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 \displaystyle S_n(x;q) = \frac{1}{(q;q)_n}{}_1\phi_1(q^{-n},0;q,-q^{n+1}x), }

${\displaystyle \displaystyle S_{n}(x;q)={\frac {1}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n},0;q,-q^{n+1}x),}$

... is translated to the CAS output ...

Semantic latex: S_n(x ; q) = \frac{1}{\qmultiPochhammersym{q}{q}{n}}{}_1 \phi_1(q^{-n} , 0 ; q , - q^{n+1} x)

Confidence: 0.64970437488336

Mathematica

Translation: Subscript[S, n][x ; q] == Divide[1,Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]Subscript[, 1]*Subscript[\[Phi], 1][(q)^(- n), 0 ; q , - (q)^(n + 1)* x]

Information

Sub Equations

Subscript[S, n][x ; q] = Divide[1,Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]Subscript[, 1]*Subscript[\[Phi], 1][(q)^(- n), 0 ; q , - (q)^(n + 1)* x]

Free variables

Subscript[\[Phi], 1]

n

q

x

Symbol info

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

q-Multi-Pochhammer symbol; Example: \qmultiPochhammersym{a_1,\ldots,a_n}{q}{n}

Will be translated to: Alternative translations: [Product[QPochhammer[Part[{$0},i],$1,$2],{i,1,Length[{$0}]}]]Relevant links to definitions: DLMF: http://dlmf.nist.gov/17.2.E5 Mathematica:

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \qmultiPochhammersym [\qmultiPochhammersym]

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

(LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \qmultiPochhammersym [\qmultiPochhammersym]

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$\displaystyle S_{n}(x;q)={\frac {1}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n},0;q,-q^{n+1}x)$

Is part of

$\displaystyle S_{n}(x;q)={\frac {1}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n},0;q,-q^{n+1}x)$

Complete translation information:

{
  "id" : "FORMULA_6171ea08252695e5defc7cd78ae352ff",
  "formula" : "S_n(x;q) = \\frac{1}{(q;q)_n}{}_1\\phi_1(q^{-n},0;q,-q^{n+1}x)",
  "semanticFormula" : "S_n(x ; q) = \\frac{1}{\\qmultiPochhammersym{q}{q}{n}}{}_1 \\phi_1(q^{-n} , 0 ; q , - q^{n+1} x)",
  "confidence" : 0.6497043748833582,
  "translations" : {
    "Mathematica" : {
      "translation" : "Subscript[S, n][x ; q] == Divide[1,Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]Subscript[, 1]*Subscript[\\[Phi], 1][(q)^(- n), 0 ; q , - (q)^(n + 1)* x]",
      "translationInformation" : {
        "subEquations" : [ "Subscript[S, n][x ; q] = Divide[1,Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]Subscript[, 1]*Subscript[\\[Phi], 1][(q)^(- n), 0 ; q , - (q)^(n + 1)* x]" ],
        "freeVariables" : [ "Subscript[\\[Phi], 1]", "n", "q", "x" ],
        "tokenTranslations" : {
          "\\phi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "S" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\qmultiPochhammersym" : "q-Multi-Pochhammer symbol; Example: \\qmultiPochhammersym{a_1,\\ldots,a_n}{q}{n}\nWill be translated to: \nAlternative translations: [Product[QPochhammer[Part[{$0},i],$1,$2],{i,1,Length[{$0}]}]]Relevant links to definitions:\nDLMF:         http://dlmf.nist.gov/17.2.E5\nMathematica:  "
        }
      },
      "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: \\qmultiPochhammersym [\\qmultiPochhammersym]"
        }
      },
      "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: \\qmultiPochhammersym [\\qmultiPochhammersym]"
        }
      },
      "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" : [ "\\displaystyle   S_n(x;q) = \\frac{1}{(q;q)_n}{}_1\\phi_1(q^{-n},0;q,-q^{n+1}x)" ],
  "isPartOf" : [ "\\displaystyle   S_n(x;q) = \\frac{1}{(q;q)_n}{}_1\\phi_1(q^{-n},0;q,-q^{n+1}x)" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	{{distinguish\|Stieltjes polynomial}} {{for\|the generalized Stieltjes–Wigert polynomials\|q-Laguerre polynomials}} In mathematics, '''Stieltjes–Wigert polynomials''' (named after [[Thomas Jan Stieltjes]] and [[Carl Severin Wigert]]) are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], for the weight function <ref>Up to a constant factor this is ''w''(''q''<sup>−1/2</sup>''x'') for the weight function ''w'' in Szegő (1975), Section 2.7. See also Koornwinder et al. (2010), Section 18.27(vi).</ref> :<math> w(x) = \frac{k}{\sqrt{\pi}} x^{-1/2} \exp(-k^2\log^2 x)</math> on the positive real line ''x'' > 0. The [[moment problem]] for the Stieltjes–Wigert polynomials is indeterminate; in other words, there are many other measures giving the same family of orthogonal polynomials (see [[Krein's condition]]). Koekoek et al. (2010) give in Section 14.27 a detailed list of the properties of these polynomials. ==Definition== The polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by<ref>Up to a constant factor ''S''<sub>''n''</sub>(''x'';''q'')=''p''<sub>''n''</sub>(''q''<sup>−1/2</sup>''x'') for ''p''<sub>''n''</sub>(''x'') in Szegő (1975), Section 2.7.</ref> :<math>\displaystyle S_n(x;q) = \frac{1}{(q;q)_n}{}_1\phi_1(q^{-n},0;q,-q^{n+1}x), </math> where :<math> q = \exp \left(-\frac{1}{2k^2} \right) .</math> ==Orthogonality== Since the [[moment problem]] for these polynomials is indeterminate there are many different weight functions on [0,∞] for which they are orthogonal. Two examples of such weight functions are :<math>\frac{1}{(-x,-qx^{-1};q)_\infty}</math> and :<math>\frac{k}{\sqrt{\pi}} x^{-1/2} \exp \left(-k^2 \log^2 x \right) .</math> ==Notes== {{reflist}} ==References== {{Citation \| last1=Gasper \| first1=George \| last2=Rahman \| first2=Mizan \| title=Basic hypergeometric series \| publisher=[[Cambridge University Press]] \| edition=2nd \| series=Encyclopedia of Mathematics and its Applications \| isbn=978-0-521-83357-8 \| doi=10.2277/0521833574 \| mr=2128719 \| year=2004 \| volume=96}} {{Citation \| last1=Koekoek \| first1=Roelof \| last2=Lesky \| first2=Peter A. \| last3=Swarttouw \| first3=René F. \| title=Hypergeometric orthogonal polynomials and their q-analogues \| publisher=[[Springer-Verlag]] \| location=Berlin, New York \| series=Springer Monographs in Mathematics \| isbn=978-3-642-05013-8 \| doi=10.1007/978-3-642-05014-5 \| mr=2656096 \| year=2010}} {{dlmf\|title=Ch. 18, Orthogonal polynomials\|url=http://dlmf.nist.gov/18\|first=Tom H. \|last=Koornwinder\|first2=Roderick S. C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F. \|last4=Swarttouw}} {{Citation \| last1=Szegő \| first1=Gábor \| title=Orthogonal Polynomials \| publisher=Colloquium Publications 23, American Mathematical Society, Fourth Edition\| isbn=978-0-8218-1023-1 \| mr=0372517 \| year=1975}} {{Citation \| last1=Stieltjes \| first1=T. -J. \| title=Recherches sur les fractions continues \| url=http://www.numdam.org/numdam-bin/item?id=AFST_1995_6_4_1_J1_0 \| language=French \| jfm=25.0326.01 \| mr = 1344720 \| year=1894 \| journal=Ann. Fac. Sci. Toulouse \| volume=VIII \| pages=1–122 \| doi=10.5802/afst.108}} {{cite journal \| first1= Xiang-Sheng \| last1=Wang \| first2=Roderick \| last2=Wong \|title= Uniform asymptotics of some q-orthogonal polynomials \|journal = J. Math. Anal. Appl. \| year=2010 \| volume=364 \| number=1 \|pages=79–87 \| doi=10.1016/j.jmaa.2009.10.038 }} *{{Citation \| last1=Wigert \| first1=S. \| title=Sur les polynomes orthogonaux et l'approximation des fonctions continues \| language=French \| jfm=49.0296.01 \| year=1923 \| journal=Arkiv för matematik, astronomi och fysik \| volume=17 \| pages=1–15}} {{DEFAULTSORT:Stieltjes-Wigert polynomials}} [[Category:Orthogonal polynomials]] [[Category:Special hypergeometric functions]]
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LaTeX to CAS translator

Mathematica

Information

Tests

Symbolic

Numeric

SymPy

Information

Tests

Symbolic

Numeric

Maple

Information

Tests

Symbolic

Numeric

Dependency Graph Information

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