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 K^{\text{aff}}_n (q^{-x};p;N;q) = {_2\varphi_1} \left( \begin{matrix} q^{-n} & 0 & q^{-x} \\ pq & q^{-N} \end{matrix} ; q,q \right), \qquad n=0,1,2,\ldots, N}

${\displaystyle K_{n}^{\text{aff}}(q^{-x};p;N;q)={_{2}\varphi _{1}}\left({\begin{matrix}q^{-n}&0&q^{-x}\\pq&q^{-N}\end{matrix}};q,q\right),\qquad n=0,1,2,\ldots ,N}$

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

Semantic latex: K ^{\text{aff}}_n (q^{-x};p;N;q) = {_2\varphi_1} \left( \begin{matrix} q^{-n} & 0 & q^{-x} \\ pq & q^{-N} \end{matrix} ; q,q \right), \qquad n=0,1,2,\ldots, N {}( )

Confidence: 0

Mathematica

Translation:

Information

Symbol info

(LaTeX -> Mathematica) An unknown or missing element occurred: Empty expression tag. Unable to translate:

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

(LaTeX -> SymPy) An unknown or missing element occurred: Empty expression tag. Unable to translate:

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

(LaTeX -> Maple) An unknown or missing element occurred: Empty expression tag. Unable to translate:

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$q$

$K_{n}^{\text{aff}}(q^{-x};p;N;q)={_{2}\varphi _{1}}\left({\begin{matrix}q^{-n}&0&q^{-x}\\pq&q^{-N}\end{matrix}};q,q\right),\qquad n=0,1,2,\ldots ,N$

Is part of

$K_{n}^{\text{aff}}(q^{-x};p;N;q)={_{2}\varphi _{1}}\left({\begin{matrix}q^{-n}&0&q^{-x}\\pq&q^{-N}\end{matrix}};q,q\right),\qquad n=0,1,2,\ldots ,N$

Complete translation information:

{
  "id" : "FORMULA_a70cd332638ae11e407ba8d628ee3505",
  "formula" : "K^{\\text{aff}}_n (q^{-x};p;N;q) = {_2\\varphi_1} \\left( \\begin{matrix} \nq^{-n} & 0 & q^{-x} \\\\ \npq & q^{-N} \\end{matrix} ; q,q \\right), \\qquad n=0,1,2,\\ldots, N",
  "semanticFormula" : "K ^{\\text{aff}}_n (q^{-x};p;N;q) = {_2\\varphi_1} \\left( \\begin{matrix} \nq^{-n} & 0 & q^{-x} \\\\ \npq & q^{-N} \\end{matrix} ; q,q \\right), \\qquad n=0,1,2,\\ldots, N           {}(    )",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Mathematica) An unknown or missing element occurred: Empty expression tag. Unable to translate: "
        }
      },
      "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) An unknown or missing element occurred: Empty expression tag. Unable to translate: "
        }
      },
      "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) An unknown or missing element occurred: Empty expression tag. Unable to translate: "
        }
      },
      "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" : [ "q", "K^{\\text{aff}}_n (q^{-x};p;N;q) = {_2\\varphi_1} \\left( \\begin{matrix} q^{-n} & 0 & q^{-x} \\\\ pq & q^{-N} \\end{matrix} ; q,q \\right), \\qquad n=0,1,2,\\ldots, N" ],
  "isPartOf" : [ "K^{\\text{aff}}_n (q^{-x};p;N;q) = {_2\\varphi_1} \\left( \\begin{matrix} q^{-n} & 0 & q^{-x} \\\\ pq & q^{-N} \\end{matrix} ; q,q \\right), \\qquad n=0,1,2,\\ldots, N" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	In mathematics, the '''affine ''q''-Krawtchouk polynomials''' are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by Carlitz and Hodges. {{harvs\|txt \| 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\|loc=14}} give a detailed list of their properties. ==Definition== The polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by <ref>Roelof Koekoek, Hypergeometric Orthogonal Polynomials and its q-Analogues, p501,Springer,2010</ref> : <math> K^{\text{aff}}_n (q^{-x};p;N;q) = {_2\varphi_1} \left( \begin{matrix} q^{-n} & 0 & q^{-x} \\ pq & q^{-N} \end{matrix} ; q,q \right), \qquad n=0,1,2,\ldots, N</math> ==Orthogonality== {{Empty section\|date=September 2011}} ==Recurrence and difference relations== {{Empty section\|date=September 2011}} ==Rodrigues formula== {{Empty section\|date=September 2011}} ==Generating function== {{Empty section\|date=September 2011}} ==Relation to other polynomials== Affine q-Krawtchouk polynomials → [[Little q-Laguerre polynomials]]： : <math>\lim_{a \to 1}=K_n^\text{aff}(q^{x-N};p,N\mid q)=p_n(q^x;p,q)</math> ==References== {{Reflist}} {{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\|id=18\|first=Tom H. \|last=Koornwinder\|first2=Roderick S. C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F. \|last4=Swarttouw}} {{Citation \| last1=Stanton \| first1=Dennis \| title=Three addition theorems for some q-Krawtchouk polynomials \| doi=10.1007/BF01447435 \| mr=608153 \| year=1981 \| journal=Geometriae Dedicata \| issn=0046-5755 \| volume=10 \| issue=1 \| pages=403–425}} [[Category:Orthogonal polynomials]] [[Category:Q-analogs]] [[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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