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 \begin{Bmatrix} j_1 & j_2 & j_3\\ j_4 & j_5 & j_6\\ j_7 & j_8 & 0 \end{Bmatrix} = \frac{\delta_{j_3,j_6} \delta_{j_7,j_8}}{\sqrt{(2j_3+1)(2j_7+1)}} (-1)^{j_2+j_3+j_4+j_7} \begin{Bmatrix} j_1 & j_2 & j_3\\ j_5 & j_4 & j_7 \end{Bmatrix}. }
... is translated to the CAS output ...
Semantic latex: \Wignersixjsym{j_1}{j_2}{j_3}{j_4}{j_5}{j_6} = \frac{\delta_{j_3,j_6} \delta_{j_7,j_8}}{\sqrt{(2j_3+1)(2j_7+1)}}(- 1)^{j_2+j_3+j_4+j_7} \Wignersixjsym{j_1}{j_2}{j_3}{j_5}{j_4}{j_7}
Confidence: 0.6615186698232
Mathematica
Translation: SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}] == Divide[Subscript[\[Delta], Subscript[j, 3], Subscript[j, 6]]*Subscript[\[Delta], Subscript[j, 7], Subscript[j, 8]],Sqrt[(2*Subscript[j, 3]+ 1)*(2*Subscript[j, 7]+ 1)]]*(- 1)^(Subscript[j, 2]+ Subscript[j, 3]+ Subscript[j, 4]+ Subscript[j, 7])* SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 5], Subscript[j, 4], Subscript[j, 7]}]
Information
Sub Equations
- SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}] = Divide[Subscript[\[Delta], Subscript[j, 3], Subscript[j, 6]]*Subscript[\[Delta], Subscript[j, 7], Subscript[j, 8]],Sqrt[(2*Subscript[j, 3]+ 1)*(2*Subscript[j, 7]+ 1)]]*(- 1)^(Subscript[j, 2]+ Subscript[j, 3]+ Subscript[j, 4]+ Subscript[j, 7])* SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 5], Subscript[j, 4], Subscript[j, 7]}]
Free variables
- Subscript[\[Delta], Subscript[j, 3], Subscript[j, 6]]
- Subscript[\[Delta], Subscript[j, 7], Subscript[j, 8]]
- Subscript[j, 1]
- Subscript[j, 2]
- Subscript[j, 3]
- Subscript[j, 4]
- Subscript[j, 5]
- Subscript[j, 6]
- Subscript[j, 7]
- Subscript[j, 8]
Symbol info
- Could be the first Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
- 6j symbol; Example: \Wignersixjsym@@{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}
Will be translated to: SixJSymbol[{$0, $1, $2}, {$3, $4, $5}] Relevant links to definitions: DLMF: http://dlmf.nist.gov/34.4#E1 Mathematica: https://reference.wolfram.com/language/ref/SixJSymbol.html
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \Wignersixjsym [\Wignersixjsym]
Tests
Symbolic
Numeric
Maple
Translation:
Information
Symbol info
- (LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \Wignersixjsym [\Wignersixjsym]
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Complete translation information:
{
"id" : "FORMULA_19bca66e005ee051bccdd40121c32838",
"formula" : "\\begin{Bmatrix}\n j_1 & j_2 & j_3\\\\\n j_4 & j_5 & j_6\\\\\n j_7 & j_8 & 0\n \\end{Bmatrix}\n = \n \\frac{\\delta_{j_3,j_6} \\delta_{j_7,j_8}}{\\sqrt{(2j_3+1)(2j_7+1)}}\n (-1)^{j_2+j_3+j_4+j_7}\n \\begin{Bmatrix}\n j_1 & j_2 & j_3\\\\\n j_5 & j_4 & j_7\n \\end{Bmatrix}",
"semanticFormula" : "\\Wignersixjsym{j_1}{j_2}{j_3}{j_4}{j_5}{j_6} = \\frac{\\delta_{j_3,j_6} \\delta_{j_7,j_8}}{\\sqrt{(2j_3+1)(2j_7+1)}}(- 1)^{j_2+j_3+j_4+j_7} \\Wignersixjsym{j_1}{j_2}{j_3}{j_5}{j_4}{j_7}",
"confidence" : 0.6615186698232001,
"translations" : {
"Mathematica" : {
"translation" : "SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}] == Divide[Subscript[\\[Delta], Subscript[j, 3], Subscript[j, 6]]*Subscript[\\[Delta], Subscript[j, 7], Subscript[j, 8]],Sqrt[(2*Subscript[j, 3]+ 1)*(2*Subscript[j, 7]+ 1)]]*(- 1)^(Subscript[j, 2]+ Subscript[j, 3]+ Subscript[j, 4]+ Subscript[j, 7])* SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 5], Subscript[j, 4], Subscript[j, 7]}]",
"translationInformation" : {
"subEquations" : [ "SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 4], Subscript[j, 5], Subscript[j, 6]}] = Divide[Subscript[\\[Delta], Subscript[j, 3], Subscript[j, 6]]*Subscript[\\[Delta], Subscript[j, 7], Subscript[j, 8]],Sqrt[(2*Subscript[j, 3]+ 1)*(2*Subscript[j, 7]+ 1)]]*(- 1)^(Subscript[j, 2]+ Subscript[j, 3]+ Subscript[j, 4]+ Subscript[j, 7])* SixJSymbol[{Subscript[j, 1], Subscript[j, 2], Subscript[j, 3]}, {Subscript[j, 5], Subscript[j, 4], Subscript[j, 7]}]" ],
"freeVariables" : [ "Subscript[\\[Delta], Subscript[j, 3], Subscript[j, 6]]", "Subscript[\\[Delta], Subscript[j, 7], Subscript[j, 8]]", "Subscript[j, 1]", "Subscript[j, 2]", "Subscript[j, 3]", "Subscript[j, 4]", "Subscript[j, 5]", "Subscript[j, 6]", "Subscript[j, 7]", "Subscript[j, 8]" ],
"tokenTranslations" : {
"\\delta" : "Could be the first Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
"\\Wignersixjsym" : "6j symbol; Example: \\Wignersixjsym@@{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}\nWill be translated to: SixJSymbol[{$0, $1, $2}, {$3, $4, $5}]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/34.4#E1\nMathematica: https://reference.wolfram.com/language/ref/SixJSymbol.html"
}
},
"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) No translation possible for given token: Cannot extract information from feature set: \\Wignersixjsym [\\Wignersixjsym]"
}
},
"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) No translation possible for given token: Cannot extract information from feature set: \\Wignersixjsym [\\Wignersixjsym]"
}
},
"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" : [ ],
"includes" : [ "j", "\\begin{Bmatrix} j_1 & j_2 & j_3\\\\ j_4 & j_5 & j_6\\\\ j_7 & j_8 & 0 \\end{Bmatrix} = \\frac{\\delta_{j_3,j_6} \\delta_{j_7,j_8}}{\\sqrt{(2j_3+1)(2j_7+1)}} (-1)^{j_2+j_3+j_4+j_7} \\begin{Bmatrix} j_1 & j_2 & j_3\\\\ j_5 & j_4 & j_7 \\end{Bmatrix}", "_{4}" ],
"isPartOf" : [ "\\begin{Bmatrix} j_1 & j_2 & j_3\\\\ j_4 & j_5 & j_6\\\\ j_7 & j_8 & 0 \\end{Bmatrix} = \\frac{\\delta_{j_3,j_6} \\delta_{j_7,j_8}}{\\sqrt{(2j_3+1)(2j_7+1)}} (-1)^{j_2+j_3+j_4+j_7} \\begin{Bmatrix} j_1 & j_2 & j_3\\\\ j_5 & j_4 & j_7 \\end{Bmatrix}" ],
"definiens" : [ ]
}