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 c_n(q^{-x};a;q) = {}_2\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/a)}

${\displaystyle \displaystyle c_{n}(q^{-x};a;q)={}_{2}\phi _{1}(q^{-n},q^{-x};0;q,-q^{n+1}/a)}$

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

Semantic latex: c_n(q^{-x} ; a ; q) = \qgenhyperphi{2}{1}@{q^{-n} , q^{-x}}{0}{q}{- q^{n+1} / a}

Confidence: 0.4332221213489

Mathematica

Translation: Subscript[c, n][(q)^(- x); a ; q] == QHypergeometricPFQ[{(q)^(- n), (q)^(- x)},{0},q,- (q)^(n + 1)/a]

Information

Sub Equations

Subscript[c, n][(q)^(- x); a ; q] = QHypergeometricPFQ[{(q)^(- n), (q)^(- x)},{0},q,- (q)^(n + 1)/a]

Free variables

a

n

q

x

Symbol info

basic hypergeometric (or $q$-hypergeometric) function; Example: \qgenhyperphi{r}{s}@@@{a_1,...,a_r}{b_1,...,b_s}{q}{z}

Will be translated to: QHypergeometricPFQ[{$2},{$3},$4,$5] Relevant links to definitions: DLMF: http://dlmf.nist.gov/17.4#E1 Mathematica: https://reference.wolfram.com/language/ref/QHypergeometricPFQ.html

Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$\displaystyle c_{n}(q^{-x};a;q)={}_{2}\phi _{1}(q^{-n},q^{-x};0;q,-q^{n+1}/a)$

Is part of

$\displaystyle c_{n}(q^{-x};a;q)={}_{2}\phi _{1}(q^{-n},q^{-x};0;q,-q^{n+1}/a)$

Complete translation information:

{
  "id" : "FORMULA_738d8499ee4772023bda6917eb9a2ba2",
  "formula" : "c_n(q^{-x};a;q) = {}_2\\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/a)",
  "semanticFormula" : "c_n(q^{-x} ; a ; q) = \\qgenhyperphi{2}{1}@{q^{-n} , q^{-x}}{0}{q}{- q^{n+1} / a}",
  "confidence" : 0.433222121348905,
  "translations" : {
    "Mathematica" : {
      "translation" : "Subscript[c, n][(q)^(- x); a ; q] == QHypergeometricPFQ[{(q)^(- n), (q)^(- x)},{0},q,- (q)^(n + 1)/a]",
      "translationInformation" : {
        "subEquations" : [ "Subscript[c, n][(q)^(- x); a ; q] = QHypergeometricPFQ[{(q)^(- n), (q)^(- x)},{0},q,- (q)^(n + 1)/a]" ],
        "freeVariables" : [ "a", "n", "q", "x" ],
        "tokenTranslations" : {
          "\\qgenhyperphi" : "basic hypergeometric (or $q$-hypergeometric) function; Example: \\qgenhyperphi{r}{s}@@@{a_1,...,a_r}{b_1,...,b_s}{q}{z}\nWill be translated to: QHypergeometricPFQ[{$2},{$3},$4,$5]\nRelevant links to definitions:\nDLMF:         http://dlmf.nist.gov/17.4#E1\nMathematica:  https://reference.wolfram.com/language/ref/QHypergeometricPFQ.html",
          "c" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
        }
      },
      "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) No translation possible for given token: Cannot extract information from feature set: \\qgenhyperphi [\\qgenhyperphi]"
        }
      },
      "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) No translation possible for given token: Cannot extract information from feature set: \\qgenhyperphi [\\qgenhyperphi]"
        }
      },
      "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" : [ "\\displaystyle c_n(q^{-x};a;q) = {}_2\\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/a)" ],
  "isPartOf" : [ "\\displaystyle c_n(q^{-x};a;q) = {}_2\\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/a)" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	{{DISPLAYTITLE:''q''-Charlier polynomials }} In mathematics, the '''''q''-Charlier polynomials''' are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]]. {{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 '''q-Charlier polynomials''' are given in terms of the [[basic hypergeometric function]] by :<math>\displaystyle c_n(q^{-x};a;q) = {}_2\phi_1(q^{-n},q^{-x};0;q,-q^{n+1}/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=June 2015}} ==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=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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