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 \alpha}
... is translated to the CAS output ...
Semantic latex: \alpha
Confidence: 0
Mathematica
Translation: \[Alpha]
Information
Sub Equations
- \[Alpha]
Free variables
- \[Alpha]
Symbol info
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
SymPy
Translation: Symbol('alpha')
Information
Sub Equations
- Symbol('alpha')
Free variables
- Symbol('alpha')
Symbol info
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
Maple
Translation: alpha
Information
Sub Equations
- alpha
Free variables
- alpha
Symbol info
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
Description
- free variable in the expression
- LaCASt
- equation
- article
- value
- example
- maple
- next equation in the same article
- different variant
- hypergeometric function in entry
- part
- test calculation
- Jacobi polynomial
- introduction
- context of Jacobi polynomial
- other MOI
- Pochhammer 's symbol
- value on the real axis
- variable in the expression
- counterexample
- comma
- dependency graph from Jacobi polynomial
- entire equation
- value in the figure
- ingoing dependency
- argument
- case of the Jacobi polynomial
- Continuous q-Laguerre polynomial
- definition
- editor of the Wikipedia article
- example of the definition
- hypergeometric function
- outgoing dependency
- case
- Jacobi polynomial in arxiv.org
- part of any other MOI
- right
Complete translation information:
{
"id" : "FORMULA_7b7f9dbfea05c83784f8b85149852f08",
"formula" : "\\alpha",
"semanticFormula" : "\\alpha",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "\\[Alpha]",
"translationInformation" : {
"subEquations" : [ "\\[Alpha]" ],
"freeVariables" : [ "\\[Alpha]" ],
"tokenTranslations" : {
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : "Symbol('alpha')",
"translationInformation" : {
"subEquations" : [ "Symbol('alpha')" ],
"freeVariables" : [ "Symbol('alpha')" ],
"tokenTranslations" : {
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : "alpha",
"translationInformation" : {
"subEquations" : [ "alpha" ],
"freeVariables" : [ "alpha" ],
"tokenTranslations" : {
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : 6,
"sentence" : 38,
"word" : 11
}, {
"section" : 7,
"sentence" : 46,
"word" : 21
}, {
"section" : 7,
"sentence" : 51,
"word" : 20
} ],
"includes" : [ ],
"isPartOf" : [ "P_n^{(\\alpha,\\beta)}(z)", "P_n^{(\\alpha,\\beta)}(x)", "P_n^{(\\alpha,\\beta)}(z)=\\frac{(\\alpha+1)_n}{n!}\\,{}_2F_1\\left(-n,1+\\alpha+\\beta+n;\\alpha+1;\\tfrac{1}{2}(1-z)\\right)", "(\\alpha+1)_n", "P_n^{(\\alpha,\\beta)} (z) = \\frac{\\Gamma (\\alpha+n+1)}{n!\\Gamma (\\alpha+\\beta+n+1)} \\sum_{m=0}^n \\binom{n}{m} \\frac{\\Gamma (\\alpha + \\beta + n + m + 1)}{\\Gamma (\\alpha + m + 1)} \\left(\\frac{z-1}{2}\\right)^m", "P_n^{(\\alpha,\\beta)}(z)=\\frac{(\\alpha+1)_n}{n!}{}_2F_1\\left(-n,1+\\alpha+\\beta+n;\\alpha+1;\\tfrac{1}{2}(1-z)\\right)", "\\alpha = \\frac{3}{2}, \\beta = \\frac{3}{2}, n = 2, z = -\\frac{1}{2}+\\frac{\\sqrt{3i}}{2}", "\\alpha, \\beta", "
to avoid the problem with the leading underscore. Hence, our extracted formula was not complete and missed the second half of the expression.\n\n:
<math>P_{n}^{(\\alpha)}(x|q)=\\frac{(q^\\alpha+1;q)_{n}}{(q;q)_{n}}", "_{3}\\Phi_{2}(q^{-n},q^{\\alpha/2+1/4}e^{i\\theta},q^{\\alpha/2+1/4}*e^{-i\\theta};q^{\\alpha+1},0|q,q)", "{}_1F_2 \\left (1,\\tfrac{3}{2}, \\alpha+\\tfrac{3}{2},-\\tfrac{z^2}{4} \\right )", "P_n^{(\\alpha, \\beta)}(x)" ],
"definiens" : [ {
"definition" : "free variable in the expression",
"score" : 0.6868127962055571
}, {
"definition" : "LaCASt",
"score" : 0.6832128166678701
}, {
"definition" : "equation",
"score" : 0.47302923924385665
}, {
"definition" : "article",
"score" : 0.43192078100150877
}, {
"definition" : "value",
"score" : 0.39003297808777854
}, {
"definition" : "example",
"score" : 0.34367477537222385
}, {
"definition" : "maple",
"score" : 0.34367477537222385
}, {
"definition" : "next equation in the same article",
"score" : 0.34300328264235563
}, {
"definition" : "different variant",
"score" : 0.3430032723960334
}, {
"definition" : "hypergeometric function in entry",
"score" : 0.3430032723960334
}, {
"definition" : "part",
"score" : 0.3430032723960334
}, {
"definition" : "test calculation",
"score" : 0.31698488450476003
}, {
"definition" : "Jacobi polynomial",
"score" : 0.31685382325256645
}, {
"definition" : "introduction",
"score" : 0.316314146497048
}, {
"definition" : "context of Jacobi polynomial",
"score" : 0.3163133815285695
}, {
"definition" : "other MOI",
"score" : 0.3163133815285695
}, {
"definition" : "Pochhammer 's symbol",
"score" : 0.3163133815285695
}, {
"definition" : "value on the real axis",
"score" : 0.3163133815285695
}, {
"definition" : "variable in the expression",
"score" : 0.3163133815285695
}, {
"definition" : "counterexample",
"score" : 0.2764794514438846
}, {
"definition" : "comma",
"score" : 0.27647944119756235
}, {
"definition" : "dependency graph from Jacobi polynomial",
"score" : 0.27647944119756235
}, {
"definition" : "entire equation",
"score" : 0.27647944119756235
}, {
"definition" : "value in the figure",
"score" : 0.27647944119756235
}, {
"definition" : "ingoing dependency",
"score" : 0.2292230264066729
}, {
"definition" : "argument",
"score" : 0.2292222614381945
}, {
"definition" : "case of the Jacobi polynomial",
"score" : 0.2292222614381945
}, {
"definition" : "Continuous q-Laguerre polynomial",
"score" : 0.2292222614381945
}, {
"definition" : "definition",
"score" : 0.2292222614381945
}, {
"definition" : "editor of the Wikipedia article",
"score" : 0.2292222614381945
}, {
"definition" : "example of the definition",
"score" : 0.2292222614381945
}, {
"definition" : "hypergeometric function",
"score" : 0.2292222614381945
}, {
"definition" : "outgoing dependency",
"score" : 0.2292222614381945
}, {
"definition" : "case",
"score" : 0.1805
}, {
"definition" : "Jacobi polynomial in arxiv.org",
"score" : 0.1805
}, {
"definition" : "part of any other MOI",
"score" : 0.1805
}, {
"definition" : "right",
"score" : 0.1805
} ]
}