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 P_n^{(\alpha,\beta)}(x)= \sum_{s=0}^n {n+\alpha\choose n-s}{n+\beta \choose s} \left(\frac{x-1}{2}\right)^{s} \left(\frac{x+1}{2}\right)^{n-s}}
... is translated to the CAS output ...
Semantic latex: \JacobipolyP{\alpha}{\beta}{n}@{x} = \sum_{s=0}^n{n+\alpha\choose n-s}{n+\beta \choose s}(\frac{x-1}{2})^{s}(\frac{x+1}{2})^{n-s}
Confidence: 0.89530287320794
Mathematica
Translation: JacobiP[n, \[Alpha], \[Beta], x] == Sum[Binomial[n + \[Alpha],n - s]*Binomial[n + \[Beta],s]*(Divide[x - 1,2])^(s)*(Divide[x + 1,2])^(n - s), {s, 0, n}, GenerateConditions->None]
Information
Sub Equations
- JacobiP[n, \[Alpha], \[Beta], x] = Sum[Binomial[n + \[Alpha],n - s]*Binomial[n + \[Beta],s]*(Divide[x - 1,2])^(s)*(Divide[x + 1,2])^(n - s), {s, 0, n}, GenerateConditions->None]
Free variables
- \[Alpha]
- \[Beta]
- n
- x
Symbol info
- Jacobi polynomial; Example: \JacobipolyP{\alpha}{\beta}{n}@{x}
Will be translated to: JacobiP[$2, $0, $1, $3] Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r2 Mathematica: https://reference.wolfram.com/language/ref/JacobiP.html?q=JacobiP
- 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
Test expression: (JacobiP[n, \[Alpha], \[Beta], x])-(Sum[Binomial[n + \[Alpha],n - s]*Binomial[n + \[Beta],s]*(Divide[x - 1,2])^(s)*(Divide[x + 1,2])^(n - s), {s, 0, n}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: jacobi(n, Symbol('alpha'), Symbol('beta'), x) == Sum(binomial(n + Symbol('alpha'),n - s)*binomial(n + Symbol('beta'),s)*((x - 1)/(2))**(s)*((x + 1)/(2))**(n - s), (s, 0, n))
Information
Sub Equations
- jacobi(n, Symbol('alpha'), Symbol('beta'), x) = Sum(binomial(n + Symbol('alpha'),n - s)*binomial(n + Symbol('beta'),s)*((x - 1)/(2))**(s)*((x + 1)/(2))**(n - s), (s, 0, n))
Free variables
- Symbol('alpha')
- Symbol('beta')
- n
- x
Symbol info
- Jacobi polynomial; Example: \JacobipolyP{\alpha}{\beta}{n}@{x}
Will be translated to: jacobi($2, $0, $1, $3) Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r2 SymPy: https://docs.sympy.org/latest/modules/functions/special.html#jacobi-polynomials
- 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: JacobiP(n, alpha, beta, x) = sum(binomial(n + alpha,n - s)*binomial(n + beta,s)*((x - 1)/(2))^(s)*((x + 1)/(2))^(n - s), s = 0..n)
Information
Sub Equations
- JacobiP(n, alpha, beta, x) = sum(binomial(n + alpha,n - s)*binomial(n + beta,s)*((x - 1)/(2))^(s)*((x + 1)/(2))^(n - s), s = 0..n)
Free variables
- alpha
- beta
- n
- x
Symbol info
- Jacobi polynomial; Example: \JacobipolyP{\alpha}{\beta}{n}@{x}
Will be translated to: JacobiP($2, $0, $1, $3) Relevant links to definitions: DLMF: http://dlmf.nist.gov/18.3#T1.t1.r2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=JacobiP
- 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
Includes
Description
- integer
- Gamma function
- Jacobi polynomial
Complete translation information:
{
"id" : "FORMULA_928ae1a1423003c84cfa0f8765957889",
"formula" : "P_n^{(\\alpha,\\beta)}(x)= \\sum_{s=0}^n {n+\\alpha\\choose n-s}{n+\\beta \\choose s} \\left(\\frac{x-1}{2}\\right)^{s} \\left(\\frac{x+1}{2}\\right)^{n-s}",
"semanticFormula" : "\\JacobipolyP{\\alpha}{\\beta}{n}@{x} = \\sum_{s=0}^n{n+\\alpha\\choose n-s}{n+\\beta \\choose s}(\\frac{x-1}{2})^{s}(\\frac{x+1}{2})^{n-s}",
"confidence" : 0.8953028732079359,
"translations" : {
"Mathematica" : {
"translation" : "JacobiP[n, \\[Alpha], \\[Beta], x] == Sum[Binomial[n + \\[Alpha],n - s]*Binomial[n + \\[Beta],s]*(Divide[x - 1,2])^(s)*(Divide[x + 1,2])^(n - s), {s, 0, n}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "JacobiP[n, \\[Alpha], \\[Beta], x] = Sum[Binomial[n + \\[Alpha],n - s]*Binomial[n + \\[Beta],s]*(Divide[x - 1,2])^(s)*(Divide[x + 1,2])^(n - s), {s, 0, n}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Alpha]", "\\[Beta]", "n", "x" ],
"tokenTranslations" : {
"\\JacobipolyP" : "Jacobi polynomial; Example: \\JacobipolyP{\\alpha}{\\beta}{n}@{x}\nWill be translated to: JacobiP[$2, $0, $1, $3]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r2\nMathematica: https://reference.wolfram.com/language/ref/JacobiP.html?q=JacobiP",
"\\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" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "JacobiP[n, \\[Alpha], \\[Beta], x]",
"rhs" : "Sum[Binomial[n + \\[Alpha],n - s]*Binomial[n + \\[Beta],s]*(Divide[x - 1,2])^(s)*(Divide[x + 1,2])^(n - s), {s, 0, n}, GenerateConditions->None]",
"testExpression" : "(JacobiP[n, \\[Alpha], \\[Beta], x])-(Sum[Binomial[n + \\[Alpha],n - s]*Binomial[n + \\[Beta],s]*(Divide[x - 1,2])^(s)*(Divide[x + 1,2])^(n - s), {s, 0, n}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "jacobi(n, Symbol('alpha'), Symbol('beta'), x) == Sum(binomial(n + Symbol('alpha'),n - s)*binomial(n + Symbol('beta'),s)*((x - 1)/(2))**(s)*((x + 1)/(2))**(n - s), (s, 0, n))",
"translationInformation" : {
"subEquations" : [ "jacobi(n, Symbol('alpha'), Symbol('beta'), x) = Sum(binomial(n + Symbol('alpha'),n - s)*binomial(n + Symbol('beta'),s)*((x - 1)/(2))**(s)*((x + 1)/(2))**(n - s), (s, 0, n))" ],
"freeVariables" : [ "Symbol('alpha')", "Symbol('beta')", "n", "x" ],
"tokenTranslations" : {
"\\JacobipolyP" : "Jacobi polynomial; Example: \\JacobipolyP{\\alpha}{\\beta}{n}@{x}\nWill be translated to: jacobi($2, $0, $1, $3)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r2\nSymPy: https://docs.sympy.org/latest/modules/functions/special.html#jacobi-polynomials",
"\\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"
}
}
},
"Maple" : {
"translation" : "JacobiP(n, alpha, beta, x) = sum(binomial(n + alpha,n - s)*binomial(n + beta,s)*((x - 1)/(2))^(s)*((x + 1)/(2))^(n - s), s = 0..n)",
"translationInformation" : {
"subEquations" : [ "JacobiP(n, alpha, beta, x) = sum(binomial(n + alpha,n - s)*binomial(n + beta,s)*((x - 1)/(2))^(s)*((x + 1)/(2))^(n - s), s = 0..n)" ],
"freeVariables" : [ "alpha", "beta", "n", "x" ],
"tokenTranslations" : {
"\\JacobipolyP" : "Jacobi polynomial; Example: \\JacobipolyP{\\alpha}{\\beta}{n}@{x}\nWill be translated to: JacobiP($2, $0, $1, $3)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/18.3#T1.t1.r2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=JacobiP",
"\\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"
}
}
}
},
"positions" : [ {
"section" : 3,
"sentence" : 0,
"word" : 11
} ],
"includes" : [ "x", "P_{n}^{(\\alpha, \\beta)}(x)", "n", "s", "P_{n}^{(\\alpha, \\beta)}", "\\alpha,\\beta" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "integer",
"score" : 0.7125985104912714
}, {
"definition" : "Gamma function",
"score" : 0.6859086196238077
}, {
"definition" : "Jacobi polynomial",
"score" : 0.6859086196238077
} ]
}