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}(z) = \frac{z^{\alpha+1}}{2^{\alpha}\sqrt{\pi} \Gamma \left (\alpha+\tfrac{3}{2} \right )} {}_1F_2 \left (1,\tfrac{3}{2}, \alpha+\tfrac{3}{2},-\tfrac{z^2}{4} \right ).}
... is translated to the CAS output ...
Semantic latex: \StruveH{\alpha}@{z} = \frac{z^{\alpha+1}}{2^{\alpha} \sqrt{\cpi} \EulerGamma@{\alpha + \tfrac{3}{2}}}{}_1 F_2(1 , \tfrac{3}{2} , \alpha + \tfrac{3}{2} , - \tfrac{z^2}{4})
Confidence: 0.65998166233304
Mathematica
Translation: StruveH[\[Alpha], z] == Divide[(z)^(\[Alpha]+ 1),(2)^\[Alpha]*Sqrt[Pi]*Gamma[\[Alpha]+Divide[3,2]]]Subscript[, 1]*Subscript[F, 2][1 ,Divide[3,2], \[Alpha]+Divide[3,2], -Divide[(z)^(2),4]]
Information
Sub Equations
- StruveH[\[Alpha], z] = Divide[(z)^(\[Alpha]+ 1),(2)^\[Alpha]*Sqrt[Pi]*Gamma[\[Alpha]+Divide[3,2]]]Subscript[, 1]*Subscript[F, 2][1 ,Divide[3,2], \[Alpha]+Divide[3,2], -Divide[(z)^(2),4]]
Free variables
- \[Alpha]
- z
Symbol info
- 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
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, z) = ((z)^(alpha + 1))/((2)^(alpha)*sqrt(Pi)*GAMMA(alpha +(3)/(2)))[1]*F[2](1 ,(3)/(2), alpha +(3)/(2), -((z)^(2))/(4))
Information
Sub Equations
- StruveH(alpha, z) = ((z)^(alpha + 1))/((2)^(alpha)*sqrt(Pi)*GAMMA(alpha +(3)/(2)))[1]*F[2](1 ,(3)/(2), alpha +(3)/(2), -((z)^(2))/(4))
Free variables
- alpha
- z
Symbol info
- 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
- hypergeometric function
- Gauss
- term
- order
- Struve
Complete translation information:
{
"id" : "FORMULA_6dc2da7f595d2f199fbc15768167f006",
"formula" : "\\mathbf{H}_{\\alpha}(z) = \\frac{z^{\\alpha+1}}{2^{\\alpha}\\sqrt{\\pi} \\Gamma \\left (\\alpha+\\tfrac{3}{2} \\right )} {}_1F_2 \\left (1,\\tfrac{3}{2}, \\alpha+\\tfrac{3}{2},-\\tfrac{z^2}{4} \\right )",
"semanticFormula" : "\\StruveH{\\alpha}@{z} = \\frac{z^{\\alpha+1}}{2^{\\alpha} \\sqrt{\\cpi} \\EulerGamma@{\\alpha + \\tfrac{3}{2}}}{}_1 F_2(1 , \\tfrac{3}{2} , \\alpha + \\tfrac{3}{2} , - \\tfrac{z^2}{4})",
"confidence" : 0.6599816623330422,
"translations" : {
"Mathematica" : {
"translation" : "StruveH[\\[Alpha], z] == Divide[(z)^(\\[Alpha]+ 1),(2)^\\[Alpha]*Sqrt[Pi]*Gamma[\\[Alpha]+Divide[3,2]]]Subscript[, 1]*Subscript[F, 2][1 ,Divide[3,2], \\[Alpha]+Divide[3,2], -Divide[(z)^(2),4]]",
"translationInformation" : {
"subEquations" : [ "StruveH[\\[Alpha], z] = Divide[(z)^(\\[Alpha]+ 1),(2)^\\[Alpha]*Sqrt[Pi]*Gamma[\\[Alpha]+Divide[3,2]]]Subscript[, 1]*Subscript[F, 2][1 ,Divide[3,2], \\[Alpha]+Divide[3,2], -Divide[(z)^(2),4]]" ],
"freeVariables" : [ "\\[Alpha]", "z" ],
"tokenTranslations" : {
"\\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",
"F" : "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" : "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: \\StruveH [\\StruveH]"
}
},
"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" : "StruveH(alpha, z) = ((z)^(alpha + 1))/((2)^(alpha)*sqrt(Pi)*GAMMA(alpha +(3)/(2)))[1]*F[2](1 ,(3)/(2), alpha +(3)/(2), -((z)^(2))/(4))",
"translationInformation" : {
"subEquations" : [ "StruveH(alpha, z) = ((z)^(alpha + 1))/((2)^(alpha)*sqrt(Pi)*GAMMA(alpha +(3)/(2)))[1]*F[2](1 ,(3)/(2), alpha +(3)/(2), -((z)^(2))/(4))" ],
"freeVariables" : [ "alpha", "z" ],
"tokenTranslations" : {
"\\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",
"F" : "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"
}
},
"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" : 6,
"sentence" : 2,
"word" : 31
} ],
"includes" : [ "_{1}F_{2}", "\\mathbf{K}_\\alpha(x)", "\\alpha", "\\Gamma(z)", "\\mathbf{H}_{\\alpha}(x)", "\\mathbf{L}_{\\alpha}(x)", "\\mathbf{H}_{\\alpha}(z)", "Y_{\\alpha}(x)", "\\mathbf{M}_\\alpha(x)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "hypergeometric function",
"score" : 0.8692920440198258
}, {
"definition" : "Gauss",
"score" : 0.6954080343007951
}, {
"definition" : "term",
"score" : 0.6288842031023242
}, {
"definition" : "order",
"score" : 0.48771694939097315
}, {
"definition" : "Struve",
"score" : 0.48771694939097315
} ]
}