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 _3F_2([-n, \alpha+\beta+n+1, -x], [\alpha+1, -N], 1)}

${\displaystyle _{3}F_{2}([-n,\alpha +\beta +n+1,-x],[\alpha +1,-N],1)}$

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

Semantic latex: _3F_2([-n, \alpha+\beta+n+1, -x], [\alpha+1, -N], 1)

Confidence: 0

Mathematica

Translation: Subscript[$0, 3]*Subscript[F, 2][[- n , \[Alpha]+ \[Beta]+ n + 1 , - x],[\[Alpha]+ 1 , - N], 1]

Information

Sub Equations

Subscript[$0, 3]*Subscript[F, 2][[- n , \[Alpha]+ \[Beta]+ n + 1 , - x],[\[Alpha]+ 1 , - N], 1]

Free variables

N

\[Alpha]

\[Beta]

n

x

Symbol info

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.

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

Tests

Symbolic

Numeric

SymPy

Translation: Symbol('{$0}_{3}')*Symbol('{F}_{2}')([- n , Symbol('alpha')+ Symbol('beta')+ n + 1 , - x],[Symbol('alpha')+ 1 , - N], 1)

Information

Sub Equations

Symbol('{$0}_{3}')*Symbol('{F}_{2}')([- n , Symbol('alpha')+ Symbol('beta')+ n + 1 , - x],[Symbol('alpha')+ 1 , - N], 1)

Free variables

N

Symbol('alpha')

Symbol('beta')

n

x

Symbol info

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.

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

Tests

Symbolic

Numeric

Maple

Translation: $0[3]*F[2]([- n , alpha + beta + n + 1 , - x],[alpha + 1 , - N], 1)

Information

Sub Equations

$0[3]*F[2]([- n , alpha + beta + n + 1 , - x],[alpha + 1 , - N], 1)

Free variables

N

alpha

beta

n

x

Symbol info

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.

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

Tests

Symbolic

Numeric

Dependency Graph Information

Description

q-Hahn polynomial

Hahn polynomial

limit q

substitution

definition of q-Hahn polynomial

Quantum q-Krawtchouk polynomial

Complete translation information:

{
  "id" : "FORMULA_037ffd975749408e4aa73f8d3f1c0b90",
  "formula" : "_3F_2([-n, \\alpha+\\beta+n+1, -x], [\\alpha+1, -N], 1)",
  "semanticFormula" : "_3F_2([-n, \\alpha+\\beta+n+1, -x], [\\alpha+1, -N], 1)",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "Subscript[$0, 3]*Subscript[F, 2][[- n , \\[Alpha]+ \\[Beta]+ n + 1 , - x],[\\[Alpha]+ 1 , - N], 1]",
      "translationInformation" : {
        "subEquations" : [ "Subscript[$0, 3]*Subscript[F, 2][[- n , \\[Alpha]+ \\[Beta]+ n + 1 , - x],[\\[Alpha]+ 1 , - N], 1]" ],
        "freeVariables" : [ "N", "\\[Alpha]", "\\[Beta]", "n", "x" ],
        "tokenTranslations" : {
          "\\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",
          "F" : "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" : "Symbol('{$0}_{3}')*Symbol('{F}_{2}')([- n , Symbol('alpha')+ Symbol('beta')+ n + 1 , - x],[Symbol('alpha')+ 1 , - N], 1)",
      "translationInformation" : {
        "subEquations" : [ "Symbol('{$0}_{3}')*Symbol('{F}_{2}')([- n , Symbol('alpha')+ Symbol('beta')+ n + 1 , - x],[Symbol('alpha')+ 1 , - N], 1)" ],
        "freeVariables" : [ "N", "Symbol('alpha')", "Symbol('beta')", "n", "x" ],
        "tokenTranslations" : {
          "\\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",
          "F" : "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" : [ ]
      }
    },
    "Maple" : {
      "translation" : "$0[3]*F[2]([- n , alpha + beta + n + 1 , - x],[alpha + 1 , - N], 1)",
      "translationInformation" : {
        "subEquations" : [ "$0[3]*F[2]([- n , alpha + beta + n + 1 , - x],[alpha + 1 , - N], 1)" ],
        "freeVariables" : [ "N", "alpha", "beta", "n", "x" ],
        "tokenTranslations" : {
          "\\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",
          "F" : "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" : [ ]
      }
    }
  },
  "positions" : [ {
    "section" : 2,
    "sentence" : 0,
    "word" : 35
  } ],
  "includes" : [ ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "q-Hahn polynomial",
    "score" : 0.7244849196070415
  }, {
    "definition" : "Hahn polynomial",
    "score" : 0.7141619147451186
  }, {
    "definition" : "limit q",
    "score" : 0.6954080343007951
  }, {
    "definition" : "substitution",
    "score" : 0.5816270233429564
  }, {
    "definition" : "definition of q-Hahn polynomial",
    "score" : 0.5329047619047619
  }, {
    "definition" : "Quantum q-Krawtchouk polynomial",
    "score" : 0.5329047619047619
  } ]
}

Specify your own input

Formula input
Wikitext context	{{see also\|continuous q-Hahn polynomials\|dual q-Hahn polynomials\|continuous dual q-Hahn polynomials}} {{DISPLAYTITLE: ''q''-Hahn polynomials}} In mathematics, the '''''q''-Hahn 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 polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by <math>Q_n(x;a,b,N;q)=\;_{3}\phi_2\left[\begin{matrix} q^-n & abq^n+1 & x \\ aq & q^-N \end{matrix} ; q,q \right] </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== q-Hahn polynomials→ [[Quantum q-Krawtchouk polynomials]]： <math>\lim_{a \to \infty}Q_{n}(q^-{x};a;p,N\|q)=K_{n}^{qtm}(q^-{x};p,N;q)</math> q-Hahn polynomials→ [[Hahn polynomials]] make the substitution<math>\alpha=q^{\alpha}</math>,<math>\beta=q^{\beta}</math> into definition of q-Hahn polynomials, and find the limit q→1, we obtain ： <math>_3F_2([-n, \alpha+\beta+n+1, -x], [\alpha+1, -N], 1)</math>，which is exactly [[Hahn polynomials]]. ==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}} {{cite journal\|last1=Costas-Santos\|first1=R.S.\|last2=Sánchez-Lara\|first2=J.F.\|title=Orthogonality of ''q''-polynomials for non-standard parameters\|journal=Journal of Approximation Theory\|date=September 2011\|volume=163\|issue=9\|pages=1246–1268\|doi=10.1016/j.jat.2011.04.005\|arxiv=1002.4657}} [[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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