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)}(z) = \frac{(-1)^n}{2^n n!} (1-z)^{-\alpha} (1+z)^{-\beta} \frac{d^n}{dz^n} \left\{ (1-z)^\alpha (1+z)^\beta \left (1 - z^2 \right )^n \right\}.}
... is translated to the CAS output ...
Semantic latex: \JacobipolyP{\alpha}{\beta}{n}@{z} = \frac{(-1)^n}{2^n n!}(1 - z)^{-\alpha}(1 + z)^{-\beta} \deriv [n]{ }{z} \{(1 - z)^\alpha(1 + z)^\beta(1 - z^2)^n \}
Confidence: 0.70338171203013
Mathematica
Translation: JacobiP[n, \[Alpha], \[Beta], z] == Divide[(- 1)^(n),(2)^(n)* (n)!]*(1 - z)^(- \[Alpha])*(1 + z)^(- \[Beta])* D[(1 - z)^\[Alpha]*(1 + z)^\[Beta]*(1 - (z)^(2))^(n), {z, n}]
Information
Sub Equations
- JacobiP[n, \[Alpha], \[Beta], z] = Divide[(- 1)^(n),(2)^(n)* (n)!]*(1 - z)^(- \[Alpha])*(1 + z)^(- \[Beta])* D[(1 - z)^\[Alpha]*(1 + z)^\[Beta]*(1 - (z)^(2))^(n), {z, n}]
Free variables
- \[Alpha]
- \[Beta]
- n
- z
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.
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: D[$1, {$2, $0}] Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 Mathematica: https://reference.wolfram.com/language/ref/D.html
Tests
Symbolic
Test expression: (JacobiP[n, \[Alpha], \[Beta], z])-(Divide[(- 1)^(n),(2)^(n)* (n)!]*(1 - z)^(- \[Alpha])*(1 + z)^(- \[Beta])* D[(1 - z)^\[Alpha]*(1 + z)^\[Beta]*(1 - (z)^(2))^(n), {z, n}])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: jacobi(n, Symbol('alpha'), Symbol('beta'), z) == ((- 1)**(n))/((2)**(n)* factorial(n))*(1 - z)**(- Symbol('alpha'))*(1 + z)**(- Symbol('beta'))* diff((1 - z)**(Symbol('alpha'))*(1 + z)**(Symbol('beta'))*(1 - (z)**(2))**(n), z, n)
Information
Sub Equations
- jacobi(n, Symbol('alpha'), Symbol('beta'), z) = ((- 1)**(n))/((2)**(n)* factorial(n))*(1 - z)**(- Symbol('alpha'))*(1 + z)**(- Symbol('beta'))* diff((1 - z)**(Symbol('alpha'))*(1 + z)**(Symbol('beta'))*(1 - (z)**(2))**(n), z, n)
Free variables
- Symbol('alpha')
- Symbol('beta')
- n
- z
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.
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: diff($1, $2, $0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 SymPy: https://docs.sympy.org/latest/tutorial/calculus.html#derivatives
Tests
Symbolic
Numeric
Maple
Translation: JacobiP(n, alpha, beta, z) = ((- 1)^(n))/((2)^(n)* factorial(n))*(1 - z)^(- alpha)*(1 + z)^(- beta)* diff((1 - z)^(alpha)*(1 + z)^(beta)*(1 - (z)^(2))^(n), [z$(n)])
Information
Sub Equations
- JacobiP(n, alpha, beta, z) = ((- 1)^(n))/((2)^(n)* factorial(n))*(1 - z)^(- alpha)*(1 + z)^(- beta)* diff((1 - z)^(alpha)*(1 + z)^(beta)*(1 - (z)^(2))^(n), [z$(n)])
Free variables
- alpha
- beta
- n
- z
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.
- Derivative; Example: \deriv[n]{f}{x}
Will be translated to: diff($1, [$2$($0)]) Relevant links to definitions: DLMF: http://dlmf.nist.gov/1.4#E4 Maple: https://www.maplesoft.com/support/help/Maple/view.aspx?path=diff
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- Rodrigues ' formula
- equivalent definition
Complete translation information:
{
"id" : "FORMULA_b98cc2a3c71764be8bc7fe354e54ebf7",
"formula" : "P_n^{(\\alpha,\\beta)}(z) = \\frac{(-1)^n}{2^n n!} (1-z)^{-\\alpha} (1+z)^{-\\beta} \\frac{d^n}{dz^n} \\left\\{ (1-z)^\\alpha (1+z)^\\beta \\left (1 - z^2 \\right )^n \\right\\}",
"semanticFormula" : "\\JacobipolyP{\\alpha}{\\beta}{n}@{z} = \\frac{(-1)^n}{2^n n!}(1 - z)^{-\\alpha}(1 + z)^{-\\beta} \\deriv [n]{ }{z} \\{(1 - z)^\\alpha(1 + z)^\\beta(1 - z^2)^n \\}",
"confidence" : 0.7033817120301267,
"translations" : {
"Mathematica" : {
"translation" : "JacobiP[n, \\[Alpha], \\[Beta], z] == Divide[(- 1)^(n),(2)^(n)* (n)!]*(1 - z)^(- \\[Alpha])*(1 + z)^(- \\[Beta])* D[(1 - z)^\\[Alpha]*(1 + z)^\\[Beta]*(1 - (z)^(2))^(n), {z, n}]",
"translationInformation" : {
"subEquations" : [ "JacobiP[n, \\[Alpha], \\[Beta], z] = Divide[(- 1)^(n),(2)^(n)* (n)!]*(1 - z)^(- \\[Alpha])*(1 + z)^(- \\[Beta])* D[(1 - z)^\\[Alpha]*(1 + z)^\\[Beta]*(1 - (z)^(2))^(n), {z, n}]" ],
"freeVariables" : [ "\\[Alpha]", "\\[Beta]", "n", "z" ],
"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",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: D[$1, {$2, $0}]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nMathematica: https://reference.wolfram.com/language/ref/D.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" : "JacobiP[n, \\[Alpha], \\[Beta], z]",
"rhs" : "Divide[(- 1)^(n),(2)^(n)* (n)!]*(1 - z)^(- \\[Alpha])*(1 + z)^(- \\[Beta])* D[(1 - z)^\\[Alpha]*(1 + z)^\\[Beta]*(1 - (z)^(2))^(n), {z, n}]",
"testExpression" : "(JacobiP[n, \\[Alpha], \\[Beta], z])-(Divide[(- 1)^(n),(2)^(n)* (n)!]*(1 - z)^(- \\[Alpha])*(1 + z)^(- \\[Beta])* D[(1 - z)^\\[Alpha]*(1 + z)^\\[Beta]*(1 - (z)^(2))^(n), {z, n}])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "jacobi(n, Symbol('alpha'), Symbol('beta'), z) == ((- 1)**(n))/((2)**(n)* factorial(n))*(1 - z)**(- Symbol('alpha'))*(1 + z)**(- Symbol('beta'))* diff((1 - z)**(Symbol('alpha'))*(1 + z)**(Symbol('beta'))*(1 - (z)**(2))**(n), z, n)",
"translationInformation" : {
"subEquations" : [ "jacobi(n, Symbol('alpha'), Symbol('beta'), z) = ((- 1)**(n))/((2)**(n)* factorial(n))*(1 - z)**(- Symbol('alpha'))*(1 + z)**(- Symbol('beta'))* diff((1 - z)**(Symbol('alpha'))*(1 + z)**(Symbol('beta'))*(1 - (z)**(2))**(n), z, n)" ],
"freeVariables" : [ "Symbol('alpha')", "Symbol('beta')", "n", "z" ],
"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",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: diff($1, $2, $0)\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nSymPy: https://docs.sympy.org/latest/tutorial/calculus.html#derivatives"
}
}
},
"Maple" : {
"translation" : "JacobiP(n, alpha, beta, z) = ((- 1)^(n))/((2)^(n)* factorial(n))*(1 - z)^(- alpha)*(1 + z)^(- beta)* diff((1 - z)^(alpha)*(1 + z)^(beta)*(1 - (z)^(2))^(n), [z$(n)])",
"translationInformation" : {
"subEquations" : [ "JacobiP(n, alpha, beta, z) = ((- 1)^(n))/((2)^(n)* factorial(n))*(1 - z)^(- alpha)*(1 + z)^(- beta)* diff((1 - z)^(alpha)*(1 + z)^(beta)*(1 - (z)^(2))^(n), [z$(n)])" ],
"freeVariables" : [ "alpha", "beta", "n", "z" ],
"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",
"\\deriv1" : "Derivative; Example: \\deriv[n]{f}{x}\nWill be translated to: diff($1, [$2$($0)])\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/1.4#E4\nMaple: https://www.maplesoft.com/support/help/Maple/view.aspx?path=diff"
}
}
}
},
"positions" : [ {
"section" : 2,
"sentence" : 0,
"word" : 10
} ],
"includes" : [ "(1 - x)^{\\alpha}(1 + x)^{\\beta}", "P_{n}^{(\\alpha, \\beta)}(x)", "n", "P_{n}^{(\\alpha, \\beta)}", "\\alpha,\\beta", "z" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "Rodrigues ' formula",
"score" : 0.6859086196238077
}, {
"definition" : "equivalent definition",
"score" : 0.6460746792928004
} ]
}