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 P^\mu_{-(1/2)+i\lambda}(x)}

${\displaystyle P_{-(1/2)+i\lambda }^{\mu }(x)}$

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

Semantic latex: \assLegendreP[\mu]{-(1/2)+i\lambda}@{x}

Confidence: 0.75134718564628

Mathematica

Translation: LegendreP[-(1/2)+ i*\[Lambda], \[Mu], 3, x]

Information

Sub Equations

LegendreP[-(1/2)+ i*\[Lambda], \[Mu], 3, x]

Free variables

\[Lambda]

\[Mu]

i

x

Symbol info

associated Legendre polynomial of the first kind; Example: \assLegendreP[mu]{nu}@{z}

Will be translated to: LegendreP[$1, $0, 3, $2] Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.21#Ex1 Mathematica: https://reference.wolfram.com/language/ref/LegendreP.html

You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Mathematica uses I for this constant. If you want to translate it as a constant, use the corresponding DLMF macro \iunit

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation: LegendreP(-(1/2)+ i*lambda, mu, x)

Information

Sub Equations

LegendreP(-(1/2)+ i*lambda, mu, x)

Free variables

i

lambda

mu

x

Symbol info

associated Legendre polynomial of the first kind; Example: \assLegendreP[mu]{nu}@{z}

Will be translated to: LegendreP($1, $0, $2) Relevant links to definitions: DLMF: http://dlmf.nist.gov/14.21#Ex1 Maple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreP

You use a typical letter for a constant [the imaginary unit == the principal square root of -1].

We keep it like it is! But you should know that Maple uses I for this constant. If you want to translate it as a constant, use the corresponding DLMF macro \iunit

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$Q_{-(1/2)+i\lambda }^{\mu }(x)$

Is part of

$Q_{-(1/2)+i\lambda }^{\mu }(x)$

Description

function

Gustav Ferdinand Mehler

term of Legendre function

distance of a point

series

axis of a cone

conical function

mathematics

Mehler function

point

surface of the cone

Complete translation information:

{
  "id" : "FORMULA_7c0f853b035888614415491de677b659",
  "formula" : "P^\\mu_{-(1/2)+i\\lambda}(x)",
  "semanticFormula" : "\\assLegendreP[\\mu]{-(1/2)+i\\lambda}@{x}",
  "confidence" : 0.7513471856462801,
  "translations" : {
    "Mathematica" : {
      "translation" : "LegendreP[-(1/2)+ i*\\[Lambda], \\[Mu], 3, x]",
      "translationInformation" : {
        "subEquations" : [ "LegendreP[-(1/2)+ i*\\[Lambda], \\[Mu], 3, x]" ],
        "freeVariables" : [ "\\[Lambda]", "\\[Mu]", "i", "x" ],
        "tokenTranslations" : {
          "\\assLegendreP1" : "associated Legendre polynomial of the first kind; Example: \\assLegendreP[mu]{nu}@{z}\nWill be translated to: LegendreP[$1, $0, 3, $2]\nRelevant links to definitions:\nDLMF:         http://dlmf.nist.gov/14.21#Ex1\nMathematica:  https://reference.wolfram.com/language/ref/LegendreP.html",
          "i" : "You use a typical letter for a constant [the imaginary unit == the principal square root of -1].\nWe keep it like it is! But you should know that Mathematica uses I for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\iunit\n"
        }
      },
      "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" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\assLegendreP [\\assLegendreP]"
        }
      },
      "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" : "LegendreP(-(1/2)+ i*lambda, mu, x)",
      "translationInformation" : {
        "subEquations" : [ "LegendreP(-(1/2)+ i*lambda, mu, x)" ],
        "freeVariables" : [ "i", "lambda", "mu", "x" ],
        "tokenTranslations" : {
          "\\assLegendreP1" : "associated Legendre polynomial of the first kind; Example: \\assLegendreP[mu]{nu}@{z}\nWill be translated to: LegendreP($1, $0, $2)\nRelevant links to definitions:\nDLMF:  http://dlmf.nist.gov/14.21#Ex1\nMaple: https://www.maplesoft.com/support/help/maple/view.aspx?path=LegendreP",
          "i" : "You use a typical letter for a constant [the imaginary unit == the principal square root of -1].\nWe keep it like it is! But you should know that Maple uses I for this constant.\nIf you want to translate it as a constant, use the corresponding DLMF macro \\iunit\n"
        }
      },
      "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" : 0,
    "word" : 30
  }, {
    "section" : 0,
    "sentence" : 1,
    "word" : 2
  } ],
  "includes" : [ "Q^\\mu_{-(1/2)+i\\lambda}(x)" ],
  "isPartOf" : [ "Q^\\mu_{-(1/2)+i\\lambda}(x)" ],
  "definiens" : [ {
    "definition" : "function",
    "score" : 0.847667420073609
  }, {
    "definition" : "Gustav Ferdinand Mehler",
    "score" : 0.6432331635625809
  }, {
    "definition" : "term of Legendre function",
    "score" : 0.6288842031023242
  }, {
    "definition" : "distance of a point",
    "score" : 0.6033992232315736
  }, {
    "definition" : "series",
    "score" : 0.6033992232315736
  }, {
    "definition" : "axis of a cone",
    "score" : 0.5074197820340112
  }, {
    "definition" : "conical function",
    "score" : 0.48771694939097315
  }, {
    "definition" : "mathematics",
    "score" : 0.48771694939097315
  }, {
    "definition" : "Mehler function",
    "score" : 0.44936883129115235
  }, {
    "definition" : "point",
    "score" : 0.4238838514204018
  }, {
    "definition" : "surface of the cone",
    "score" : 0.3719049079581628
  } ]
}

Specify your own input

Formula input
Wikitext context	In [[mathematics]], '''conical functions''' or '''Mehler functions''' are [[function (mathematics)\|functions]] which can be expressed in terms of [[Legendre function]]s of the first and second kind, <math>P^\mu_{-(1/2)+i\lambda}(x)</math> and <math>Q^\mu_{-(1/2)+i\lambda}(x).</math> The functions <math>P^\mu_{-(1/2)+i\lambda}(x)</math> were introduced by [[Gustav Ferdinand Mehler]], in 1868, when expanding in series the distance of a point on the axis of a cone to a point located on the surface of the cone. Mehler used the notation <math>K^\mu(x)</math> to represent these functions. He obtained integral representation and series of functions representations for them. He also established an addition theorem for the conical functions. [[Carl Neumann]] obtained an expansion of the functions <math>K^\mu(x)</math> in terms of the [[Legendre polynomials]] in 1881. Leonhardt introduced for the conical functions the equivalent of the [[spherical harmonics]] in 1882. ==External links== {{dlmf\|first=T. M. \|last=Dunster\|id=14.20\|title=Conical (or Mehler) Functions}} G. F. Mehler "[http://www.digizeitschriften.de/resolveppn/GDZPPN002153386 Ueber die Vertheilung der statischen Elektricität in einem von zwei Kugelkalotten begrenzten Körper]" ''Journal für die reine und angewandte Mathematik'' '''68''', 134 (1868). * G. F. Mehler "[http://www.digizeitschriften.de/resolveppn/GDZPPN002246112 Ueber eine mit den Kugel- und Cylinderfunctionen verwandte Function und ihre Anwendung in der Theorie der Elektricitätsvertheilung]" ''Mathematische Annalen'' '''18''' p. 161 (1881). * C. Neumann "[http://www.digizeitschriften.de/resolveppn/GDZPPN002246120 Ueber die Mehler'schen Kegelfunctionen und deren Anwendung auf elektrostatische Probleme]" ''Mathematische Annalen'' '''18''' p. 195 (1881). * G. Leonhardt "[http://www.digizeitschriften.de/resolveppn/GDZPPN002246694 Integraleigenschaften der adjungirten Kegelfunctionen]" ''Mathematische Annalen'' '''19''' p. 578 (1882). * {{MathWorld\|title=Conical function\|urlname=ConicalFunction}} * Milton Abramowitz and Irene Stegun (Eds.) ''[[Abramowitz and Stegun\|Handbook of Mathematical Functions]]'' (Dover, 1972) [http://www.math.sfu.ca/~cbm/aands/page_337.htm p. 337] * A. Gil, J. Segura, N. M. Temme "[http://oai.cwi.nl/oai/asset/13868/13868A.pdf Computing the conical function $P^{\mu}_{-1/2+i\tau}(x)$]" ''SIAM J. Sci. Comput.'' 31(3), 1716–1741 (2009). * Tiwari, U. N.; Pandey, J. N. The Mehler-Fock transform of distributions. ''Rocky Mountain J. Math.'' 10 (1980), no. 2, 401–408. [[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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