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 \Phi(z,s,a+x)=\sum_{k=0}^\infty \Phi(z,s+k,a)(s)_{k}\frac{(-x)^k}{k!};|x|<\Re(a), }
... is translated to the CAS output ...
Semantic latex: \Phi(z , s , a + x) = \sum_{k=0}^\infty \Phi(z , s + k , a) \Pochhammersym{s}{k} \frac{(-x)^k}{k!} ;|x|< \realpart(a)
Confidence: 0.68872262762278
Mathematica
Translation: \[CapitalPhi][z , s , a + x] == \[CapitalPhi][z , s + k , a]* Pochhammer[s, k]*Divide[(- x)^(k),(k)!] Sum[Abs[x] , {k, 0, Infinity}, GenerateConditions->None]< Re[a]
Information
Free variables
- \[CapitalPhi]
- a
- s
- x
- z
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Real part of a complex number; Example: \realpart@@{z}
Will be translated to: Re[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.9#E2 Mathematica: https://reference.wolfram.com/language/ref/Re.html
- Pochhammer symbol; Example: \Pochhammersym{a}{n}
Will be translated to: Pochhammer[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#iii Mathematica: https://reference.wolfram.com/language/ref/Pochhammer.html
Tests
Symbolic
Test expression: \[CapitalPhi]*(z , s , a + x)
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Test expression: \[CapitalPhi]*(z , s + k , a)*Pochhammer[s, k]*Divide[(- x)^(k),(k)!] Abs[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: \Pochhammersym [\Pochhammersym]
Tests
Symbolic
Numeric
Maple
Translation: Phi(z , s , a + x) = Phi(z , s + k , a)* pochhammer(s, k)*((- x)^(k))/(factorial(k)); sum(abs(x) , k = 0..infinity)< Re(a)
Information
Free variables
- Phi
- a
- s
- x
- z
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Real part of a complex number; Example: \realpart@@{z}
Will be translated to: Re($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.9#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Re
- Pochhammer symbol; Example: \Pochhammersym{a}{n}
Will be translated to: pochhammer($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/5.2#iii Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=pochhammer
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_8fea482fce70d2e53ce9ef321efd2406",
"formula" : "\\Phi(z,s,a+x)=\\sum_{k=0}^\\infty \\Phi(z,s+k,a)(s)_{k}\\frac{(-x)^k}{k!};|x|<\\realpart(a)",
"semanticFormula" : "\\Phi(z , s , a + x) = \\sum_{k=0}^\\infty \\Phi(z , s + k , a) \\Pochhammersym{s}{k} \\frac{(-x)^k}{k!} ;|x|< \\realpart(a)",
"confidence" : 0.6887226276227827,
"translations" : {
"Mathematica" : {
"translation" : "\\[CapitalPhi][z , s , a + x] == \\[CapitalPhi][z , s + k , a]* Pochhammer[s, k]*Divide[(- x)^(k),(k)!]\n Sum[Abs[x] , {k, 0, Infinity}, GenerateConditions->None]< Re[a]",
"translationInformation" : {
"freeVariables" : [ "\\[CapitalPhi]", "a", "s", "x", "z" ],
"tokenTranslations" : {
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\realpart" : "Real part of a complex number; Example: \\realpart@@{z}\nWill be translated to: Re[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.9#E2\nMathematica: https://reference.wolfram.com/language/ref/Re.html",
"\\Pochhammersym" : "Pochhammer symbol; Example: \\Pochhammersym{a}{n}\nWill be translated to: Pochhammer[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#iii\nMathematica: https://reference.wolfram.com/language/ref/Pochhammer.html"
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 2,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 2,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "\\[CapitalPhi]*(z , s , a + x)",
"rhs" : "",
"testExpression" : "\\[CapitalPhi]*(z , s , a + x)",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
}, {
"lhs" : "\\[CapitalPhi]*(z , s + k , a)*Pochhammer[s, k]*Divide[(- x)^(k),(k)!]\n Abs[x]",
"rhs" : "",
"testExpression" : "\\[CapitalPhi]*(z , s + k , a)*Pochhammer[s, k]*Divide[(- x)^(k),(k)!]\n Abs[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: \\Pochhammersym [\\Pochhammersym]"
}
}
},
"Maple" : {
"translation" : "Phi(z , s , a + x) = Phi(z , s + k , a)* pochhammer(s, k)*((- x)^(k))/(factorial(k)); sum(abs(x) , k = 0..infinity)< Re(a)",
"translationInformation" : {
"freeVariables" : [ "Phi", "a", "s", "x", "z" ],
"tokenTranslations" : {
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\realpart" : "Real part of a complex number; Example: \\realpart@@{z}\nWill be translated to: Re($0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.9#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Re",
"\\Pochhammersym" : "Pochhammer symbol; Example: \\Pochhammersym{a}{n}\nWill be translated to: pochhammer($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/5.2#iii\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=pochhammer"
}
}
}
},
"positions" : [ ],
"includes" : [ "a", "(s)_{k}", "\\Phi(z,s,a)", "z", "s", "\\Phi(z,s,a+x)=\\sum_{k=0}^\\infty \\Phi(z,s+k,a)(s)_{k}\\frac{(-x)^k}{k!};|x|<\\Re(a)" ],
"isPartOf" : [ "\\Phi(z,s,a+x)=\\sum_{k=0}^\\infty \\Phi(z,s+k,a)(s)_{k}\\frac{(-x)^k}{k!};|x|<\\Re(a)" ],
"definiens" : [ ]
}