LaTeX to CAS translator

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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 Q_v^\mu(x)= \cos(\mu\pi)\left(\frac{1+x}{1-x}\right)^{\mu/2}\frac{F(v+1,-v;1-\mu;1/2-2/x)} {\Gamma(1-\mu ) }}

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

Semantic latex: Q_v^\mu(x) = \cos(\mu \cpi)(\frac{1+x}{1-x})^{\mu/2} \frac{F(v+1,-v;1-\mu;1/2-2/x)} {\Gamma(1-\mu ) }

Confidence: 0

Mathematica

Translation: (Subscript[Q, v])^\[Mu][x] == Cos[\[Mu]*Pi]*(Divide[1 + x,1 - x])^(\[Mu]/2)*Divide[F[v + 1 , - v ; 1 - \[Mu]; 1/2 - 2/x],\[CapitalGamma]*(1 - \[Mu])]

Information

Sub Equations

  • (Subscript[Q, v])^\[Mu][x] = Cos[\[Mu]*Pi]*(Divide[1 + x,1 - x])^(\[Mu]/2)*Divide[F[v + 1 , - v ; 1 - \[Mu]; 1/2 - 2/x],\[CapitalGamma]*(1 - \[Mu])]

Free variables

  • \[CapitalGamma]
  • \[Mu]
  • v
  • x

Symbol info

  • Cosine; Example: \cos@@{z}

Will be translated to: Cos[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Mathematica: https://reference.wolfram.com/language/ref/Cos.html

  • Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
  • Pi was translated to: Pi
  • Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Tests

Symbolic
Numeric

SymPy

Translation: (Symbol('{Q}_{v}'))**(Symbol('mu'))(x) == cos(Symbol('mu')*pi)*((1 + x)/(1 - x))**(Symbol('mu')/2)*(F(v + 1 , - v ; 1 - Symbol('mu'); 1/2 - 2/x))/(Symbol('Gamma')*(1 - Symbol('mu')))

Information

Sub Equations

  • (Symbol('{Q}_{v}'))**(Symbol('mu'))(x) = cos(Symbol('mu')*pi)*((1 + x)/(1 - x))**(Symbol('mu')/2)*(F(v + 1 , - v ; 1 - Symbol('mu'); 1/2 - 2/x))/(Symbol('Gamma')*(1 - Symbol('mu')))

Free variables

  • Symbol('Gamma')
  • Symbol('mu')
  • v
  • x

Symbol info

  • Cosine; Example: \cos@@{z}

Will be translated to: cos($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#cos

  • Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
  • Pi was translated to: pi
  • Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Tests

Symbolic
Numeric

Maple

Translation: (Q[v])^(mu)(x) = cos(mu*Pi)*((1 + x)/(1 - x))^(mu/2)*(F(v + 1 , - v ; 1 - mu ; 1/2 - 2/x))/(Gamma*(1 - mu))

Information

Sub Equations

  • (Q[v])^(mu)(x) = cos(mu*Pi)*((1 + x)/(1 - x))^(mu/2)*(F(v + 1 , - v ; 1 - mu ; 1/2 - 2/x))/(Gamma*(1 - mu))

Free variables

  • Gamma
  • mu
  • v
  • x

Symbol info

  • Cosine; Example: \cos@@{z}

Will be translated to: cos($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E2 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos

  • Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
  • Pi was translated to: Pi
  • Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).

Tests

Symbolic
Numeric

Dependency Graph Information

Includes

Description

  • mu
  • frac
  • v
  • TeX Source
  • f
  • Formula
  • Gamma
  • Gold ID
  • link
  • mu/2
  • pi
  • Q_v
  • x

Complete translation information: 

{
  "id" : "FORMULA_b5ab87b9cd2da05be00884345889d9e3",
  "formula" : "Q_v^\\mu(x)= \\cos(\\mu\\pi)\\left(\\frac{1+x}{1-x}\\right)^{\\mu/2}\\frac{F(v+1,-v;1-\\mu;1/2-2/x)}  {\\Gamma(1-\\mu ) }",
  "semanticFormula" : "Q_v^\\mu(x) = \\cos(\\mu \\cpi)(\\frac{1+x}{1-x})^{\\mu/2} \\frac{F(v+1,-v;1-\\mu;1/2-2/x)}  {\\Gamma(1-\\mu ) }",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "(Subscript[Q, v])^\\[Mu][x] == Cos[\\[Mu]*Pi]*(Divide[1 + x,1 - x])^(\\[Mu]/2)*Divide[F[v + 1 , - v ; 1 - \\[Mu]; 1/2 - 2/x],\\[CapitalGamma]*(1 - \\[Mu])]",
      "translationInformation" : {
        "subEquations" : [ "(Subscript[Q, v])^\\[Mu][x] = Cos[\\[Mu]*Pi]*(Divide[1 + x,1 - x])^(\\[Mu]/2)*Divide[F[v + 1 , - v ; 1 - \\[Mu]; 1/2 - 2/x],\\[CapitalGamma]*(1 - \\[Mu])]" ],
        "freeVariables" : [ "\\[CapitalGamma]", "\\[Mu]", "v", "x" ],
        "tokenTranslations" : {
          "\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: Cos[$0]\nRelevant links to definitions:\nDLMF:         http://dlmf.nist.gov/4.14#E2\nMathematica:  https://reference.wolfram.com/language/ref/Cos.html",
          "Q" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\cpi" : "Pi was translated to: Pi",
          "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('{Q}_{v}'))**(Symbol('mu'))(x) == cos(Symbol('mu')*pi)*((1 + x)/(1 - x))**(Symbol('mu')/2)*(F(v + 1 , - v ; 1 - Symbol('mu'); 1/2 - 2/x))/(Symbol('Gamma')*(1 - Symbol('mu')))",
      "translationInformation" : {
        "subEquations" : [ "(Symbol('{Q}_{v}'))**(Symbol('mu'))(x) = cos(Symbol('mu')*pi)*((1 + x)/(1 - x))**(Symbol('mu')/2)*(F(v + 1 , - v ; 1 - Symbol('mu'); 1/2 - 2/x))/(Symbol('Gamma')*(1 - Symbol('mu')))" ],
        "freeVariables" : [ "Symbol('Gamma')", "Symbol('mu')", "v", "x" ],
        "tokenTranslations" : {
          "\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: cos($0)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/4.14#E2\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#cos",
          "Q" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\cpi" : "Pi was translated to: pi",
          "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" : "(Q[v])^(mu)(x) = cos(mu*Pi)*((1 + x)/(1 - x))^(mu/2)*(F(v + 1 , - v ; 1 - mu ; 1/2 - 2/x))/(Gamma*(1 - mu))",
      "translationInformation" : {
        "subEquations" : [ "(Q[v])^(mu)(x) = cos(mu*Pi)*((1 + x)/(1 - x))^(mu/2)*(F(v + 1 , - v ; 1 - mu ; 1/2 - 2/x))/(Gamma*(1 - mu))" ],
        "freeVariables" : [ "Gamma", "mu", "v", "x" ],
        "tokenTranslations" : {
          "\\cos" : "Cosine; Example: \\cos@@{z}\nWill be translated to: cos($0)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/4.14#E2\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=cos",
          "Q" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\cpi" : "Pi was translated to: Pi",
          "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" : 1,
    "sentence" : 0,
    "word" : 8
  } ],
  "includes" : [ "+1", ";1/2-2", "+1}{", "+ 1 , -", "; 1/2 - 2", "+ 1, -" ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "mu",
    "score" : 0.932084296835645
  }, {
    "definition" : "frac",
    "score" : 0.8214845700845856
  }, {
    "definition" : "v",
    "score" : 0.8214845700845856
  }, {
    "definition" : "TeX Source",
    "score" : 0.722
  }, {
    "definition" : "f",
    "score" : 0.6601229053380933
  }, {
    "definition" : "Formula",
    "score" : 0.6601229053380933
  }, {
    "definition" : "Gamma",
    "score" : 0.6601229053380933
  }, {
    "definition" : "Gold ID",
    "score" : 0.6601229053380933
  }, {
    "definition" : "link",
    "score" : 0.6601229053380933
  }, {
    "definition" : "mu/2",
    "score" : 0.6601229053380933
  }, {
    "definition" : "pi",
    "score" : 0.6601229053380933
  }, {
    "definition" : "Q_v",
    "score" : 0.6601229053380933
  }, {
    "definition" : "x",
    "score" : 0.6601229053380933
  } ]
}

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