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_v(x,y)+K_{-v}(y,x)=\frac{2x^\frac{v}{2}}{y^\frac{v}{2}}K_v(2\sqrt{xy})}

${\displaystyle K_{v}(x,y)+K_{-v}(y,x)={\frac {2x^{\frac {v}{2}}}{y^{\frac {v}{2}}}}K_{v}(2{\sqrt {xy}})}$

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

Semantic latex: K_v(x,y)+K_{-v}(y,x)=\frac{2x^\frac{v}{2}}{y^\frac{v}{2}}K_v(2\sqrt{xy})

Confidence: 0

Mathematica

Translation: Subscript[K, v][x , y]+ Subscript[K, - v][y , x] == Divide[2*(x)^(Divide[v,2]),(y)^(Divide[v,2])]*Subscript[K, v][2*Sqrt[x*y]]

Information

Sub Equations

Subscript[K, v][x , y]+ Subscript[K, - v][y , x] = Divide[2*(x)^(Divide[v,2]),(y)^(Divide[v,2])]*Subscript[K, v][2*Sqrt[x*y]]

Free variables

v

x

y

Symbol info

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

Tests

Symbolic

Numeric

SymPy

Translation: Symbol('{K}_{v}')(x , y)+ Symbol('{K}_{- v}')(y , x) == (2*(x)**((v)/(2)))/((y)**((v)/(2)))*Symbol('{K}_{v}')(2*sqrt(x*y))

Information

Sub Equations

Symbol('{K}_{v}')(x , y)+ Symbol('{K}_{- v}')(y , x) = (2*(x)**((v)/(2)))/((y)**((v)/(2)))*Symbol('{K}_{v}')(2*sqrt(x*y))

Free variables

v

x

y

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation: K[v](x , y)+ K[- v](y , x) = (2*(x)^((v)/(2)))/((y)^((v)/(2)))*K[v](2*sqrt(x*y))

Information

Sub Equations

K[v](x , y)+ K[- v](y , x) = (2*(x)^((v)/(2)))/((y)^((v)/(2)))*K[v](2*sqrt(x*y))

Free variables

v

x

y

Symbol info

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$K_{v}(x,y)$

Description

advantage

associated Anger -- Weber function

type incomplete-version of Bessel function

example

Digital Library of Mathematical Functions

Complete translation information:

{
  "id" : "FORMULA_62b147a0c3c33d24c41822951707dc6d",
  "formula" : "K_v(x,y)+K_{-v}(y,x)=\\frac{2x^\\frac{v}{2}}{y^\\frac{v}{2}}K_v(2\\sqrt{xy})",
  "semanticFormula" : "K_v(x,y)+K_{-v}(y,x)=\\frac{2x^\\frac{v}{2}}{y^\\frac{v}{2}}K_v(2\\sqrt{xy})",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "Subscript[K, v][x , y]+ Subscript[K, - v][y , x] == Divide[2*(x)^(Divide[v,2]),(y)^(Divide[v,2])]*Subscript[K, v][2*Sqrt[x*y]]",
      "translationInformation" : {
        "subEquations" : [ "Subscript[K, v][x , y]+ Subscript[K, - v][y , x] = Divide[2*(x)^(Divide[v,2]),(y)^(Divide[v,2])]*Subscript[K, v][2*Sqrt[x*y]]" ],
        "freeVariables" : [ "v", "x", "y" ],
        "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" : "Symbol('{K}_{v}')(x , y)+ Symbol('{K}_{- v}')(y , x) == (2*(x)**((v)/(2)))/((y)**((v)/(2)))*Symbol('{K}_{v}')(2*sqrt(x*y))",
      "translationInformation" : {
        "subEquations" : [ "Symbol('{K}_{v}')(x , y)+ Symbol('{K}_{- v}')(y , x) = (2*(x)**((v)/(2)))/((y)**((v)/(2)))*Symbol('{K}_{v}')(2*sqrt(x*y))" ],
        "freeVariables" : [ "v", "x", "y" ],
        "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[v](x , y)+ K[- v](y , x) = (2*(x)^((v)/(2)))/((y)^((v)/(2)))*K[v](2*sqrt(x*y))",
      "translationInformation" : {
        "subEquations" : [ "K[v](x , y)+ K[- v](y , x) = (2*(x)^((v)/(2)))/((y)^((v)/(2)))*K[v](2*sqrt(x*y))" ],
        "freeVariables" : [ "v", "x", "y" ],
        "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" : 1,
    "sentence" : 0,
    "word" : 1
  } ],
  "includes" : [ "K_v(x,y)" ],
  "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]]
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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

Specify your own input

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