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 \mathrm{Gi}(x) = \frac{1}{\pi} \int_0^\infty \sin\left(\frac{t^3}{3} + xt\right)\, dt,}

${\displaystyle \mathrm {Gi} (x)={\frac {1}{\pi }}\int _{0}^{\infty }\sin \left({\frac {t^{3}}{3}}+xt\right)\,dt,}$

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

Semantic latex: \ScorerGi@{x} = \frac{1}{\cpi} \int_0^\infty \sin(\frac{t^3}{3} + xt) \diff{t}

Confidence: 0.71446280208853

Mathematica

Translation: ScorerGi[x] == Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}, GenerateConditions->None]

Information

Sub Equations

ScorerGi[x] = Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}, GenerateConditions->None]

Free variables

x

Symbol info

Scorer function Gi; Example: \ScorerGi@{z}

Will be translated to: ScorerGi[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/9.12#i Mathematica: https://reference.wolfram.com/language/ref/ScorerGi.html

Pi was translated to: Pi

Sine; Example: \sin@@{z}

Will be translated to: Sin[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Mathematica: https://reference.wolfram.com/language/ref/Sin.html

Tests

Symbolic

Test expression: (ScorerGi[x])-(Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}, GenerateConditions->None])

ERROR:

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

Numeric

SymPy

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation: AiryBi(x)*(int(AiryAi(t), t = (x) .. infinity))+AiryAi(x)*(int(AiryBi(t), t = 0 .. (x))) = (1)/(Pi)*int(sin(((t)^(3))/(3)+ x*t), t = 0..infinity)

Information

Sub Equations

AiryBi(x)*(int(AiryAi(t), t = (x) .. infinity))+AiryAi(x)*(int(AiryBi(t), t = 0 .. (x))) = (1)/(Pi)*int(sin(((t)^(3))/(3)+ x*t), t = 0..infinity)

Free variables

x

Symbol info

Scorer function Gi; Example: \ScorerGi@{z}

Will be translated to: Alternative translations: [AiryBi($0)*(int(AiryAi(t), t = ($0) .. infinity))+AiryAi($0)*(int(AiryBi(t), t = 0 .. ($0)))]Relevant links to definitions: DLMF: http://dlmf.nist.gov/9.12#i Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Airy

Pi was translated to: Pi

Sine; Example: \sin@@{z}

Will be translated to: sin($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$x$

$x)$

$\mathrm {Gi} (x)={\frac {1}{\pi }}\int _{0}^{\infty }\sin \left({\frac {t^{3}}{3}}+xt\right)\,dt$

Is part of

$\mathrm {Gi} (x)={\frac {1}{\pi }}\int _{0}^{\infty }\sin \left({\frac {t^{3}}{3}}+xt\right)\,dt$

Complete translation information:

{
  "id" : "FORMULA_df9c8c7c4c42c2db05ff36460f65cf90",
  "formula" : "\\mathrm{Gi}(x) = \\frac{1}{\\pi} \\int_0^\\infty \\sin\\left(\\frac{t^3}{3} + xt\\right) dt",
  "semanticFormula" : "\\ScorerGi@{x} = \\frac{1}{\\cpi} \\int_0^\\infty \\sin(\\frac{t^3}{3} + xt) \\diff{t}",
  "confidence" : 0.7144628020885297,
  "translations" : {
    "Mathematica" : {
      "translation" : "ScorerGi[x] == Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}, GenerateConditions->None]",
      "translationInformation" : {
        "subEquations" : [ "ScorerGi[x] = Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}, GenerateConditions->None]" ],
        "freeVariables" : [ "x" ],
        "tokenTranslations" : {
          "\\ScorerGi" : "Scorer function Gi; Example: \\ScorerGi@{z}\nWill be translated to: ScorerGi[$0]\nRelevant links to definitions:\nDLMF:         http://dlmf.nist.gov/9.12#i\nMathematica:  https://reference.wolfram.com/language/ref/ScorerGi.html",
          "\\cpi" : "Pi was translated to: Pi",
          "\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: Sin[$0]\nRelevant links to definitions:\nDLMF:         http://dlmf.nist.gov/4.14#E1\nMathematica:  https://reference.wolfram.com/language/ref/Sin.html"
        }
      },
      "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" : "ScorerGi[x]",
          "rhs" : "Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}, GenerateConditions->None]",
          "testExpression" : "(ScorerGi[x])-(Divide[1,Pi]*Integrate[Sin[Divide[(t)^(3),3]+ x*t], {t, 0, Infinity}, GenerateConditions->None])",
          "testCalculations" : [ {
            "result" : "ERROR",
            "testTitle" : "Simple",
            "testExpression" : null,
            "resultExpression" : null,
            "wasAborted" : false,
            "conditionallySuccessful" : false
          } ]
        } ]
      }
    },
    "SymPy" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\ScorerGi [\\ScorerGi]"
        }
      }
    },
    "Maple" : {
      "translation" : "AiryBi(x)*(int(AiryAi(t), t = (x) .. infinity))+AiryAi(x)*(int(AiryBi(t), t = 0 .. (x))) = (1)/(Pi)*int(sin(((t)^(3))/(3)+ x*t), t = 0..infinity)",
      "translationInformation" : {
        "subEquations" : [ "AiryBi(x)*(int(AiryAi(t), t = (x) .. infinity))+AiryAi(x)*(int(AiryBi(t), t = 0 .. (x))) = (1)/(Pi)*int(sin(((t)^(3))/(3)+ x*t), t = 0..infinity)" ],
        "freeVariables" : [ "x" ],
        "tokenTranslations" : {
          "\\ScorerGi" : "Scorer function Gi; Example: \\ScorerGi@{z}\nWill be translated to: \nAlternative translations: [AiryBi($0)*(int(AiryAi(t), t = ($0) .. infinity))+AiryAi($0)*(int(AiryBi(t), t = 0 .. ($0)))]Relevant links to definitions:\nDLMF:  http://dlmf.nist.gov/9.12#i\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=Airy",
          "\\cpi" : "Pi was translated to: Pi",
          "\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: sin($0)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/4.14#E1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=sin"
        }
      }
    }
  },
  "positions" : [ ],
  "includes" : [ "x", "x)", "\\mathrm{Gi}(x) = \\frac{1}{\\pi} \\int_0^\\infty \\sin\\left(\\frac{t^3}{3} + xt\\right)\\, dt" ],
  "isPartOf" : [ "\\mathrm{Gi}(x) = \\frac{1}{\\pi} \\int_0^\\infty \\sin\\left(\\frac{t^3}{3} + xt\\right)\\, dt" ],
  "definiens" : [ ]
}

Specify your own input

Formula input
Wikitext context	[[File:Mplwp Scorers Gi Hi.svg\|300px\|thumb\|[[Graph of a function\|Graph]] of <math>\mathrm{Gi}(x)</math> and <math>\mathrm{Hi}(x)</math>]] In [[mathematics]], the '''Scorer's functions''' are [[special function]]s studied by {{harvtxt\|Scorer\|1950}} and denoted Gi(''x'') and Hi(''x''). Hi(''x'') and Gi(''x'') solve the equation :<math>y''(x) - x\ y(x) = \frac{1}{\pi}</math> and are given by :<math>\mathrm{Gi}(x) = \frac{1}{\pi} \int_0^\infty \sin\left(\frac{t^3}{3} + xt\right)\, dt,</math> :<math>\mathrm{Hi}(x) = \frac{1}{\pi} \int_0^\infty \exp\left(-\frac{t^3}{3} + xt\right)\, dt.</math> The Scorer's functions can also be defined in terms of [[Airy function]]s: :<math>\begin{align} \mathrm{Gi}(x) &{}= \mathrm{Bi}(x) \int_x^\infty \mathrm{Ai}(t) \, dt + \mathrm{Ai}(x) \int_0^x \mathrm{Bi}(t) \, dt, \\ \mathrm{Hi}(x) &{}= \mathrm{Bi}(x) \int_{-\infty}^x \mathrm{Ai}(t) \, dt - \mathrm{Ai}(x) \int_{-\infty}^x \mathrm{Bi}(t) \, dt. \end{align} </math> ==References== * {{dlmf\|title= Scorer functions \|id=9.12\|first=F. W. J.\|last= Olver}} *{{Citation \| last1=Scorer \| first1=R. S. \| title=Numerical evaluation of integrals of the form <math>I=\int^{x_2}_{x_{1}}f(x)e^{i\phi(x)}dx</math> and the tabulation of the function <math>{\rm Gi} (z)=\frac{1}{\pi}\int^\infty_0{\rm sin}\left(uz+\frac 13 u^3\right)du</math> \| doi=10.1093/qjmam/3.1.107 \| mr=0037604 \|id=\| year=1950 \| journal=The Quarterly Journal of Mechanics and Applied Mathematics \| issn=0033-5614 \| volume=3 \| pages=107–112}} [[Category:Special functions]] {{mathanalysis-stub}}
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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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