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 d^j_{m'm}(\phi) =\left[ \frac{(j+m)!(j-m)!}{(j+m')!(j-m')!}\right]^{\frac{1}{2}} \left(\sin\tfrac{\phi}{2}\right)^{m-m'} \left(\cos\tfrac{\phi}{2}\right)^{m+m'} P_{j-m}^{(m-m',m+m')}(\cos \phi).}
... is translated to the CAS output ...
Semantic latex: d_{m'm}^j(\phi) = [\frac{(j+m)!(j-m)!}{(j+m')!(j-m')!}]^{\frac{1}{2}}(\sin \tfrac{\phi}{2})^{m-m'}(\cos \tfrac{\phi}{2})^{m+m'} \JacobipolyP{m - m '}{m + m '}{j-m}@{\cos \phi}
Confidence: 0.86627249984448
Mathematica
Translation:
Information
Symbol info
- (LaTeX -> Mathematica) The input LaTeX is invalid: Primes can only be translated behind semantic macros (differentiation primes) but not in other places.
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) The input LaTeX is invalid: Primes can only be translated behind semantic macros (differentiation primes) but not in other places.
Tests
Symbolic
Numeric
Maple
Translation:
Information
Symbol info
- (LaTeX -> Maple) The input LaTeX is invalid: Primes can only be translated behind semantic macros (differentiation primes) but not in other places.
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- expression of the Wigner d-matrix
- expression
- term of Jacobi polynomial
Complete translation information:
{
"id" : "FORMULA_adb31e6dc814328e8bfc8b3f900eee59",
"formula" : "d^j_{m'm}(\\phi) =\\left[ \\frac{(j+m)!(j-m)!}{(j+m')!(j-m')!}\\right]^{\\frac{1}{2}} \\left(\\sin\\tfrac{\\phi}{2}\\right)^{m-m'} \\left(\\cos\\tfrac{\\phi}{2}\\right)^{m+m'} P_{j-m}^{(m-m',m+m')}(\\cos \\phi)",
"semanticFormula" : "d_{m'm}^j(\\phi) = [\\frac{(j+m)!(j-m)!}{(j+m')!(j-m')!}]^{\\frac{1}{2}}(\\sin \\tfrac{\\phi}{2})^{m-m'}(\\cos \\tfrac{\\phi}{2})^{m+m'} \\JacobipolyP{m - m '}{m + m '}{j-m}@{\\cos \\phi}",
"confidence" : 0.8662724998444776,
"translations" : {
"Mathematica" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> Mathematica) The input LaTeX is invalid: Primes can only be translated behind semantic macros (differentiation primes) but not in other places."
}
},
"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) The input LaTeX is invalid: Primes can only be translated behind semantic macros (differentiation primes) but not in other places."
}
},
"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" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> Maple) The input LaTeX is invalid: Primes can only be translated behind semantic macros (differentiation primes) but not in other places."
}
},
"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" : 12,
"sentence" : 0,
"word" : 21
} ],
"includes" : [ "P_{n}^{(\\alpha, \\beta)}", "P_{n}^{(\\alpha, \\beta)}(x)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "expression of the Wigner d-matrix",
"score" : 0.7125985104912714
}, {
"definition" : "expression",
"score" : 0.5988174995334326
}, {
"definition" : "term of Jacobi polynomial",
"score" : 0.5988174995334326
} ]
}