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 \gamma(\alpha,x;b)+\Gamma(\alpha,x;b)=2b^\frac{\alpha}{2}K_\alpha(2\sqrt b)}

${\displaystyle \gamma (\alpha ,x;b)+\Gamma (\alpha ,x;b)=2b^{\frac {\alpha }{2}}K_{\alpha }(2{\sqrt {b}})}$

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

Semantic latex: \gamma(\alpha,x;b)+\Gamma(\alpha,x;b)=2b^\frac{\alpha}{2}K_\alpha(2\sqrt b)

Confidence: 0

Mathematica

Translation: \[Gamma][\[Alpha], x ; b]+ \[CapitalGamma][\[Alpha], x ; b] == 2*(b)^(Divide[\[Alpha],2])* Subscript[K, \[Alpha]][2*Sqrt[b]]

Information

Sub Equations

\[Gamma][\[Alpha], x ; b]+ \[CapitalGamma][\[Alpha], x ; b] = 2*(b)^(Divide[\[Alpha],2])* Subscript[K, \[Alpha]][2*Sqrt[b]]

Free variables

\[Alpha]

\[CapitalGamma]

\[Gamma]

b

x

Symbol info

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

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

Could be the second Feigenbaum constant.

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

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

Tests

Symbolic

Numeric

SymPy

Translation: Symbol('gamma')(Symbol('alpha'), x ; b)+ Symbol('Gamma')(Symbol('alpha'), x ; b) == 2*(b)**((Symbol('alpha'))/(2))* Symbol('{K}_{Symbol('alpha')}')(2*sqrt(b))

Information

Sub Equations

Symbol('gamma')(Symbol('alpha'), x ; b)+ Symbol('Gamma')(Symbol('alpha'), x ; b) = 2*(b)**((Symbol('alpha'))/(2))* Symbol('{K}_{Symbol('alpha')}')(2*sqrt(b))

Free variables

Symbol('Gamma')

Symbol('alpha')

Symbol('gamma')

b

x

Symbol info

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

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

Could be the second Feigenbaum constant.

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

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

Tests

Symbolic

Numeric

Maple

Translation: gamma(alpha , x ; b)+ Gamma(alpha , x ; b) = 2*(b)^((alpha)/(2))* K[alpha](2*sqrt(b))

Information

Sub Equations

gamma(alpha , x ; b)+ Gamma(alpha , x ; b) = 2*(b)^((alpha)/(2))* K[alpha](2*sqrt(b))

Free variables

Gamma

alpha

b

gamma

x

Symbol info

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

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

Could be the second Feigenbaum constant.

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

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

Tests

Symbolic

Numeric

Dependency Graph Information

Description

advantage

associated Anger -- Weber function

type incomplete-version of Bessel function

example

Digital Library of Mathematical Functions

Complete translation information:

{
  "id" : "FORMULA_e896ade5ca052f1eff24aaf9237b0517",
  "formula" : "\\gamma(\\alpha,x;b)+\\Gamma(\\alpha,x;b)=2b^\\frac{\\alpha}{2}K_\\alpha(2\\sqrt b)",
  "semanticFormula" : "\\gamma(\\alpha,x;b)+\\Gamma(\\alpha,x;b)=2b^\\frac{\\alpha}{2}K_\\alpha(2\\sqrt b)",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "\\[Gamma][\\[Alpha], x ; b]+ \\[CapitalGamma][\\[Alpha], x ; b] == 2*(b)^(Divide[\\[Alpha],2])* Subscript[K, \\[Alpha]][2*Sqrt[b]]",
      "translationInformation" : {
        "subEquations" : [ "\\[Gamma][\\[Alpha], x ; b]+ \\[CapitalGamma][\\[Alpha], x ; b] = 2*(b)^(Divide[\\[Alpha],2])* Subscript[K, \\[Alpha]][2*Sqrt[b]]" ],
        "freeVariables" : [ "\\[Alpha]", "\\[CapitalGamma]", "\\[Gamma]", "b", "x" ],
        "tokenTranslations" : {
          "K" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
          "\\Gamma" : "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('gamma')(Symbol('alpha'), x ; b)+ Symbol('Gamma')(Symbol('alpha'), x ; b) == 2*(b)**((Symbol('alpha'))/(2))* Symbol('{K}_{Symbol('alpha')}')(2*sqrt(b))",
      "translationInformation" : {
        "subEquations" : [ "Symbol('gamma')(Symbol('alpha'), x ; b)+ Symbol('Gamma')(Symbol('alpha'), x ; b) = 2*(b)**((Symbol('alpha'))/(2))* Symbol('{K}_{Symbol('alpha')}')(2*sqrt(b))" ],
        "freeVariables" : [ "Symbol('Gamma')", "Symbol('alpha')", "Symbol('gamma')", "b", "x" ],
        "tokenTranslations" : {
          "K" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
          "\\Gamma" : "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" : "gamma(alpha , x ; b)+ Gamma(alpha , x ; b) = 2*(b)^((alpha)/(2))* K[alpha](2*sqrt(b))",
      "translationInformation" : {
        "subEquations" : [ "gamma(alpha , x ; b)+ Gamma(alpha , x ; b) = 2*(b)^((alpha)/(2))* K[alpha](2*sqrt(b))" ],
        "freeVariables" : [ "Gamma", "alpha", "b", "gamma", "x" ],
        "tokenTranslations" : {
          "K" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n",
          "\\Gamma" : "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" : 4
  } ],
  "includes" : [ ],
  "isPartOf" : [ ],
  "definiens" : [ {
    "definition" : "advantage",
    "score" : 0.7125985104912714
  }, {
    "definition" : "associated Anger -- Weber function",
    "score" : 0.6460746792928004
  }, {
    "definition" : "type incomplete-version of Bessel function",
    "score" : 0.6460746792928004
  }, {
    "definition" : "example",
    "score" : 0.5500952380952381
  }, {
    "definition" : "Digital Library of Mathematical Functions",
    "score" : 0.5049074255814494
  } ]
}

Specify your own input

Formula input
Wikitext context	Some mathematicians defined this type incomplete-version of [[Bessel function]] or this type generalized-version of [[incomplete gamma function]]:<ref>{{cite web\|url=https://www.rdocumentation.org/packages/DistributionUtils/versions/0.6-0/topics/incompleteBesselK\|title=incompleteBesselK function \| R Documentation\|website=www.rdocumentation.org}}</ref><ref>{{cite web\|url=https://rdrr.io/cran/DistributionUtils/man/incompleteBesselK.html\|title=incompleteBesselK: The Incomplete Bessel K Function in DistributionUtils: Distribution Utilities\|website=rdrr.io}}</ref><ref>{{cite journal\|url=https://core.ac.uk/download/pdf/81935301.pdf \|title=Incomplete Bessel, generalized incomplete gamma, or leaky aquifer functions\|doi=10.1016/j.cam.2007.04.008 \|accessdate=2020-01-08 \|volume=215 \|year=2008 \|journal=Journal of Computational and Applied Mathematics \|pages=260–269 \| last1 = Harris \| first1 = Frank E.}}</ref><ref>{{cite web\|url=https://www.researchgate.net/publication/322252136 \|title=Generalized incomplete gamma function and its application \|date=2018-01-14 \|accessdate=2020-01-08}}</ref><ref>{{Cite document \|url=https://pdfs.semanticscholar.org/a9e7/670316180056694f2603aebafa84db950878.pdf \|title=Archived copy \|s2cid=126117454 \|access-date=2019-12-23 \|archive-url=https://web.archive.org/web/20191223111958/https://pdfs.semanticscholar.org/a9e7/670316180056694f2603aebafa84db950878.pdf \|archive-date=2019-12-23 \|url-status=dead }}</ref> :<math>K_v(x,y)=\int_1^\infty\frac{e^{-xt-\frac{y}{t}}}{t^{v+1}}~dt</math> :<math>\gamma(\alpha,x;b)=\int_0^xt^{\alpha-1}e^{-t-\frac{b}{t}}~dt</math> :<math>\Gamma(\alpha,x;b)=\int_x^\infty t^{\alpha-1}e^{-t-\frac{b}{t}}~dt</math> ==Properties== :<math>K_v(x,y)=x^v\Gamma(-v,x;xy)</math> :<math>K_v(x,y)+K_{-v}(y,x)=\frac{2x^\frac{v}{2}}{y^\frac{v}{2}}K_v(2\sqrt{xy})</math> :<math>\gamma(\alpha,x;0)=\gamma(\alpha,x)</math> :<math>\Gamma(\alpha,x;0)=\Gamma(\alpha,x)</math> :<math>\gamma(\alpha,x;b)+\Gamma(\alpha,x;b)=2b^\frac{\alpha}{2}K_\alpha(2\sqrt b)</math> One of the advantage of defining this type incomplete-version of [[Bessel function]] <math>K_v(x,y)</math> is that even for example the '''associated Anger–Weber function''' defined in [[Digital Library of Mathematical Functions]]<ref>{{dlmf\|id=11.10\|title=Anger-Weber Functions\|first=R. B. \|last=Paris}}</ref> can related: :<math>\mathbf{A}_\nu(z)=\frac{1}{\pi}\int_0^\infty e^{-\nu t-z\sinh t}~dt=\frac{1}{\pi}\int_0^\infty e^{-(\nu+1)t-\frac{ze^t}{2}+\frac{z}{2e^t}}~d(e^t)=\frac{1}{\pi}\int_1^\infty\frac{e^{-\frac{zt}{2}+\frac{z}{2t}}}{t^{\nu+1}}~dt=\frac{1}{\pi}K_\nu\left(\frac{z}{2},-\frac{z}{2}\right)</math> ===recurrence relations=== <math>K_v(x,y)</math> satisfy this [[recurrence relation]]: :<math>xK_{v-1}(x,y)+vK_v(x,y)-yK_{v+1}(x,y)=e^{-x-y}</math> ==References== {{Reflist}} [[Category:Special functions]] [[Category:Special hypergeometric functions]] [[Category:Functions and mappings]]
	Purge cached results.

LaTeX to CAS translator

Mathematica

Information

Tests

Symbolic

Numeric

SymPy

Information

Tests

Symbolic

Numeric

Maple

Information

Tests

Symbolic

Numeric

Dependency Graph Information

Specify your own input

Navigation menu

Search