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_n^{(c)} (s,a,b)=\frac{(a-b+1)_n(a+c+1)_n}{n!} {}_3F_2(-n,a-s,a+s+1;a-b+a,a+c+1;1)}

${\displaystyle w_{n}^{(c)}(s,a,b)={\frac {(a-b+1)_{n}(a+c+1)_{n}}{n!}}{}_{3}F_{2}(-n,a-s,a+s+1;a-b+a,a+c+1;1)}$

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

Semantic latex: w_n^{(c)} (s,a,b)=\frac{(a-b+1)_n(a+c+1)_n}{n!} {}_3F_2(-n,a-s,a+s+1;a-b+a,a+c+1;1)

Confidence: 0

Mathematica

Translation: (Subscript[w, n])^(c)[s , a , b] == Divide[Subscript[a - b + 1, n]*Subscript[a + c + 1, n],(n)!]Subscript[, 3]*Subscript[F, 2][- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1]

Information

Sub Equations

(Subscript[w, n])^(c)[s , a , b] = Divide[Subscript[a - b + 1, n]*Subscript[a + c + 1, n],(n)!]Subscript[, 3]*Subscript[F, 2][- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1]

Free variables

a

b

c

n

s

Symbol info

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

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

Tests

Symbolic

Numeric

SymPy

Translation: (Symbol('{w}_{n}'))**(c)(s , a , b) == (Symbol('{a - b + 1}_{n}')*Symbol('{a + c + 1}_{n}'))/(factorial(n))Symbol('{}_{3}')*Symbol('{F}_{2}')(- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1)

Information

Sub Equations

(Symbol('{w}_{n}'))**(c)(s , a , b) = (Symbol('{a - b + 1}_{n}')*Symbol('{a + c + 1}_{n}'))/(factorial(n))Symbol('{}_{3}')*Symbol('{F}_{2}')(- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1)

Free variables

a

b

c

n

s

Symbol info

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

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

Tests

Symbolic

Numeric

Maple

Translation: (w[n])^(c)(s , a , b) = (a - b + 1[n]*a + c + 1[n])/(factorial(n))[3]*F[2](- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1)

Information

Sub Equations

(w[n])^(c)(s , a , b) = (a - b + 1[n]*a + c + 1[n])/(factorial(n))[3]*F[2](- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1)

Free variables

a

b

c

n

s

Symbol info

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

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$n$

Description

non-uniform lattice

parameter

Complete translation information:

{
  "id" : "FORMULA_265d8b134d483a1a7050a52a2fe6bf6c",
  "formula" : "w_n^{(c)} (s,a,b)=\\frac{(a-b+1)_n(a+c+1)_n}{n!} {}_3F_2(-n,a-s,a+s+1;a-b+a,a+c+1;1)",
  "semanticFormula" : "w_n^{(c)} (s,a,b)=\\frac{(a-b+1)_n(a+c+1)_n}{n!} {}_3F_2(-n,a-s,a+s+1;a-b+a,a+c+1;1)",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "(Subscript[w, n])^(c)[s , a , b] == Divide[Subscript[a - b + 1, n]*Subscript[a + c + 1, n],(n)!]Subscript[, 3]*Subscript[F, 2][- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1]",
      "translationInformation" : {
        "subEquations" : [ "(Subscript[w, n])^(c)[s , a , b] = Divide[Subscript[a - b + 1, n]*Subscript[a + c + 1, n],(n)!]Subscript[, 3]*Subscript[F, 2][- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1]" ],
        "freeVariables" : [ "a", "b", "c", "n", "s" ],
        "tokenTranslations" : {
          "F" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "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" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    },
    "SymPy" : {
      "translation" : "(Symbol('{w}_{n}'))**(c)(s , a , b) == (Symbol('{a - b + 1}_{n}')*Symbol('{a + c + 1}_{n}'))/(factorial(n))Symbol('{}_{3}')*Symbol('{F}_{2}')(- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1)",
      "translationInformation" : {
        "subEquations" : [ "(Symbol('{w}_{n}'))**(c)(s , a , b) = (Symbol('{a - b + 1}_{n}')*Symbol('{a + c + 1}_{n}'))/(factorial(n))Symbol('{}_{3}')*Symbol('{F}_{2}')(- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1)" ],
        "freeVariables" : [ "a", "b", "c", "n", "s" ],
        "tokenTranslations" : {
          "F" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "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" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    },
    "Maple" : {
      "translation" : "(w[n])^(c)(s , a , b) = (a - b + 1[n]*a + c + 1[n])/(factorial(n))[3]*F[2](- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1)",
      "translationInformation" : {
        "subEquations" : [ "(w[n])^(c)(s , a , b) = (a - b + 1[n]*a + c + 1[n])/(factorial(n))[3]*F[2](- n , a - s , a + s + 1 ; a - b + a , a + c + 1 ; 1)" ],
        "freeVariables" : [ "a", "b", "c", "n", "s" ],
        "tokenTranslations" : {
          "F" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "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" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    }
  },
  "positions" : [ {
    "section" : 0,
    "sentence" : 1,
    "word" : 12
  } ],
  "includes" : [ "n" ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "non-uniform lattice",
    "score" : 0.6460746792928004
  }, {
    "definition" : "parameter",
    "score" : 0.5988174995334326
  } ]
}

Specify your own input

Formula input
Wikitext context	In mathematics, the '''dual Hahn polynomials''' are a family of [[orthogonal polynomials]] in the [[Askey scheme]] of hypergeometric orthogonal polynomials. They are defined on a non-uniform lattice <math>x(s)=s(s+1)</math> and are defined as :<math>w_n^{(c)} (s,a,b)=\frac{(a-b+1)_n(a+c+1)_n}{n!} {}_3F_2(-n,a-s,a+s+1;a-b+a,a+c+1;1)</math> for <math>n=0,1,...,N-1</math> and the parameters <math>a,b,c</math> are restricted to <math>-\frac{1}{2}<a<b, \|c\|<1+a, b=a+N</math>. Note that <math>(u)_k</math> is the [[falling and rising factorials]], otherwise known as the Pochhammer symbol, and <math>{}_3F_2(\cdot)</math> is the [[generalized hypergeometric function]]s {{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. ==Orthogonality== The Dual Hahn polynomials have the orthogonality condition :<math>\sum^{b-1}_{s=a}w_n^{(c)}(s,a,b)w_m^{(c)}(s,a,b)\rho(s)[\Delta x(s-\frac{1}{2}) ]=\delta_{nm}d_n^2</math> for <math>n,m=0,1,...,N-1</math>. Where <math>\Delta x(s)=x(s+1)-x(s)</math>, :<math>\rho(s)=\frac{\Gamma(a+s+1)\Gamma(c+s+1)}{\Gamma(s-a+1)\Gamma(b-s)\Gamma(b+s+1)\Gamma(s-c+1)}</math> and :<math>d_n^2=\frac{\Gamma(a+c+n+a)}{n!(b-a-n-1)!\Gamma(b-c-n)}</math> ==Numerical Instability== As the value of <math>n</math> increases, the values that the discrete polynomials obtain also increases. As a result, to obtain [[numerical stability]] in calculating the polynomials you would use the renormalised Dual Hahn Polynomial as defined as :<math>\hat w_n^{(c)}(s,a,b)=w_n^{(c)}(s,a,b)\sqrt{\frac{\rho(s)}{d_n^2}[\Delta x(s-\frac{1}{2})]}</math> for <math>n=0,1,...,N-1</math>. Then the orthogonality condition becomes :<math>\sum^{b-1}_{s=a}\hat w_n^{(c)}(s,a,b)\hat w_m^{(c)}(s,a,b)=\delta_{m,n}</math> for <math>n,m=0,1,...,N-1</math> ==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== The Hahn polynomials, <math>h_n(x,N;\alpha,\beta)</math>, is defined on the uniform lattice <math>x(s)=s</math>, and the parameters <math>a,b,c</math> are defined as <math>a=(\alpha+\beta)/2,b=a+N,c=(\beta-\alpha)/2</math>. Then setting <math>\alpha=\beta=0</math> the [[Hahn polynomials]] become the [[Tchebichef polynomials]]. Note that the Dual Hahn polynomials have a ''q''-analog with an extra parameter ''q'' known as the [[Dual Hahn Q-polynomials]] [[Racah polynomials]] are a generalization of dual Hahn polynomials ==References== {{Citation\| last1= Zhu\| first1 = Hongqing\| title=Image analysis by discrete orthogonal dual Hahn moments\| journal = Pattern Recognition Letters\| volume = 28\| issue = 13\| pages = 1688–1704\|doi = 10.1016/j.patrec.2007.04.013\|year=2007\| url = https://www.hal.inserm.fr/inserm-00189813/file/Image_analysis_Hahn.pdf}} {{Citation \| last1=Hahn \| first1=Wolfgang \| title=Über Orthogonalpolynome, die q-Differenzengleichungen genügen \| doi=10.1002/mana.19490020103 \| mr=0030647 \| year=1949 \| journal=[[Mathematische Nachrichten]] \| issn=0025-584X \| volume=2 \| issue=1–2 \| pages=4–34}} {{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=18.19\|title=Hahn Class: Definitions\|first=Tom H. \|last=Koornwinder\|first2=Roderick S. C.\|last2= Wong\|first3=Roelof \|last3=Koekoek\|\|first4=René F. \|last4=Swarttouw}} [[Category:Special hypergeometric functions]] [[Category:Orthogonal polynomials]]
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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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