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 E(x, y; u) := \sum_{n=0}^\infty u^n \, \psi_n (x) \, \psi_n (y) = \frac{1}{\sqrt{\pi (1 - u^2)}} \, \exp\left(-\frac{1 - u}{1 + u} \, \frac{(x + y)^2}{4} - \frac{1 + u}{1 - u} \, \frac{(x - y)^2}{4}\right)}

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

Semantic latex: E(x , y ; u) : = \sum_{n=0}^\infty u^n \psi_n(x) \psi_n(y) = \frac{1}{\sqrt{\cpi(1 - u^2)}} \exp(- \frac{1 - u}{1 + u} \frac{(x + y)^2}{4} - \frac{1 + u}{1 - u} \frac{(x - y)^2}{4})

Confidence: 0

Mathematica

Translation: E[x_, y_, u_] := Sum[(u)^(n)* Subscript[\[Psi], n][x]* Subscript[\[Psi], n][y], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,Sqrt[Pi*(1 - (u)^(2))]]*Exp[-Divide[1 - u,1 + u]*Divide[(x + y)^(2),4]-Divide[1 + u,1 - u]*Divide[(x - y)^(2),4]]

Information

Sub Equations

  • E[x_, y_, u_] := Sum[(u)^(n)* Subscript[\[Psi], n][x]* Subscript[\[Psi], n][y], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,Sqrt[Pi*(1 - (u)^(2))]]*Exp[-Divide[1 - u,1 + u]*Divide[(x + y)^(2),4]-Divide[1 + u,1 - u]*Divide[(x - y)^(2),4]]

Free variables

  • Subscript[\[Psi], n]
  • u
  • x
  • y

Symbol info

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

Tests

Symbolic
Numeric

SymPy

Translation: null

Information

Sub Equations

  • null

Free variables

  • Symbol('{Symbol('psi')}_{n}')
  • u
  • x
  • y

Symbol info

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

Tests

Symbolic
Numeric

Maple

Translation: E := (x, y, u) -> sum((u)^(n)* psi[n](x)* psi[n](y), n = 0..infinity) = (1)/(sqrt(Pi*(1 - (u)^(2))))*exp(-(1 - u)/(1 + u)*((x + y)^(2))/(4)-(1 + u)/(1 - u)*((x - y)^(2))/(4))

Information

Sub Equations

  • E := (x, y, u) -> sum((u)^(n)* psi[n](x)* psi[n](y), n = 0..infinity) = (1)/(sqrt(Pi*(1 - (u)^(2))))*exp(-(1 - u)/(1 + u)*((x + y)^(2))/(4)-(1 + u)/(1 - u)*((x - y)^(2))/(4))

Free variables

  • psi[n]
  • u
  • x
  • y

Symbol info

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

Tests

Symbolic
Numeric

Dependency Graph Information

Includes

  • Failed to parse (syntax error): {\displaystyle )^2}{4})}
  • Failed to parse (syntax error): {\displaystyle )^2}{4}}
  • Failed to parse (syntax error): {\displaystyle )^2}{4} -}
  • Failed to parse (syntax error): {\displaystyle ^2)}}}
  • Failed to parse (syntax error): {\displaystyle ^2)}}}
  • Failed to parse (syntax error): {\displaystyle =0}^}

Is part of

Complete translation information: 

{
  "id" : "FORMULA_7498c98645ade00576713b93e95a5f1a",
  "formula" : "E(x, y; u) := \\sum_{n=0}^\\infty u^n  \\psi_n (x)  \\psi_n (y) = \\frac{1}{\\sqrt{\\pi (1 - u^2)}}  \\exp\\left(-\\frac{1 - u}{1 + u}  \\frac{(x + y)^2}{4} - \\frac{1 + u}{1 - u}  \\frac{(x - y)^2}{4}\\right)",
  "semanticFormula" : "E(x , y ; u) : = \\sum_{n=0}^\\infty u^n \\psi_n(x) \\psi_n(y) = \\frac{1}{\\sqrt{\\cpi(1 - u^2)}} \\exp(- \\frac{1 - u}{1 + u} \\frac{(x + y)^2}{4} - \\frac{1 + u}{1 - u} \\frac{(x - y)^2}{4})",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "E[x_, y_, u_] := Sum[(u)^(n)* Subscript[\\[Psi], n][x]* Subscript[\\[Psi], n][y], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,Sqrt[Pi*(1 - (u)^(2))]]*Exp[-Divide[1 - u,1 + u]*Divide[(x + y)^(2),4]-Divide[1 + u,1 - u]*Divide[(x - y)^(2),4]]",
      "translationInformation" : {
        "subEquations" : [ "E[x_, y_, u_] := Sum[(u)^(n)* Subscript[\\[Psi], n][x]* Subscript[\\[Psi], n][y], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,Sqrt[Pi*(1 - (u)^(2))]]*Exp[-Divide[1 - u,1 + u]*Divide[(x + y)^(2),4]-Divide[1 + u,1 - u]*Divide[(x - y)^(2),4]]" ],
        "freeVariables" : [ "Subscript[\\[Psi], n]", "u", "x", "y" ],
        "tokenTranslations" : {
          "\\psi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\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",
          "E" : "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" : "null",
      "translationInformation" : {
        "subEquations" : [ "null" ],
        "freeVariables" : [ "Symbol('{Symbol('psi')}_{n}')", "u", "x", "y" ],
        "tokenTranslations" : {
          "\\psi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\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",
          "E" : "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" : "E := (x, y, u) -> sum((u)^(n)* psi[n](x)* psi[n](y), n = 0..infinity) = (1)/(sqrt(Pi*(1 - (u)^(2))))*exp(-(1 - u)/(1 + u)*((x + y)^(2))/(4)-(1 + u)/(1 - u)*((x - y)^(2))/(4))",
      "translationInformation" : {
        "subEquations" : [ "E := (x, y, u) -> sum((u)^(n)* psi[n](x)* psi[n](y), n = 0..infinity) = (1)/(sqrt(Pi*(1 - (u)^(2))))*exp(-(1 - u)/(1 + u)*((x + y)^(2))/(4)-(1 + u)/(1 - u)*((x - y)^(2))/(4))" ],
        "freeVariables" : [ "psi[n]", "u", "x", "y" ],
        "tokenTranslations" : {
          "\\psi" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\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",
          "E" : "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" : [ ],
  "includes" : [ ")^2}{4})", "E(x, y; u) := \\sum_{n=0}^\\infty u^n \\, \\psi_n (x) \\, \\psi_n (y) = \\frac{1}{\\sqrt{\\pi (1 - u^2)}} \\, \\exp\\left(-\\frac{1 - u}{1 + u} \\, \\frac{(x + y)^2}{4} - \\frac{1 + u}{1 - u} \\, \\frac{(x - y)^2}{4}\\right)", ")^2}{4}", ")^2}{4} -", "^2)}}", "^2)}}", "=0}^", "= 0" ],
  "isPartOf" : [ "E(x, y; u) := \\sum_{n=0}^\\infty u^n \\, \\psi_n (x) \\, \\psi_n (y) = \\frac{1}{\\sqrt{\\pi (1 - u^2)}} \\, \\exp\\left(-\\frac{1 - u}{1 + u} \\, \\frac{(x + y)^2}{4} - \\frac{1 + u}{1 - u} \\, \\frac{(x - y)^2}{4}\\right)" ],
  "definiens" : [ ]
}

Specify your own input

 
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