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) = \sum_{m=0}^\infty \frac{(-1)^m}{\Gamma \left (m+\frac{3}{2} \right ) \Gamma \left (m+\alpha+\frac{3}{2} \right )} \left({\frac{z}{2}}\right)^{2m+\alpha+1},}
... is translated to the CAS output ...
Semantic latex: \StruveH{\alpha}@{z} = \sum_{m=0}^\infty \frac{(-1)^m}{\EulerGamma@{m + \frac{3}{2}} \EulerGamma@{m + \alpha + \frac{3}{2}}}({\frac{z}{2}})^{2m+\alpha+1}
Confidence: 0.85867763172474
Mathematica
Translation: StruveH[\[Alpha], z] == Sum[Divide[(- 1)^(m),Gamma[m +Divide[3,2]]*Gamma[m + \[Alpha]+Divide[3,2]]]*(Divide[z,2])^(2*m + \[Alpha]+ 1), {m, 0, Infinity}, GenerateConditions->None]
Information
Sub Equations
- StruveH[\[Alpha], z] = Sum[Divide[(- 1)^(m),Gamma[m +Divide[3,2]]*Gamma[m + \[Alpha]+Divide[3,2]]]*(Divide[z,2])^(2*m + \[Alpha]+ 1), {m, 0, Infinity}, GenerateConditions->None]
Free variables
- \[Alpha]
- z
Symbol info
- 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.
- 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
- 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], z])-(Sum[Divide[(- 1)^(m),Gamma[m +Divide[3,2]]*Gamma[m + \[Alpha]+Divide[3,2]]]*(Divide[z,2])^(2*m + \[Alpha]+ 1), {m, 0, Infinity}, GenerateConditions->None])
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, z) = sum(((- 1)^(m))/(GAMMA(m +(3)/(2))*GAMMA(m + alpha +(3)/(2)))*((z)/(2))^(2*m + alpha + 1), m = 0..infinity)
Information
Sub Equations
- StruveH(alpha, z) = sum(((- 1)^(m))/(GAMMA(m +(3)/(2))*GAMMA(m + alpha +(3)/(2)))*((z)/(2))^(2*m + alpha + 1), m = 0..infinity)
Free variables
- alpha
- z
Symbol info
- 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.
- 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
- 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
- gamma function
- power series
- Struve
Complete translation information:
{
"id" : "FORMULA_7a2f8e9616a5d6155cf21f91fe6bf5e1",
"formula" : "\\mathbf{H}_\\alpha(z) = \\sum_{m=0}^\\infty \\frac{(-1)^m}{\\Gamma \\left (m+\\frac{3}{2} \\right ) \\Gamma \\left (m+\\alpha+\\frac{3}{2} \\right )} \\left({\\frac{z}{2}}\\right)^{2m+\\alpha+1}",
"semanticFormula" : "\\StruveH{\\alpha}@{z} = \\sum_{m=0}^\\infty \\frac{(-1)^m}{\\EulerGamma@{m + \\frac{3}{2}} \\EulerGamma@{m + \\alpha + \\frac{3}{2}}}({\\frac{z}{2}})^{2m+\\alpha+1}",
"confidence" : 0.858677631724739,
"translations" : {
"Mathematica" : {
"translation" : "StruveH[\\[Alpha], z] == Sum[Divide[(- 1)^(m),Gamma[m +Divide[3,2]]*Gamma[m + \\[Alpha]+Divide[3,2]]]*(Divide[z,2])^(2*m + \\[Alpha]+ 1), {m, 0, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "StruveH[\\[Alpha], z] = Sum[Divide[(- 1)^(m),Gamma[m +Divide[3,2]]*Gamma[m + \\[Alpha]+Divide[3,2]]]*(Divide[z,2])^(2*m + \\[Alpha]+ 1), {m, 0, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Alpha]", "z" ],
"tokenTranslations" : {
"\\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",
"\\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",
"\\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], z]",
"rhs" : "Sum[Divide[(- 1)^(m),Gamma[m +Divide[3,2]]*Gamma[m + \\[Alpha]+Divide[3,2]]]*(Divide[z,2])^(2*m + \\[Alpha]+ 1), {m, 0, Infinity}, GenerateConditions->None]",
"testExpression" : "(StruveH[\\[Alpha], z])-(Sum[Divide[(- 1)^(m),Gamma[m +Divide[3,2]]*Gamma[m + \\[Alpha]+Divide[3,2]]]*(Divide[z,2])^(2*m + \\[Alpha]+ 1), {m, 0, Infinity}, GenerateConditions->None])",
"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, z) = sum(((- 1)^(m))/(GAMMA(m +(3)/(2))*GAMMA(m + alpha +(3)/(2)))*((z)/(2))^(2*m + alpha + 1), m = 0..infinity)",
"translationInformation" : {
"subEquations" : [ "StruveH(alpha, z) = sum(((- 1)^(m))/(GAMMA(m +(3)/(2))*GAMMA(m + alpha +(3)/(2)))*((z)/(2))^(2*m + alpha + 1), m = 0..infinity)" ],
"freeVariables" : [ "alpha", "z" ],
"tokenTranslations" : {
"\\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",
"\\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",
"\\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" : 2,
"sentence" : 0,
"word" : 11
} ],
"includes" : [ "\\mathbf{K}_\\alpha(x)", "\\mathbf{L}_{\\alpha}(x)", "\\alpha", "\\mathbf{H}_{\\alpha}(z)", "\\mathbf{H}_{\\alpha}(x)", "\\mathbf{M}_\\alpha(x)", "\\Gamma(z)", "Y_{\\alpha}(x)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "gamma function",
"score" : 0.7125985104912714
}, {
"definition" : "power series",
"score" : 0.6460746792928004
}, {
"definition" : "Struve",
"score" : 0.6460746792928004
} ]
}