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 p_n(x;a|q) = {}_2\phi_1(q^{-n},0;aq;q,qx) = \frac{1}{(a^{-1}q^{-n};q)_n}{}_2\phi_0(q^{-n},x^{-1};;q,x/a) }

${\displaystyle \displaystyle p_{n}(x;a|q)={}_{2}\phi _{1}(q^{-n},0;aq;q,qx)={\frac {1}{(a^{-1}q^{-n};q)_{n}}}{}_{2}\phi _{0}(q^{-n},x^{-1};;q,x/a)}$

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

Semantic latex: p_n(x ; a|q) = \qgenhyperphi{2}{1}@{q^{-n} , 0}{aq}{q}{qx} = \frac{1}{\qmultiPochhammersym{a^{-1} q^{-n}}{q}{n}}{}_2 \phi_0(q^{-n} , x^{-1} ; ; q , x / a)

Confidence: 0.54479948447456

Mathematica

Translation:

Information

Symbol info

(LaTeX -> Mathematica) Parenthesis mismatch in expression: Bracket-Error: open bracket | reached )

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

(LaTeX -> SymPy) Parenthesis mismatch in expression: Bracket-Error: open bracket | reached )

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

(LaTeX -> Maple) Parenthesis mismatch in expression: Bracket-Error: open bracket | reached )

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$q$

$p_{n}(x;a|q)$

$\displaystyle p_{n}(x;a|q)={}_{2}\phi _{1}(q^{-n},0;aq;q,qx)={\frac {1}{(a^{-1}q^{-n};q)_{n}}}{}_{2}\phi _{0}(q^{-n},x^{-1};;q,x/a)$

Is part of

$\displaystyle p_{n}(x;a|q)={}_{2}\phi _{1}(q^{-n},0;aq;q,qx)={\frac {1}{(a^{-1}q^{-n};q)_{n}}}{}_{2}\phi _{0}(q^{-n},x^{-1};;q,x/a)$

Complete translation information:

{
  "id" : "FORMULA_d7ea1994d0201f402af0cdf0cdc3956d",
  "formula" : "p_n(x;a|q) = {}_2\\phi_1(q^{-n},0;aq;q,qx) = \\frac{1}{(a^{-1}q^{-n};q)_n}{}_2\\phi_0(q^{-n},x^{-1};;q,x/a)",
  "semanticFormula" : "p_n(x ; a|q) = \\qgenhyperphi{2}{1}@{q^{-n} , 0}{aq}{q}{qx} = \\frac{1}{\\qmultiPochhammersym{a^{-1} q^{-n}}{q}{n}}{}_2 \\phi_0(q^{-n} , x^{-1} ; ; q , x / a)",
  "confidence" : 0.5447994844745645,
  "translations" : {
    "Mathematica" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Mathematica) Parenthesis mismatch in expression: Bracket-Error: open bracket | reached )"
        }
      },
      "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) Parenthesis mismatch in expression: Bracket-Error: open bracket | reached )"
        }
      },
      "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) Parenthesis mismatch in expression: Bracket-Error: open bracket | reached )"
        }
      },
      "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", "p_{n}(x;a|q)", "\\displaystyle  p_n(x;a|q) = {}_2\\phi_1(q^{-n},0;aq;q,qx) = \\frac{1}{(a^{-1}q^{-n};q)_n}{}_2\\phi_0(q^{-n},x^{-1};;q,x/a)" ],
  "isPartOf" : [ "\\displaystyle  p_n(x;a|q) = {}_2\\phi_1(q^{-n},0;aq;q,qx) = \\frac{1}{(a^{-1}q^{-n};q)_n}{}_2\\phi_0(q^{-n},x^{-1};;q,x/a)" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	In mathematics, the '''little ''q''-Laguerre polynomials''' ''p''<sub>''n''</sub>(''x'';''a''\|''q'') or '''Wall polynomials''' ''W''<sub>''n''</sub>(''x''; ''b'',''q'') are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]] closely related to a continued fraction studied by {{harvs\|txt\|last=Wall\|authorlink=Hubert Stanley Wall\|year=1941}}. (The term "Wall polynomial" is also used for an unrelated [[Wall polynomial]] in the theory of classical groups.) {{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>\displaystyle p_n(x;a\|q) = {}_2\phi_1(q^{-n},0;aq;q,qx) = \frac{1}{(a^{-1}q^{-n};q)_n}{}_2\phi_0(q^{-n},x^{-1};;q,x/a) </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}} == See also == [http://drmf.wmflabs.org/wiki/Little_q-Laguerre_/_Wall] ==References== {{Citation \| last1=Chihara \| first1=Theodore Seio \| title=An introduction to orthogonal polynomials \| url=https://books.google.com/books?id=IkCJSQAACAAJ \| publisher=Gordon and Breach Science Publishers \| location=New York \| series=Mathematics and its Applications \| isbn=978-0-677-04150-6 \| mr=0481884 \|id= Reprinted by Dover 2011 \| year=1978 \| volume=13}} {{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}} {{Citation \| last1=Van Assche \| first1=Walter \| last2=Koornwinder \| first2=Tom H. \| title=Asymptotic behaviour for Wall polynomials and the addition formula for little q-Legendre polynomials \| doi=10.1137/0522019 \| mr=1080161 \| year=1991 \| journal=SIAM Journal on Mathematical Analysis \| issn=0036-1410 \| volume=22 \| issue=1 \| pages=302–311\| url=https://ir.cwi.nl/pub/1603 }} {{Citation \| last1=Wall \| first1=H. S. \| title=A continued fraction related to some partition formulas of Euler \| jstor=2303599 \| mr=0003641 \| year=1941 \| journal=[[American Mathematical Monthly\|The American Mathematical Monthly]] \| issn=0002-9890 \| volume=48 \| issue=2 \| pages=102–108\| doi=10.1080/00029890.1941.11991074 }} [[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

Specify your own input

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