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 P_1^{(\lambda)}(x;\phi)=2(\lambda\cos\phi + x\sin\phi)}

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

Semantic latex: P_1^{(\lambda)}(x;\phi)=2(\lambda\cos\phi + x\sin\phi)

Confidence: 0

Mathematica

Translation: (Subscript[P, 1])^(\[Lambda])[x ; \[Phi]] == 2*(\[Lambda]*Cos[\[Phi]]+ x*Sin[\[Phi]])

Information

Sub Equations

  • (Subscript[P, 1])^(\[Lambda])[x ; \[Phi]] = 2*(\[Lambda]*Cos[\[Phi]]+ x*Sin[\[Phi]])

Free variables

  • \[Lambda]
  • \[Phi]
  • x

Symbol info

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

  • Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.

But this system doesn't know how to translate it as a constant. It was translated as a general letter.

  • 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
Numeric

SymPy

Translation: (Symbol('{P}_{1}'))**(Symbol('lambda'))(x ; Symbol('phi')) == 2*(Symbol('lambda')*cos(Symbol('phi'))+ x*sin(Symbol('phi')))

Information

Sub Equations

  • (Symbol('{P}_{1}'))**(Symbol('lambda'))(x ; Symbol('phi')) = 2*(Symbol('lambda')*cos(Symbol('phi'))+ x*sin(Symbol('phi')))

Free variables

  • Symbol('lambda')
  • Symbol('phi')
  • x

Symbol info

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

  • Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.

But this system doesn't know how to translate it as a constant. It was translated as a general letter.

  • Sine; Example: \sin@@{z}

Will be translated to: sin($0) Relevant links to definitions: DLMF: http://dlmf.nist.gov/4.14#E1 SymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#sin

Tests

Symbolic
Numeric

Maple

Translation: (P[1])^(lambda)(x ; phi) = 2*(lambda*cos(phi)+ x*sin(phi))

Information

Sub Equations

  • (P[1])^(lambda)(x ; phi) = 2*(lambda*cos(phi)+ x*sin(phi))

Free variables

  • lambda
  • phi
  • x

Symbol info

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

  • Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.

But this system doesn't know how to translate it as a constant. It was translated as a general letter.

  • 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

  • Failed to parse (syntax error): {\displaystyle 1^{(}

Description

  • phi
  • lambda
  • x
  • TeX Source
  • Formula
  • Gold ID
  • cos
  • link
  • p
  • sin

Complete translation information: 

{
  "id" : "FORMULA_96d19b4b504f801548c69064d662043b",
  "formula" : "P_1^{(\\lambda)}(x;\\phi)=2(\\lambda\\cos\\phi + x\\sin\\phi)",
  "semanticFormula" : "P_1^{(\\lambda)}(x;\\phi)=2(\\lambda\\cos\\phi + x\\sin\\phi)",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "(Subscript[P, 1])^(\\[Lambda])[x ; \\[Phi]] == 2*(\\[Lambda]*Cos[\\[Phi]]+ x*Sin[\\[Phi]])",
      "translationInformation" : {
        "subEquations" : [ "(Subscript[P, 1])^(\\[Lambda])[x ; \\[Phi]] = 2*(\\[Lambda]*Cos[\\[Phi]]+ x*Sin[\\[Phi]])" ],
        "freeVariables" : [ "\\[Lambda]", "\\[Phi]", "x" ],
        "tokenTranslations" : {
          "P" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\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",
          "\\phi" : "Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
          "\\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" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "crashed" : false,
        "testCalculationsGroup" : [ ]
      }
    },
    "SymPy" : {
      "translation" : "(Symbol('{P}_{1}'))**(Symbol('lambda'))(x ; Symbol('phi')) == 2*(Symbol('lambda')*cos(Symbol('phi'))+ x*sin(Symbol('phi')))",
      "translationInformation" : {
        "subEquations" : [ "(Symbol('{P}_{1}'))**(Symbol('lambda'))(x ; Symbol('phi')) = 2*(Symbol('lambda')*cos(Symbol('phi'))+ x*sin(Symbol('phi')))" ],
        "freeVariables" : [ "Symbol('lambda')", "Symbol('phi')", "x" ],
        "tokenTranslations" : {
          "P" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\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",
          "\\phi" : "Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
          "\\sin" : "Sine; Example: \\sin@@{z}\nWill be translated to: sin($0)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/4.14#E1\nSymPy: https://docs.sympy.org/latest/modules/functions/elementary.html#sin"
        }
      },
      "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" : "(P[1])^(lambda)(x ; phi) = 2*(lambda*cos(phi)+ x*sin(phi))",
      "translationInformation" : {
        "subEquations" : [ "(P[1])^(lambda)(x ; phi) = 2*(lambda*cos(phi)+ x*sin(phi))" ],
        "freeVariables" : [ "lambda", "phi", "x" ],
        "tokenTranslations" : {
          "P" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\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",
          "\\phi" : "Could be the golden ratio == golden mean == golden section == extreme and mean ratio == medial section == divine proportion == divine section == golden proportion == golden cut == golden number.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
          "\\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"
        }
      },
      "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^{(", ")=2(" ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "phi",
    "score" : 0.8536099109960977
  }, {
    "definition" : "lambda",
    "score" : 0.7795898934682262
  }, {
    "definition" : "x",
    "score" : 0.7795898934682262
  }, {
    "definition" : "TeX Source",
    "score" : 0.722
  }, {
    "definition" : "Formula",
    "score" : 0.6896778755706364
  }, {
    "definition" : "Gold ID",
    "score" : 0.6629879847031728
  }, {
    "definition" : "cos",
    "score" : 0.6231540443721655
  }, {
    "definition" : "link",
    "score" : 0.6231540443721655
  }, {
    "definition" : "p",
    "score" : 0.6231540443721655
  }, {
    "definition" : "sin",
    "score" : 0.6231540443721655
  } ]
}

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