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 h_n(ix;q^{-1}) = i^n\hat h_n(x;q)}

${\displaystyle h_{n}(ix;q^{-1})=i^{n}{\hat {h}}_{n}(x;q)}$

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

Semantic latex: \discqHermitepolyhI{n}@{\iunit x}{q^{-1}} = \iunit^n \discqHermitepolyhI{}@{}{}

Confidence: 0.84293097654618

Mathematica

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

${\hat {h}}_{n}(x;q)$

$q$

$h_{n}(x;q)$

Description

Hermite polynomial

term of basic hypergeometric function

Al-Salam -- Carlitz polynomial

Complete translation information:

{
  "id" : "FORMULA_b9974285610b7a82c94b6a504726df8c",
  "formula" : "h_n(ix;q^{-1}) = i^n\\hat h_n(x;q)",
  "semanticFormula" : "\\discqHermitepolyhI{n}@{\\iunit x}{q^{-1}} = \\iunit^n \\discqHermitepolyhI{}@{}{}",
  "confidence" : 0.8429309765461831,
  "translations" : {
    "Mathematica" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Mathematica) No translation possible for given token: Cannot extract information from feature set: \\discqHermitepolyhI [\\discqHermitepolyhI]"
        }
      }
    },
    "SymPy" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\discqHermitepolyhI [\\discqHermitepolyhI]"
        }
      }
    },
    "Maple" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \\discqHermitepolyhI [\\discqHermitepolyhI]"
        }
      }
    }
  },
  "positions" : [ {
    "section" : 1,
    "sentence" : 0,
    "word" : 27
  } ],
  "includes" : [ "\\hat{h}_{n}(x;q)", "q", "h_{n}(x;q)" ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "Hermite polynomial",
    "score" : 0.6460746792928004
  }, {
    "definition" : "term of basic hypergeometric function",
    "score" : 0.6460746792928004
  }, {
    "definition" : "Al-Salam -- Carlitz polynomial",
    "score" : 0.5500952380952381
  } ]
}

Specify your own input

Formula input
Wikitext context	{{DISPLAYTITLE: Discrete ''q''-Hermite polynomials }} {{technical\|date=April 2017}} In mathematics, the '''discrete ''q''-Hermite polynomials''' are two closely related families ''h''<sub>''n''</sub>(''x'';''q'') and ''ĥ''<sub>''n''</sub>(''x'';''q'') of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by {{harvs\|txt\|last1=Al-Salam\|last2=Carlitz\|year=1965}}. {{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 discrete ''q''-Hermite polynomials are given in terms of [[basic hypergeometric function]]s and the [[Al-Salam–Carlitz polynomials]] by :<math>\displaystyle h_n(x;q)=q^{\binom{n}{2}}{}_2\phi_1(q^{-n},x^{-1};0;q,-qx) = x^n{}_2\phi_0(q^{-n},q^{-n+1};;q^2,q^{2n-1}/x^2) = U_n^{(-1)}(x;q) </math> :<math>\displaystyle \hat h_n(x;q)=i^{-n}q^{-\binom{n}{2}}{}_2\phi_0(q^{-n},ix;;q,-q^n) = x^n{}_2\phi_1(q^{-n},q^{-n+1};0;q^2,-q^{2}/x^2) = i^{-n}V_n^{(-1)}(ix;q) </math> and are related by :<math>h_n(ix;q^{-1}) = i^n\hat h_n(x;q)</math> ==References== {{Citation \| last1=Berg \| first1=Christian \| last2=Ismael \| first2=Mourad \| year=1994 \| title=Q-Hermite Polynomials and Classical Orthogonal Polynomials \|arxiv=math/9405213}} {{Citation \| last1=Al-Salam \| first1=W. A. \| last2=Carlitz \| first2=L. \| author2-link=Leonard_Carlitz \| title=Some orthogonal q-polynomials \| doi=10.1002/mana.19650300105 \| mr=0197804 \| year=1965 \| journal=[[Mathematische Nachrichten]] \| issn=0025-584X \| volume=30 \| issue=1–2 \| pages=47–61}} {{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= Chapter 18 Orthogonal Polynomials\|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

Specify your own input

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