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 \begin{align} H_0 (x\mid q) & = 1 \\ H_1 (x\mid q) & = 2x \\ H_2 (x\mid q) & = 4x^2 - (1-q) \\ H_3 (x\mid q) & = 8x^3 - 2x(2-q-q^2) \\ H_4 (x\mid q) & = 16x^4 - 4x^2(3-q-q^2-q^3) + (1-q-q^3+q^4) \end{align} }

${\displaystyle {\begin{aligned}H_{0}(x\mid q)&=1\\H_{1}(x\mid q)&=2x\\H_{2}(x\mid q)&=4x^{2}-(1-q)\\H_{3}(x\mid q)&=8x^{3}-2x(2-q-q^{2})\\H_{4}(x\mid q)&=16x^{4}-4x^{2}(3-q-q^{2}-q^{3})+(1-q-q^{3}+q^{4})\end{aligned}}}$

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

Semantic latex: \begin{align} H_0 (x\mid q) & = 1 \\ H_1 (x\mid q) & = 2x \\ H_2 (x\mid q) & = 4x^2 - (1-q) \\ H_3 (x\mid q) & = 8x^3 - 2x(2-q-q^2) \\ H_4 (x\mid q) & = 16x^4 - 4x^2(3-q-q^2-q^3) + (1-q-q^3+q^4) \end{align}

Confidence: 0

Mathematica

Translation:

Information

Symbol info

(LaTeX -> Mathematica) No translation possible for given token: Unknown relation. Cannot translate: \mid [\mid]

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

(LaTeX -> SymPy) No translation possible for given token: Unknown relation. Cannot translate: \mid [\mid]

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

(LaTeX -> Maple) No translation possible for given token: Unknown relation. Cannot translate: \mid [\mid]

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

${\begin{aligned}H_{0}(x\mid q)&=1\\H_{1}(x\mid q)&=2x\\H_{2}(x\mid q)&=4x^{2}-(1-q)\\H_{3}(x\mid q)&=8x^{3}-2x(2-q-q^{2})\\H_{4}(x\mid q)&=16x^{4}-4x^{2}(3-q-q^{2}-q^{3})+(1-q-q^{3}+q^{4})\end{aligned}}$

$q$

Is part of

${\begin{aligned}H_{0}(x\mid q)&=1\\H_{1}(x\mid q)&=2x\\H_{2}(x\mid q)&=4x^{2}-(1-q)\\H_{3}(x\mid q)&=8x^{3}-2x(2-q-q^{2})\\H_{4}(x\mid q)&=16x^{4}-4x^{2}(3-q-q^{2}-q^{3})+(1-q-q^{3}+q^{4})\end{aligned}}$

Complete translation information:

{
  "id" : "FORMULA_160884575fea48de4b89ddd27900e26c",
  "formula" : "\\begin{align}\nH_0 (x\\mid q) & = 1 \\\\\nH_1 (x\\mid q) & = 2x \\\\\nH_2 (x\\mid q) & = 4x^2 - (1-q) \\\\\nH_3 (x\\mid q) & = 8x^3 - 2x(2-q-q^2) \\\\\nH_4 (x\\mid q) & = 16x^4 - 4x^2(3-q-q^2-q^3) + (1-q-q^3+q^4)\n\\end{align}",
  "semanticFormula" : "\\begin{align}\nH_0 (x\\mid q) & = 1 \\\\\nH_1 (x\\mid q) & = 2x \\\\\nH_2 (x\\mid q) & = 4x^2 - (1-q) \\\\\nH_3 (x\\mid q) & = 8x^3 - 2x(2-q-q^2) \\\\\nH_4 (x\\mid q) & = 16x^4 - 4x^2(3-q-q^2-q^3) + (1-q-q^3+q^4)\n\\end{align}",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Mathematica) No translation possible for given token: Unknown relation. Cannot translate: \\mid [\\mid]"
        }
      },
      "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: Unknown relation. Cannot translate: \\mid [\\mid]"
        }
      },
      "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: Unknown relation. Cannot translate: \\mid [\\mid]"
        }
      },
      "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" : [ "\\begin{align}H_0 (x\\mid q) & = 1 \\\\H_1 (x\\mid q) & = 2x \\\\H_2 (x\\mid q) & = 4x^2 - (1-q) \\\\H_3 (x\\mid q) & = 8x^3 - 2x(2-q-q^2) \\\\H_4 (x\\mid q) & = 16x^4 - 4x^2(3-q-q^2-q^3) + (1-q-q^3+q^4)\\end{align}", "q" ],
  "isPartOf" : [ "\\begin{align}H_0 (x\\mid q) & = 1 \\\\H_1 (x\\mid q) & = 2x \\\\H_2 (x\\mid q) & = 4x^2 - (1-q) \\\\H_3 (x\\mid q) & = 8x^3 - 2x(2-q-q^2) \\\\H_4 (x\\mid q) & = 16x^4 - 4x^2(3-q-q^2-q^3) + (1-q-q^3+q^4)\\end{align}" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	{{DISPLAYTITLE: Continuous ''q''-Hermite polynomials}} In mathematics, the '''continuous ''q''-Hermite 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]]. ==Recurrence and difference relations== : <math>2x H_n(x\mid q) = H_{n+1} (x\mid q) + (1-q^n) H_{n-1} (x\mid q)</math> with the initial conditions : <math> H_0 (x\mid q) =1, H_{-1} (x\mid q) = 0</math> From the above, one can easily calculate: : <math> \begin{align} H_0 (x\mid q) & = 1 \\ H_1 (x\mid q) & = 2x \\ H_2 (x\mid q) & = 4x^2 - (1-q) \\ H_3 (x\mid q) & = 8x^3 - 2x(2-q-q^2) \\ H_4 (x\mid q) & = 16x^4 - 4x^2(3-q-q^2-q^3) + (1-q-q^3+q^4) \end{align} </math> ==Rodrigues formula== {{Empty section\|date=September 2011}} ==Generating function== : <math> \sum_{n=0}^\infty H_n(x \mid q) \frac{t^n}{(q;q)_n} = \frac{1} {\left( t e^{i \theta},t e^{-i \theta};q \right)_\infty} </math> where <math>\textstyle x=\cos \theta</math>. ==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}} [[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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