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(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\ aq&bdq&cq\\ \end{matrix};q;q\right]}

${\displaystyle p_{n}(q^{-x}+q^{x+1}cd;a,b,c,d;q)={}_{4}\phi _{3}\left[{\begin{matrix}q^{-n}&abq^{n+1}&q^{-x}&q^{x+1}cd\\aq&bdq&cq\\\end{matrix}};q;q\right]}$

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

Semantic latex: p_n(q^{-x} + q^{x+1} cd ; a , b , c , d ; q) ={}_4 \phi_3 [\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\ aq&bdq&cq\\ \end{matrix} ; q ; q]

Confidence: 0

Mathematica

Translation:

Information

Symbol info

(LaTeX -> Mathematica) An unknown or missing element occurred: Reached unknown or not yet supported expression tag: matrix

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

(LaTeX -> SymPy) An unknown or missing element occurred: Reached unknown or not yet supported expression tag: matrix

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

(LaTeX -> Maple) An unknown or missing element occurred: Reached unknown or not yet supported expression tag: matrix

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$p_{n}(q^{-x}+q^{x+1}cd;a,b,c,d;q)={}_{4}\phi _{3}\left[{\begin{matrix}q^{-n}&abq^{n+1}&q^{-x}&q^{x+1}cd\\aq&bdq&cq\\\end{matrix}};q;q\right]$

Is part of

$p_{n}(q^{-x}+q^{x+1}cd;a,b,c,d;q)={}_{4}\phi _{3}\left[{\begin{matrix}q^{-n}&abq^{n+1}&q^{-x}&q^{x+1}cd\\aq&bdq&cq\\\end{matrix}};q;q\right]$

Complete translation information:

{
  "id" : "FORMULA_4fc3d1b1738d30e449f00cd425b01446",
  "formula" : "p_n(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4\\phi_3\\left[\\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\\\\naq&bdq&cq\\\\ \\end{matrix};q;q\\right]",
  "semanticFormula" : "p_n(q^{-x} + q^{x+1} cd ; a , b , c , d ; q) ={}_4 \\phi_3 [\\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\\\\naq&bdq&cq\\\\ \\end{matrix} ; q ; q]",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Mathematica) An unknown or missing element occurred: Reached unknown or not yet supported expression tag: matrix"
        }
      },
      "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: Reached unknown or not yet supported expression tag: matrix"
        }
      },
      "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: Reached unknown or not yet supported expression tag: matrix"
        }
      },
      "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" : [ "p_n(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4\\phi_3\\left[\\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\\\aq&bdq&cq\\\\ \\end{matrix};q;q\\right]" ],
  "isPartOf" : [ "p_n(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4\\phi_3\\left[\\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\\\aq&bdq&cq\\\\ \\end{matrix};q;q\\right]" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	{{DISPLAYTITLE: ''q''-Racah polynomials}} In mathematics, the '''''q''-Racah polynomials''' are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by {{harvtxt\|Askey\|Wilson\|1979}}. {{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 :<math>p_n(q^{-x}+q^{x+1}cd;a,b,c,d;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&q^{x+1}cd\\ aq&bdq&cq\\ \end{matrix};q;q\right]</math> They are sometimes given with changes of variables as :<math>W_n(x;a,b,c,N;q) = {}_4\phi_3\left[\begin{matrix} q^{-n} &abq^{n+1}&q^{-x}&cq^{x-n}\\ aq&bcq&q^{-N}\\ \end{matrix};q;q\right]</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== {{Empty section\|date=September 2011}} q-Racah polynomials→Racah polynomials ==References== {{Citation \| last1=Askey \| first1=Richard \| last2=Wilson \| first2=James \| title=A set of orthogonal polynomials that generalize the Racah coefficients or 6-j symbols \| doi=10.1137/0510092 \| mr=541097 \| year=1979 \| journal=SIAM Journal on Mathematical Analysis \| issn=0036-1410 \| volume=10 \| issue=5 \| pages=1008–1016\| url=http://www.dtic.mil/get-tr-doc/pdf?AD=ADA054552 }} {{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\|title=\|first=Tom H. \|last=Koornwinder\|first2=Roderick S. C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F. \|last4=Swarttouw}} [[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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