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,b;q) = {}_2\phi_1(q^{-n},abq^{n+1};aq;q,xq) }

${\displaystyle \displaystyle p_{n}(x;a,b;q)={}_{2}\phi _{1}(q^{-n},abq^{n+1};aq;q,xq)}$

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

Semantic latex: \littleqJacobipolyp{n}@{x}{a}{b}{q} = \qgenhyperphi{2}{1}@{q^{-n} , abq^{n+1}}{aq}{q}{xq}

Confidence: 0.54217855287577

Mathematica

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$\displaystyle p_{n}(x;a,b;q)={}_{2}\phi _{1}(q^{-n},abq^{n+1};aq;q,xq)$

$q$

$p_{n}(x;a,b;q)$

Is part of

$\displaystyle p_{n}(x;a,b;q)={}_{2}\phi _{1}(q^{-n},abq^{n+1};aq;q,xq)$

Complete translation information:

{
  "id" : "FORMULA_c27f8c30d161af6edebe4f2a59ea5602",
  "formula" : "p_n(x;a,b;q) = {}_2\\phi_1(q^{-n},abq^{n+1};aq;q,xq)",
  "semanticFormula" : "\\littleqJacobipolyp{n}@{x}{a}{b}{q} = \\qgenhyperphi{2}{1}@{q^{-n} , abq^{n+1}}{aq}{q}{xq}",
  "confidence" : 0.542178552875767,
  "translations" : {
    "Mathematica" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Mathematica) No translation possible for given token: Cannot extract information from feature set: \\littleqJacobipolyp [\\littleqJacobipolyp]"
        }
      }
    },
    "SymPy" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\littleqJacobipolyp [\\littleqJacobipolyp]"
        }
      }
    },
    "Maple" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \\littleqJacobipolyp [\\littleqJacobipolyp]"
        }
      }
    }
  },
  "positions" : [ ],
  "includes" : [ "\\displaystyle  p_n(x;a,b;q) = {}_2\\phi_1(q^{-n},abq^{n+1};aq;q,xq)", "q", "p_{n}(x;a,b;q)" ],
  "isPartOf" : [ "\\displaystyle  p_n(x;a,b;q) = {}_2\\phi_1(q^{-n},abq^{n+1};aq;q,xq)" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	{{DISPLAYTITLE:Little ''q''-Jacobi polynomials}} In mathematics, the '''little ''q''-Jacobi polynomials''' ''p''<sub>''n''</sub>(''x'';''a'',''b'';''q'') are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], introduced by {{harvtxt\|Hahn\|1949}}. {{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 little ''q''-Jacobi polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by :<math>\displaystyle p_n(x;a,b;q) = {}_2\phi_1(q^{-n},abq^{n+1};aq;q,xq) </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}} ==Gallery== The following are a set of animation plots for Little q-Jacobi polynomials, with varying q; three density plots of imaginary, real and modulus in complex space; three set of complex 3D plots of imaginary, real and modulus of the said polynomials. {\| \|[[File:LITTLE Q-JACOBI POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT.gif\|thumb\|LITTLE Q-JACOBI POLYNOMIALS ABS COMPLEX 3D MAPLE PLOT]] \|[[File:LITTLE Q-JACOBI POLYNOMIALS IM COMPLEX 3D MAPLE PLOT.gif\|thumb\|LITTLE Q-JACOBI POLYNOMIALS IM COMPLEX 3D MAPLE PLOT]] \|[[File:LITTLE Q-JACOBI POLYNOMIALS RE COMPLEX 3D MAPLE PLOT.gif\|thumb\|LITTLE Q-JACOBI POLYNOMIALS RE COMPLEX 3D MAPLE PLOT]] \|} {\| \|[[File:LITTLE Q-JACOBI POLYNOMIALS ABS DENSITY MAPLE PLOT.gif\|thumb\|LITTLE Q-JACOBI POLYNOMIALS ABS DENSITY MAPLE PLOT]] \|[[File:LITTLE Q-JACOBI POLYNOMIALS IM DENSITY MAPLE PLOT.gif\|thumb\|LITTLE Q-JACOBI POLYNOMIALS IM DENSITY MAPLE PLOT]] \|[[File:LITTLE Q-JACOBI POLYNOMIALS RE DENSITY MAPLE PLOT.gif\|thumb\|LITTLE Q-JACOBI POLYNOMIALS RE DENSITY MAPLE PLOT]] \|} ==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=Hahn \| first1=Wolfgang \| title=Über Orthogonalpolynome, die q-Differenzengleichungen genügen \| doi=10.1002/mana.19490020103 \| mr=0030647 \| year=1949 \| journal=[[Mathematische Nachrichten]] \| issn=0025-584X \| volume=2 \| pages=4–34}} {{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}} [[Category:Orthogonal polynomials]] [[Category:Q-analogs]] [[Category:Special hypergeometric functions]]
	Purge cached results.

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

Navigation menu

Search