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 L_n^{(\alpha)}(x;q) = \frac{(q^{\alpha+1};q)_n}{(q;q)_n} {}_1\phi_1(q^{-n};q^{\alpha+1};q,-q^{n+\alpha+1}x) }

${\displaystyle \displaystyle L_{n}^{(\alpha )}(x;q)={\frac {(q^{\alpha +1};q)_{n}}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n};q^{\alpha +1};q,-q^{n+\alpha +1}x)}$

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

Semantic latex: L_n^{(\alpha)}(x ; q) = \frac{\qmultiPochhammersym{q^{\alpha+1}}{q}{n}}{\qmultiPochhammersym{q}{q}{n}} \qgenhyperphi{1}{1}@{q^{-n}}{q^{\alpha+1}}{q}{- q^{n+\alpha+1} x}

Confidence: 0.53716562906851

Mathematica

Translation: (Subscript[L, n])^(\[Alpha])[x ; q] == Divide[Product[QPochhammer[Part[{(q)^(\[Alpha]+ 1)},i],q,n],{i,1,Length[{(q)^(\[Alpha]+ 1)}]}],Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]*QHypergeometricPFQ[{(q)^(- n)},{(q)^(\[Alpha]+ 1)},q,- (q)^(n + \[Alpha]+ 1)* x]

Information

Sub Equations

(Subscript[L, n])^(\[Alpha])[x ; q] = Divide[Product[QPochhammer[Part[{(q)^(\[Alpha]+ 1)},i],q,n],{i,1,Length[{(q)^(\[Alpha]+ 1)}]}],Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]*QHypergeometricPFQ[{(q)^(- n)},{(q)^(\[Alpha]+ 1)},q,- (q)^(n + \[Alpha]+ 1)* x]

Free variables

\[Alpha]

n

q

x

Symbol info

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

Could be the second Feigenbaum constant.

But this system doesn't know how to translate it as a constant. It was translated as a general letter.

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

q-Multi-Pochhammer symbol; Example: \qmultiPochhammersym{a_1,\ldots,a_n}{q}{n}

Will be translated to: Alternative translations: [Product[QPochhammer[Part[{$0},i],$1,$2],{i,1,Length[{$0}]}]]Relevant links to definitions: DLMF: http://dlmf.nist.gov/17.2.E5 Mathematica:

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$q$

$\displaystyle L_{n}^{(\alpha )}(x;q)={\frac {(q^{\alpha +1};q)_{n}}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n};q^{\alpha +1};q,-q^{n+\alpha +1}x)$

$P_{n}^{(\alpha )}(x;q)$

Is part of

$\displaystyle L_{n}^{(\alpha )}(x;q)={\frac {(q^{\alpha +1};q)_{n}}{(q;q)_{n}}}{}_{1}\phi _{1}(q^{-n};q^{\alpha +1};q,-q^{n+\alpha +1}x)$

Complete translation information:

{
  "id" : "FORMULA_120b78b7ef96f38580a9f1e45e7764aa",
  "formula" : "L_n^{(\\alpha)}(x;q) = \\frac{(q^{\\alpha+1};q)_n}{(q;q)_n} {}_1\\phi_1(q^{-n};q^{\\alpha+1};q,-q^{n+\\alpha+1}x)",
  "semanticFormula" : "L_n^{(\\alpha)}(x ; q) = \\frac{\\qmultiPochhammersym{q^{\\alpha+1}}{q}{n}}{\\qmultiPochhammersym{q}{q}{n}} \\qgenhyperphi{1}{1}@{q^{-n}}{q^{\\alpha+1}}{q}{- q^{n+\\alpha+1} x}",
  "confidence" : 0.5371656290685125,
  "translations" : {
    "Mathematica" : {
      "translation" : "(Subscript[L, n])^(\\[Alpha])[x ; q] == Divide[Product[QPochhammer[Part[{(q)^(\\[Alpha]+ 1)},i],q,n],{i,1,Length[{(q)^(\\[Alpha]+ 1)}]}],Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]*QHypergeometricPFQ[{(q)^(- n)},{(q)^(\\[Alpha]+ 1)},q,- (q)^(n + \\[Alpha]+ 1)* x]",
      "translationInformation" : {
        "subEquations" : [ "(Subscript[L, n])^(\\[Alpha])[x ; q] = Divide[Product[QPochhammer[Part[{(q)^(\\[Alpha]+ 1)},i],q,n],{i,1,Length[{(q)^(\\[Alpha]+ 1)}]}],Product[QPochhammer[Part[{q},i],q,n],{i,1,Length[{q}]}]]*QHypergeometricPFQ[{(q)^(- n)},{(q)^(\\[Alpha]+ 1)},q,- (q)^(n + \\[Alpha]+ 1)* x]" ],
        "freeVariables" : [ "\\[Alpha]", "n", "q", "x" ],
        "tokenTranslations" : {
          "L" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
          "\\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",
          "\\qmultiPochhammersym" : "q-Multi-Pochhammer symbol; Example: \\qmultiPochhammersym{a_1,\\ldots,a_n}{q}{n}\nWill be translated to: \nAlternative translations: [Product[QPochhammer[Part[{$0},i],$1,$2],{i,1,Length[{$0}]}]]Relevant links to definitions:\nDLMF:         http://dlmf.nist.gov/17.2.E5\nMathematica:  "
        }
      },
      "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: \\qmultiPochhammersym [\\qmultiPochhammersym]"
        }
      },
      "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: \\qmultiPochhammersym [\\qmultiPochhammersym]"
        }
      },
      "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", "\\displaystyle  L_n^{(\\alpha)}(x;q) = \\frac{(q^{\\alpha+1};q)_n}{(q;q)_n} {}_1\\phi_1(q^{-n};q^{\\alpha+1};q,-q^{n+\\alpha+1}x)", "P_{n}^{(\\alpha)}(x;q)" ],
  "isPartOf" : [ "\\displaystyle  L_n^{(\\alpha)}(x;q) = \\frac{(q^{\\alpha+1};q)_n}{(q;q)_n} {}_1\\phi_1(q^{-n};q^{\\alpha+1};q,-q^{n+\\alpha+1}x)" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	{{DISPLAYTITLE: ''q''-Laguerre polynomials}} {{see also\|big q-Laguerre polynomials\|continuous q-Laguerre polynomials\|little q-Laguerre polynomials}} In mathematics, the '''''q''-Laguerre polynomials''', or '''generalized Stieltjes–Wigert polynomials''' ''P''{{su\|b=''n''\|p=(α)}}(''x'';''q'') are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]] introduced by {{harvs\|txt \| last=Moak\|first=Daniel S.\|title=The q-analogue of the Laguerre polynomials\|journal=. J. Math. Anal. Appl.\| volume=81\|issue=1\|pages=20–47\|year=1981}}. {{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''-Laguerre polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by :<math>\displaystyle L_n^{(\alpha)}(x;q) = \frac{(q^{\alpha+1};q)_n}{(q;q)_n} {}_1\phi_1(q^{-n};q^{\alpha+1};q,-q^{n+\alpha+1}x) </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}} ==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}} {{citation \| last=Moak\|first=Daniel S.\|title=The q-analogue of the Laguerre polynomials\|journal=J. Math. Anal. Appl.\| volume=81\|issue=1\|pages=20–47\|year=1981\| doi=10.1016/0022-247X(81)90048-2 \|mr=618759}} [[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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