LaTeX to CAS translator
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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-1}(x)}
... is translated to the CAS output ...
Semantic latex: p_{n-1}(x)
Confidence: 0
Mathematica
Translation: Subscript[p, n - 1][x]
Information
Sub Equations
- Subscript[p, n - 1][x]
Free variables
- n
- x
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
SymPy
Translation: Symbol('{p}_{n - 1}')(x)
Information
Sub Equations
- Symbol('{p}_{n - 1}')(x)
Free variables
- n
- x
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Maple
Translation: p[n - 1](x)
Information
Sub Equations
- p[n - 1](x)
Free variables
- n
- x
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- weight
- term of the orthogonal polynomial
- coefficient
- integral expression
- yield
- side
- polynomial
- degree
- right hand side
- Orthogonal polynomial
- scalar product
- recurrence relation
- polynomial of degree
- term in the bracket
- 3-term recurrence relation
- nth degree
- Eq
- convention
- st
- equation
- integral
- term
- i.e. monic
- infinity
- maximal degree
- Abscissas
- eigenvalue of this tridiagonal matrix
- i.e.
- matrix form
- node for the Gaussian quadrature
- so-called Jacobi matrix
- standard basis vector
- three-term recurrence relation
- zero
- dash
- derivative
- standard Legendre polynomial of m-th degree
- expression in equation
Complete translation information:
{
"id" : "FORMULA_80b978ac7277de110547f7202223932a",
"formula" : "p_{n-1}(x)",
"semanticFormula" : "p_{n-1}(x)",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "Subscript[p, n - 1][x]",
"translationInformation" : {
"subEquations" : [ "Subscript[p, n - 1][x]" ],
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"p" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
},
"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('{p}_{n - 1}')(x)",
"translationInformation" : {
"subEquations" : [ "Symbol('{p}_{n - 1}')(x)" ],
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"p" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
},
"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" : "p[n - 1](x)",
"translationInformation" : {
"subEquations" : [ "p[n - 1](x)" ],
"freeVariables" : [ "n", "x" ],
"tokenTranslations" : {
"p" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
},
"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" : 5,
"sentence" : 2,
"word" : 37
}, {
"section" : 5,
"sentence" : 7,
"word" : 5
}, {
"section" : 5,
"sentence" : 7,
"word" : 31
} ],
"includes" : [ "p_n(x)", "p_{k}(x)", "p_{n}", "p_{n}(x)", "n", "x", "n - 1", "p_r", "p_s", "1" ],
"isPartOf" : [ "w_{i} = \\frac{a_{n}}{a_{n-1}}\\frac{\\int_{a}^{b}\\omega(x)p_{n-1}\\left(x\\right)^{2}dx}{p'_{n}(x_{i})p_{n-1}(x_{i})}", "q(x) = p_{n-1}(x)", "\\int_{a}^{b}\\omega(x)\\frac{p_{n}(x)}{x-x_{i}}dx=\\frac{a_{n}}{p_{n-1}(x_{i})}\\int_{a}^{b}\\omega(x)p_{n-1}(x)x^{n-1}dx", "x^{n-1} = \\left(x^{n-1} - \\frac{p_{n-1}(x)}{a_{n-1}}\\right) + \\frac{p_{n-1}(x)}{a_{n-1}}", "\\int_{a}^{b}\\omega(x)\\frac{p_{n}(x)}{x-x_{i}}dx=\\frac{a_{n}}{a_{n-1}p_{n-1}(x_{i})}\\int_{a}^{b}\\omega(x)p_{n-1}(x)^{2}dx", "p_{n+1}(x_{i}) = (a)p_{n}(x_{i}) + (b)p_{n-1}(x_{i})", "p_{n-1}(x_{i})", "p_{r+1}(x) = (x - a_{r,r})p_r(x) - a_{r,r-1}p_{r-1}(x)\\cdots - a_{r,0}p_0(x)", "p_{r+1}(x)=(x-a_{r,r})p_r(x)-a_{r,r-1}p_{r-1}(x)", "p_{r+1}(x)=(x-a_r)p_r(x)-b_rp_{r-1}(x)", "\\tilde{P} = \\begin{bmatrix} p_0(x) & p_1(x) & \\ldots & p_{n-1}(x) \\end{bmatrix}^\\mathsf{T}", "P'_{n-1}(x)", "w_i = \\frac{2}{n(n - 1)\\left[P_{n-1}\\left(x_i\\right)\\right]^2}, \\qquad x_i \\ne \\pm 1" ],
"definiens" : [ {
"definition" : "weight",
"score" : 0.7565123458357419
}, {
"definition" : "term of the orthogonal polynomial",
"score" : 0.6601229053380933
}, {
"definition" : "coefficient",
"score" : 0.651787266688052
}, {
"definition" : "integral expression",
"score" : 0.5730317852477183
}, {
"definition" : "yield",
"score" : 0.5358240086379016
}, {
"definition" : "side",
"score" : 0.5243095238095238
}, {
"definition" : "polynomial",
"score" : 0.48394655054344304
}, {
"definition" : "degree",
"score" : 0.4369378588726675
}, {
"definition" : "right hand side",
"score" : 0.40112702334295636
}, {
"definition" : "Orthogonal polynomial",
"score" : 0.3991329087352022
}, {
"definition" : "scalar product",
"score" : 0.3991329087352022
}, {
"definition" : "recurrence relation",
"score" : 0.39913290873405927
}, {
"definition" : "polynomial of degree",
"score" : 0.3931362465968641
}, {
"definition" : "term in the bracket",
"score" : 0.36644635572940026
}, {
"definition" : "3-term recurrence relation",
"score" : 0.3548916724042835
}, {
"definition" : "nth degree",
"score" : 0.35240476190476183
}, {
"definition" : "Eq",
"score" : 0.34549018289555505
}, {
"definition" : "convention",
"score" : 0.3430032723960334
}, {
"definition" : "st",
"score" : 0.3430032723960334
}, {
"definition" : "equation",
"score" : 0.3378014767666648
}, {
"definition" : "integral",
"score" : 0.3378014767666648
}, {
"definition" : "term",
"score" : 0.31880029202809124
}, {
"definition" : "i.e. monic",
"score" : 0.31631338153357264
}, {
"definition" : "infinity",
"score" : 0.31631338153357264
}, {
"definition" : "maximal degree",
"score" : 0.31631338153357264
}, {
"definition" : "Abscissas",
"score" : 0.3163133815285695
}, {
"definition" : "eigenvalue of this tridiagonal matrix",
"score" : 0.3163133815285695
}, {
"definition" : "i.e.",
"score" : 0.3163133815285695
}, {
"definition" : "matrix form",
"score" : 0.3163133815285695
}, {
"definition" : "node for the Gaussian quadrature",
"score" : 0.3163133815285695
}, {
"definition" : "so-called Jacobi matrix",
"score" : 0.3163133815285695
}, {
"definition" : "standard basis vector",
"score" : 0.3163133815285695
}, {
"definition" : "three-term recurrence relation",
"score" : 0.3163133815285695
}, {
"definition" : "zero",
"score" : 0.3163133815285695
}, {
"definition" : "dash",
"score" : 0.27647944119756235
}, {
"definition" : "derivative",
"score" : 0.27647944119756235
}, {
"definition" : "standard Legendre polynomial of m-th degree",
"score" : 0.27647944119756235
}, {
"definition" : "expression in equation",
"score" : 0.15680028272430657
} ]
}