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 K^\mu(x)}

${\displaystyle K^{\mu }(x)}$

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

Semantic latex: K^\mu(x)

Confidence: 0

Mathematica

Translation: (K[x])^\[Mu]

Information

Sub Equations

(K[x])^\[Mu]

Free variables

\[Mu]

x

Symbol info

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

Tests

Symbolic

Numeric

SymPy

Translation: (K(x))**(Symbol('mu'))

Information

Sub Equations

(K(x))**(Symbol('mu'))

Free variables

Symbol('mu')

x

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation: (K(x))^(mu)

Information

Sub Equations

(K(x))^(mu)

Free variables

mu

x

Symbol info

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

Tests

Symbolic

Numeric

Dependency Graph Information

Description

expansion of the function

notation

Mehler

function

Carl Neumann

term of the Legendre polynomial

Complete translation information:

{
  "id" : "FORMULA_b250dc2b6221d08097fe33d63e334666",
  "formula" : "K^\\mu(x)",
  "semanticFormula" : "K^\\mu(x)",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "(K[x])^\\[Mu]",
      "translationInformation" : {
        "subEquations" : [ "(K[x])^\\[Mu]" ],
        "freeVariables" : [ "\\[Mu]", "x" ],
        "tokenTranslations" : {
          "K" : "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" : "(K(x))**(Symbol('mu'))",
      "translationInformation" : {
        "subEquations" : [ "(K(x))**(Symbol('mu'))" ],
        "freeVariables" : [ "Symbol('mu')", "x" ],
        "tokenTranslations" : {
          "K" : "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" : "(K(x))^(mu)",
      "translationInformation" : {
        "subEquations" : [ "(K(x))^(mu)" ],
        "freeVariables" : [ "mu", "x" ],
        "tokenTranslations" : {
          "K" : "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" : 0,
    "sentence" : 2,
    "word" : 4
  }, {
    "section" : 0,
    "sentence" : 5,
    "word" : 8
  } ],
  "includes" : [ ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "expansion of the function",
    "score" : 0.722
  }, {
    "definition" : "notation",
    "score" : 0.722
  }, {
    "definition" : "Mehler",
    "score" : 0.6859086196238077
  }, {
    "definition" : "function",
    "score" : 0.6460746792928004
  }, {
    "definition" : "Carl Neumann",
    "score" : 0.4741699173880385
  }, {
    "definition" : "term of the Legendre polynomial",
    "score" : 0.4741699173880385
  } ]
}

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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