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)=\frac{1}{a^s} +\sum_{m=0}^\infty (1-m-s)_m \operatorname{Li}_{s+m}(z)\frac{a^m}{m!}; |a|<1, }
... is translated to the CAS output ...
Semantic latex: \Phi(z , s , a) = \frac{1}{a^s} + \sum_{m=0}^\infty \Pochhammersym{1 - m - s}{m} \polylog{s+m}@{z} \frac{a^m}{m!} ;|a|< 1 ,
Confidence: 0.68128731809899
Mathematica
Translation: \[CapitalPhi][z , s , a] == Divide[1,(a)^(s)]+ Pochhammer[1 - m - s, m]*PolyLog[s + m, z]*Divide[(a)^(m),(m)!] Sum[Abs[a] , {m, 0, Infinity}, GenerateConditions->None]< 1
Information
Free variables
- \[CapitalPhi]
- a
- s
- z
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Polylogarithm; Example: \polylog{s}@{z}
Will be translated to: PolyLog[$0, $1] Relevant links to definitions: DLMF: http://dlmf.nist.gov/25.12#E10 Mathematica: https://reference.wolfram.com/language/ref/PolyLog.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)
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Test expression: Divide[1,(a)^(s)]+ Pochhammer[1 - m - s, m]*PolyLog[s + m, z]*Divide[(a)^(m),(m)!] Abs[a]
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) = (1)/((a)^(s))+ pochhammer(1 - m - s, m)*polylog(s + m, z)*((a)^(m))/(factorial(m)); sum(abs(a) , m = 0..infinity)< 1
Information
Free variables
- Phi
- a
- s
- z
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Polylogarithm; Example: \polylog{s}@{z}
Will be translated to: polylog($0, $1) Relevant links to definitions: DLMF: http://dlmf.nist.gov/25.12#E10 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=polylog
- 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
Complete translation information:
{
"id" : "FORMULA_e8bb2fcc0c9b2390cc30490a47c806b1",
"formula" : "\\Phi(z,s,a)=\\frac{1}{a^s}\n+\\sum_{m=0}^\\infty (1-m-s)_m \\operatorname{Li}_{s+m}(z)\\frac{a^m}{m!}; |a|<1,",
"semanticFormula" : "\\Phi(z , s , a) = \\frac{1}{a^s} + \\sum_{m=0}^\\infty \\Pochhammersym{1 - m - s}{m} \\polylog{s+m}@{z} \\frac{a^m}{m!} ;|a|< 1 ,",
"confidence" : 0.6812873180989907,
"translations" : {
"Mathematica" : {
"translation" : "\\[CapitalPhi][z , s , a] == Divide[1,(a)^(s)]+ Pochhammer[1 - m - s, m]*PolyLog[s + m, z]*Divide[(a)^(m),(m)!]\n Sum[Abs[a] , {m, 0, Infinity}, GenerateConditions->None]< 1",
"translationInformation" : {
"freeVariables" : [ "\\[CapitalPhi]", "a", "s", "z" ],
"tokenTranslations" : {
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\polylog" : "Polylogarithm; Example: \\polylog{s}@{z}\nWill be translated to: PolyLog[$0, $1]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/25.12#E10\nMathematica: https://reference.wolfram.com/language/ref/PolyLog.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)",
"rhs" : "",
"testExpression" : "\\[CapitalPhi]*(z , s , a)",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
}, {
"lhs" : "Divide[1,(a)^(s)]+ Pochhammer[1 - m - s, m]*PolyLog[s + m, z]*Divide[(a)^(m),(m)!]\n Abs[a]",
"rhs" : "",
"testExpression" : "Divide[1,(a)^(s)]+ Pochhammer[1 - m - s, m]*PolyLog[s + m, z]*Divide[(a)^(m),(m)!]\n Abs[a]",
"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) = (1)/((a)^(s))+ pochhammer(1 - m - s, m)*polylog(s + m, z)*((a)^(m))/(factorial(m)); sum(abs(a) , m = 0..infinity)< 1",
"translationInformation" : {
"freeVariables" : [ "Phi", "a", "s", "z" ],
"tokenTranslations" : {
"\\Phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\polylog" : "Polylogarithm; Example: \\polylog{s}@{z}\nWill be translated to: polylog($0, $1)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/25.12#E10\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=polylog",
"\\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", "\\Phi(z,s,a)=\\frac{1}{a^s}+\\sum_{m=0}^\\infty (1-m-s)_m \\operatorname{Li}_{s+m}(z)\\frac{a^m}{m!}; |a|<1", "\\Phi(z,s,a)", "\\operatorname{Li}_s(z)", "z", "s", "\\mathrm{Li}_n(z)" ],
"isPartOf" : [ ],
"definiens" : [ ]
}