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 w(x) = \frac{k}{\sqrt{\pi}} x^{-1/2} \exp(-k^2\log^2 x)}

${\displaystyle w(x)={\frac {k}{\sqrt {\pi }}}x^{-1/2}\exp(-k^{2}\log ^{2}x)}$

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

Semantic latex: w(x) = \frac{k}{\sqrt{\cpi}} x^{-1/2} \exp(- k^2 \log^2 x)

Confidence: 0

Mathematica

Translation: w[x] == Divide[k,Sqrt[Pi]]*(x)^(- 1/2)* Exp[- (k)^(2)* (Log[x])^(2)]

Information

Sub Equations

w[x] = Divide[k,Sqrt[Pi]]*(x)^(- 1/2)* Exp[- (k)^(2)* (Log[x])^(2)]

Free variables

k

x

Symbol info

Exponential function; Example: \exp@@{z}

Will be translated to: Exp[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E19 Mathematica: https://reference.wolfram.com/language/ref/Exp.html

Pi was translated to: Pi

Logarithm; Example: \log@@{z}

Will be translated to: Log[$0] Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 Mathematica: https://reference.wolfram.com/language/ref/Log.html

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

Tests

Symbolic

Test expression: (w*(x))-(Divide[k,Sqrt[Pi]]*(x)^(- 1/2)* Exp[- (k)^(2)* (Log[x])^(2)])

ERROR:

{
    "result": "ERROR",
    "testTitle": "Simple",
    "testExpression": null,
    "resultExpression": null,
    "wasAborted": false,
    "conditionallySuccessful": false
}

Numeric

SymPy

Translation: w(x) == (k)/(sqrt(pi))*(x)**(- 1/2)* exp(- (k)**(2)* (log(x))**(2))

Information

Sub Equations

w(x) = (k)/(sqrt(pi))*(x)**(- 1/2)* exp(- (k)**(2)* (log(x))**(2))

Free variables

k

x

Symbol info

Exponential function; Example: \exp@@{z}

Will be translated to: exp($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E19 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#exp

Pi was translated to: pi

Logarithm; Example: \log@@{z}

Will be translated to: log($0) Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#log

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

Tests

Symbolic

Numeric

Maple

Translation: w(x) = (k)/(sqrt(Pi))*(x)^(- 1/2)* exp(- (k)^(2)* (log(x))^(2))

Information

Sub Equations

w(x) = (k)/(sqrt(Pi))*(x)^(- 1/2)* exp(- (k)^(2)* (log(x))^(2))

Free variables

k

x

Symbol info

Exponential function; Example: \exp@@{z}

Will be translated to: exp($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E19 Maple: https://www.maplesoft.com/support/help/Maple/view.aspx?path=LinearAlgebra/Trace

Pi was translated to: Pi

Logarithm; Example: \log@@{z}

Will be translated to: log($0) Constraints: z != 0 Branch Cuts: (-\infty, 0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.2#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=log

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

${\frac {k}{\sqrt {\pi }}}x^{-1/2}\exp \left(-k^{2}\log ^{2}x\right)$

Description

weight function

positive real line

basic Askey scheme

family of basic hypergeometric orthogonal polynomial

mathematics

Stieltjes -- Wigert polynomial

Thomas Jan Stieltjes

Carl Severin Wigert

Complete translation information:

{
  "id" : "FORMULA_583d3b9e00bbd73091b01f368d1a82c7",
  "formula" : "w(x) = \\frac{k}{\\sqrt{\\pi}} x^{-1/2} \\exp(-k^2\\log^2 x)",
  "semanticFormula" : "w(x) = \\frac{k}{\\sqrt{\\cpi}} x^{-1/2} \\exp(- k^2 \\log^2 x)",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "w[x] == Divide[k,Sqrt[Pi]]*(x)^(- 1/2)* Exp[- (k)^(2)* (Log[x])^(2)]",
      "translationInformation" : {
        "subEquations" : [ "w[x] = Divide[k,Sqrt[Pi]]*(x)^(- 1/2)* Exp[- (k)^(2)* (Log[x])^(2)]" ],
        "freeVariables" : [ "k", "x" ],
        "tokenTranslations" : {
          "\\exp" : "Exponential function; Example: \\exp@@{z}\nWill be translated to: Exp[$0]\nRelevant links to definitions:\nDLMF:         http://dlmf.nist.gov/4.2#E19\nMathematica:  https://reference.wolfram.com/language/ref/Exp.html",
          "\\cpi" : "Pi was translated to: Pi",
          "\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: Log[$0]\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF:         http://dlmf.nist.gov/4.2#E2\nMathematica:  https://reference.wolfram.com/language/ref/Log.html",
          "w" : "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" : "ERROR",
        "numberOfTests" : 1,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 1,
        "crashed" : false,
        "testCalculationsGroup" : [ {
          "lhs" : "w*(x)",
          "rhs" : "Divide[k,Sqrt[Pi]]*(x)^(- 1/2)* Exp[- (k)^(2)* (Log[x])^(2)]",
          "testExpression" : "(w*(x))-(Divide[k,Sqrt[Pi]]*(x)^(- 1/2)* Exp[- (k)^(2)* (Log[x])^(2)])",
          "testCalculations" : [ {
            "result" : "ERROR",
            "testTitle" : "Simple",
            "testExpression" : null,
            "resultExpression" : null,
            "wasAborted" : false,
            "conditionallySuccessful" : false
          } ]
        } ]
      }
    },
    "SymPy" : {
      "translation" : "w(x) == (k)/(sqrt(pi))*(x)**(- 1/2)* exp(- (k)**(2)* (log(x))**(2))",
      "translationInformation" : {
        "subEquations" : [ "w(x) = (k)/(sqrt(pi))*(x)**(- 1/2)* exp(- (k)**(2)* (log(x))**(2))" ],
        "freeVariables" : [ "k", "x" ],
        "tokenTranslations" : {
          "\\exp" : "Exponential function; Example: \\exp@@{z}\nWill be translated to: exp($0)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/4.2#E19\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#exp",
          "\\cpi" : "Pi was translated to: pi",
          "\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: log($0)\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/4.2#E2\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#log",
          "w" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
        }
      }
    },
    "Maple" : {
      "translation" : "w(x) = (k)/(sqrt(Pi))*(x)^(- 1/2)* exp(- (k)^(2)* (log(x))^(2))",
      "translationInformation" : {
        "subEquations" : [ "w(x) = (k)/(sqrt(Pi))*(x)^(- 1/2)* exp(- (k)^(2)* (log(x))^(2))" ],
        "freeVariables" : [ "k", "x" ],
        "tokenTranslations" : {
          "\\exp" : "Exponential function; Example: \\exp@@{z}\nWill be translated to: exp($0)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/4.2#E19\nMaple: https://www.maplesoft.com/support/help/Maple/view.aspx?path=LinearAlgebra/Trace",
          "\\cpi" : "Pi was translated to: Pi",
          "\\log" : "Logarithm; Example: \\log@@{z}\nWill be translated to: log($0)\nConstraints: z != 0\nBranch Cuts: (-\\infty, 0]\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/4.2#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=log",
          "w" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
        }
      }
    }
  },
  "positions" : [ {
    "section" : 0,
    "sentence" : 0,
    "word" : 38
  } ],
  "includes" : [ "\\frac{k}{\\sqrt{\\pi}} x^{-1/2} \\exp \\left(-k^2 \\log^2 x \\right)" ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "weight function",
    "score" : 0.722
  }, {
    "definition" : "positive real line",
    "score" : 0.7125985104912714
  }, {
    "definition" : "basic Askey scheme",
    "score" : 0.6859086196238077
  }, {
    "definition" : "family of basic hypergeometric orthogonal polynomial",
    "score" : 0.6859086196238077
  }, {
    "definition" : "mathematics",
    "score" : 0.6460746792928004
  }, {
    "definition" : "Stieltjes -- Wigert polynomial",
    "score" : 0.6460746792928004
  }, {
    "definition" : "Thomas Jan Stieltjes",
    "score" : 0.5500952380952381
  }, {
    "definition" : "Carl Severin Wigert",
    "score" : 0.5049074255814494
  } ]
}

Specify your own input

Formula input
Wikitext context	{{distinguish\|Stieltjes polynomial}} {{for\|the generalized Stieltjes–Wigert polynomials\|q-Laguerre polynomials}} In mathematics, '''Stieltjes–Wigert polynomials''' (named after [[Thomas Jan Stieltjes]] and [[Carl Severin Wigert]]) are a family of basic hypergeometric [[orthogonal polynomials]] in the basic [[Askey scheme]], for the weight function <ref>Up to a constant factor this is ''w''(''q''<sup>−1/2</sup>''x'') for the weight function ''w'' in Szegő (1975), Section 2.7. See also Koornwinder et al. (2010), Section 18.27(vi).</ref> :<math> w(x) = \frac{k}{\sqrt{\pi}} x^{-1/2} \exp(-k^2\log^2 x)</math> on the positive real line ''x'' > 0. The [[moment problem]] for the Stieltjes–Wigert polynomials is indeterminate; in other words, there are many other measures giving the same family of orthogonal polynomials (see [[Krein's condition]]). Koekoek et al. (2010) give in Section 14.27 a detailed list of the properties of these polynomials. ==Definition== The polynomials are given in terms of [[basic hypergeometric function]]s and the [[Pochhammer symbol]] by<ref>Up to a constant factor ''S''<sub>''n''</sub>(''x'';''q'')=''p''<sub>''n''</sub>(''q''<sup>−1/2</sup>''x'') for ''p''<sub>''n''</sub>(''x'') in Szegő (1975), Section 2.7.</ref> :<math>\displaystyle S_n(x;q) = \frac{1}{(q;q)_n}{}_1\phi_1(q^{-n},0;q,-q^{n+1}x), </math> where :<math> q = \exp \left(-\frac{1}{2k^2} \right) .</math> ==Orthogonality== Since the [[moment problem]] for these polynomials is indeterminate there are many different weight functions on [0,∞] for which they are orthogonal. Two examples of such weight functions are :<math>\frac{1}{(-x,-qx^{-1};q)_\infty}</math> and :<math>\frac{k}{\sqrt{\pi}} x^{-1/2} \exp \left(-k^2 \log^2 x \right) .</math> ==Notes== {{reflist}} ==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\|title=Ch. 18, Orthogonal polynomials\|url=http://dlmf.nist.gov/18\|first=Tom H. \|last=Koornwinder\|first2=Roderick S. C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F. \|last4=Swarttouw}} {{Citation \| last1=Szegő \| first1=Gábor \| title=Orthogonal Polynomials \| publisher=Colloquium Publications 23, American Mathematical Society, Fourth Edition\| isbn=978-0-8218-1023-1 \| mr=0372517 \| year=1975}} {{Citation \| last1=Stieltjes \| first1=T. -J. \| title=Recherches sur les fractions continues \| url=http://www.numdam.org/numdam-bin/item?id=AFST_1995_6_4_1_J1_0 \| language=French \| jfm=25.0326.01 \| mr = 1344720 \| year=1894 \| journal=Ann. Fac. Sci. Toulouse \| volume=VIII \| pages=1–122 \| doi=10.5802/afst.108}} {{cite journal \| first1= Xiang-Sheng \| last1=Wang \| first2=Roderick \| last2=Wong \|title= Uniform asymptotics of some q-orthogonal polynomials \|journal = J. Math. Anal. Appl. \| year=2010 \| volume=364 \| number=1 \|pages=79–87 \| doi=10.1016/j.jmaa.2009.10.038 }} *{{Citation \| last1=Wigert \| first1=S. \| title=Sur les polynomes orthogonaux et l'approximation des fonctions continues \| language=French \| jfm=49.0296.01 \| year=1923 \| journal=Arkiv för matematik, astronomi och fysik \| volume=17 \| pages=1–15}} {{DEFAULTSORT:Stieltjes-Wigert polynomials}} [[Category:Orthogonal polynomials]] [[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