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 \sum_{n=-\infty}^\infty q^{n(n+1)/2}z^n = (q;q)_\infty \; (-1/z;q)_\infty \; (-zq;q)_\infty.}
... is translated to the CAS output ...
Semantic latex: \sum_{n=-\infty}^\infty q^{n(n+1)/2} z^n = \qPochhammer{q}{q}{\infty} \qPochhammer{- 1 / z}{q}{\infty} \qPochhammer{- zq}{q}{\infty}
Confidence: 0.66429558303935
Mathematica
Translation: Sum[(q)^(n*(n + 1)/2)* (z)^(n), {n, - Infinity, Infinity}, GenerateConditions->None] == QPochhammer[q, q, Infinity]*QPochhammer[- 1/z, q, Infinity]*QPochhammer[- z*q, q, Infinity]
Information
Sub Equations
- Sum[(q)^(n*(n + 1)/2)* (z)^(n), {n, - Infinity, Infinity}, GenerateConditions->None] = QPochhammer[q, q, Infinity]*QPochhammer[- 1/z, q, Infinity]*QPochhammer[- z*q, q, Infinity]
Free variables
- q
- z
Symbol info
- q-Pochhammer symbol; Example: \qPochhammer{a}{q}{n}
Will be translated to: QPochhammer[$0, $1, $2] Relevant links to definitions: DLMF: http://dlmf.nist.gov/17.2#SS1.p1 Mathematica: https://reference.wolfram.com/language/ref/QPochhammer.html
Tests
Symbolic
Test expression: (Sum[(q)^(n*(n + 1)/2)* (z)^(n), {n, - Infinity, Infinity}, GenerateConditions->None])-(QPochhammer[q, q, Infinity]*QPochhammer[- 1/z, q, Infinity]*QPochhammer[- z*q, q, Infinity])
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: \qPochhammer [\qPochhammer]
Tests
Symbolic
Numeric
Maple
Translation: sum((q)^(n*(n + 1)/2)* (z)^(n), n = - infinity..infinity) = QPochhammer(q, q, infinity)*QPochhammer(- 1/z, q, infinity)*QPochhammer(- z*q, q, infinity)
Information
Sub Equations
- sum((q)^(n*(n + 1)/2)* (z)^(n), n = - infinity..infinity) = QPochhammer(q, q, infinity)*QPochhammer(- 1/z, q, infinity)*QPochhammer(- z*q, q, infinity)
Free variables
- q
- z
Symbol info
- q-Pochhammer symbol; Example: \qPochhammer{a}{q}{n}
Will be translated to: QPochhammer($0, $1, $2) Required Packages: [QDifferenceEquations,QPochhammer] Relevant links to definitions: DLMF: http://dlmf.nist.gov/17.2#SS1.p1 Maple: https://de.maplesoft.com/support/help/Maple/view.aspx?path=QDifferenceEquations/QPochhammer
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_5bdc6b8e0f4030c5b973269171336afe",
"formula" : "\\sum_{n=-\\infty}^\\infty q^{n(n+1)/2}z^n = \n(q;q)_\\infty (-1/z;q)_\\infty (-zq;q)_\\infty",
"semanticFormula" : "\\sum_{n=-\\infty}^\\infty q^{n(n+1)/2} z^n = \\qPochhammer{q}{q}{\\infty} \\qPochhammer{- 1 / z}{q}{\\infty} \\qPochhammer{- zq}{q}{\\infty}",
"confidence" : 0.6642955830393509,
"translations" : {
"Mathematica" : {
"translation" : "Sum[(q)^(n*(n + 1)/2)* (z)^(n), {n, - Infinity, Infinity}, GenerateConditions->None] == QPochhammer[q, q, Infinity]*QPochhammer[- 1/z, q, Infinity]*QPochhammer[- z*q, q, Infinity]",
"translationInformation" : {
"subEquations" : [ "Sum[(q)^(n*(n + 1)/2)* (z)^(n), {n, - Infinity, Infinity}, GenerateConditions->None] = QPochhammer[q, q, Infinity]*QPochhammer[- 1/z, q, Infinity]*QPochhammer[- z*q, q, Infinity]" ],
"freeVariables" : [ "q", "z" ],
"tokenTranslations" : {
"\\qPochhammer" : "q-Pochhammer symbol; Example: \\qPochhammer{a}{q}{n}\nWill be translated to: QPochhammer[$0, $1, $2]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/17.2#SS1.p1\nMathematica: https://reference.wolfram.com/language/ref/QPochhammer.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" : "Sum[(q)^(n*(n + 1)/2)* (z)^(n), {n, - Infinity, Infinity}, GenerateConditions->None]",
"rhs" : "QPochhammer[q, q, Infinity]*QPochhammer[- 1/z, q, Infinity]*QPochhammer[- z*q, q, Infinity]",
"testExpression" : "(Sum[(q)^(n*(n + 1)/2)* (z)^(n), {n, - Infinity, Infinity}, GenerateConditions->None])-(QPochhammer[q, q, Infinity]*QPochhammer[- 1/z, q, Infinity]*QPochhammer[- z*q, q, Infinity])",
"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: \\qPochhammer [\\qPochhammer]"
}
}
},
"Maple" : {
"translation" : "sum((q)^(n*(n + 1)/2)* (z)^(n), n = - infinity..infinity) = QPochhammer(q, q, infinity)*QPochhammer(- 1/z, q, infinity)*QPochhammer(- z*q, q, infinity)",
"translationInformation" : {
"subEquations" : [ "sum((q)^(n*(n + 1)/2)* (z)^(n), n = - infinity..infinity) = QPochhammer(q, q, infinity)*QPochhammer(- 1/z, q, infinity)*QPochhammer(- z*q, q, infinity)" ],
"freeVariables" : [ "q", "z" ],
"tokenTranslations" : {
"\\qPochhammer" : "q-Pochhammer symbol; Example: \\qPochhammer{a}{q}{n}\nWill be translated to: QPochhammer($0, $1, $2)\nRequired Packages: [QDifferenceEquations,QPochhammer]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/17.2#SS1.p1\nMaple: https://de.maplesoft.com/support/help/Maple/view.aspx?path=QDifferenceEquations/QPochhammer"
}
}
}
},
"positions" : [ ],
"includes" : [ "\\sum_{n=-\\infty}^\\infty q^{n(n+1)/2}z^n = (q;q)_\\infty \\; (-1/z;q)_\\infty \\; (-zq;q)_\\infty", "z", "n", "q^{n}", "q" ],
"isPartOf" : [ "\\sum_{n=-\\infty}^\\infty q^{n(n+1)/2}z^n = (q;q)_\\infty \\; (-1/z;q)_\\infty \\; (-zq;q)_\\infty" ],
"definiens" : [ ]
}