \frac{(\frac{x}{2})^{\alpha-1}}{\sqrt{\cpi} \EulerGamma@{\alpha + \frac{1}{2}}} + O((\tfrac{x}{2})^{\alpha-3})
Confidence: 0.67074419509453
Mathematica
Translation: StruveH[\[Alpha], x]- BesselY[\[Alpha], x] == Divide[(Divide[x,2])^(\[Alpha]- 1),Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]+ O[(Divide[x,2])^(\[Alpha]- 3)]
Information
Sub Equations
- StruveH[\[Alpha], x]- BesselY[\[Alpha], x] = Divide[(Divide[x,2])^(\[Alpha]- 1),Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]+ O[(Divide[x,2])^(\[Alpha]- 3)]
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
- Pi was translated to: Pi
- 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.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: Gamma[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Mathematica: https://reference.wolfram.com/language/ref/Gamma.html
Tests
Symbolic
Test expression: (StruveH[\[Alpha], x]- BesselY[\[Alpha], x])-(Divide[(Divide[x,2])^(\[Alpha]- 1),Sqrt[Pi]*Gamma[\[Alpha]+Divide[1,2]]]+ O*((Divide[x,2])^(\[Alpha]- 3)))
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: \StruveH [\StruveH]
Tests
Symbolic
Numeric
Maple
Translation: StruveH(alpha, x)- BesselY(alpha, x) = (((x)/(2))^(alpha - 1))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))+ O(((x)/(2))^(alpha - 3))
Information
Sub Equations
- StruveH(alpha, x)- BesselY(alpha, x) = (((x)/(2))^(alpha - 1))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))+ O(((x)/(2))^(alpha - 3))
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
- Pi was translated to: Pi
- 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.
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Euler Gamma function; Example: \EulerGamma@{z}
Will be translated to: GAMMA($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- Neumann function
Complete translation information:
{
"id" : "FORMULA_f545056d7b45235ee294695b71a9b568",
"formula" : "\\mathbf{H}_\\alpha(x) - Y_\\alpha(x) = \\frac{\\left(\\frac{x}{2}\\right)^{\\alpha-1}}{\\sqrt{\\pi} \\Gamma \\left (\\alpha+\\frac{1}{2} \\right )} + O\\left(\\left (\\tfrac{x}{2}\\right)^{\\alpha-3}\\right)",
"semanticFormula" : "\\StruveH{\\alpha}@{x} - \\BesselY{\\alpha}@{x} = \\frac{(\\frac{x}{2})^{\\alpha-1}}{\\sqrt{\\cpi} \\EulerGamma@{\\alpha + \\frac{1}{2}}} + O((\\tfrac{x}{2})^{\\alpha-3})",
"confidence" : 0.670744195094534,
"translations" : {
"Mathematica" : {
"translation" : "StruveH[\\[Alpha], x]- BesselY[\\[Alpha], x] == Divide[(Divide[x,2])^(\\[Alpha]- 1),Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]+ O[(Divide[x,2])^(\\[Alpha]- 3)]",
"translationInformation" : {
"subEquations" : [ "StruveH[\\[Alpha], x]- BesselY[\\[Alpha], x] = Divide[(Divide[x,2])^(\\[Alpha]- 1),Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]+ O[(Divide[x,2])^(\\[Alpha]- 3)]" ],
"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",
"\\cpi" : "Pi was translated to: Pi",
"\\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",
"O" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: Gamma[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMathematica: https://reference.wolfram.com/language/ref/Gamma.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" : "StruveH[\\[Alpha], x]- BesselY[\\[Alpha], x]",
"rhs" : "Divide[(Divide[x,2])^(\\[Alpha]- 1),Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]+ O*((Divide[x,2])^(\\[Alpha]- 3))",
"testExpression" : "(StruveH[\\[Alpha], x]- BesselY[\\[Alpha], x])-(Divide[(Divide[x,2])^(\\[Alpha]- 1),Sqrt[Pi]*Gamma[\\[Alpha]+Divide[1,2]]]+ O*((Divide[x,2])^(\\[Alpha]- 3)))",
"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: \\StruveH [\\StruveH]"
}
}
},
"Maple" : {
"translation" : "StruveH(alpha, x)- BesselY(alpha, x) = (((x)/(2))^(alpha - 1))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))+ O(((x)/(2))^(alpha - 3))",
"translationInformation" : {
"subEquations" : [ "StruveH(alpha, x)- BesselY(alpha, x) = (((x)/(2))^(alpha - 1))/(sqrt(Pi)*GAMMA(alpha +(1)/(2)))+ O(((x)/(2))^(alpha - 3))" ],
"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",
"\\cpi" : "Pi was translated to: Pi",
"\\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",
"O" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\EulerGamma" : "Euler Gamma function; Example: \\EulerGamma@{z}\nWill be translated to: GAMMA($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=GAMMA"
}
}
}
},
"positions" : [ {
"section" : 4,
"sentence" : 1,
"word" : 7
} ],
"includes" : [ "\\mathbf{L}_{\\alpha}(x)", "x", "\\mathbf{K}_\\alpha(x)", "\\alpha", "\\Gamma(z)", "\\mathbf{H}_{\\alpha}(z)", "\\mathbf{H}_{\\alpha}(x)", "\\mathbf{M}_\\alpha(x)", "Y_{\\alpha}(x)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "Neumann function",
"score" : 0.7125985104912714
} ]
}