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)=\int_0^xt^{\alpha-1}e^{-t-\frac{b}{t}}~dt}

${\displaystyle \gamma (\alpha ,x;b)=\int _{0}^{x}t^{\alpha -1}e^{-t-{\frac {b}{t}}}~dt}$

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

Semantic latex: \gamma(\alpha , x ; b) = \int_0^x t^{\alpha-1} \expe^{-t-\frac{b}{t}} \diff{t}

Confidence: 0

Mathematica

Translation: \[Gamma][\[Alpha], x ; b] == Integrate[(t)^(\[Alpha]- 1)* Exp[- t -Divide[b,t]], {t, 0, x}, GenerateConditions->None]

Information

Sub Equations

\[Gamma][\[Alpha], x ; b] = Integrate[(t)^(\[Alpha]- 1)* Exp[- t -Divide[b,t]], {t, 0, x}, GenerateConditions->None]

Free variables

\[Alpha]

\[Gamma]

b

x

Symbol info

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

Recognizes e with power as the exponential function. It was translated as a function.

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.

Tests

Symbolic

Test expression: (\[Gamma]*(\[Alpha], x ; b))-(Integrate[(t)^(\[Alpha]- 1)* Exp[- t -Divide[b,t]], {t, 0, x}, GenerateConditions->None])

ERROR:

{
    "result": "ERROR",
    "testTitle": "Simple",
    "testExpression": null,
    "resultExpression": null,
    "wasAborted": false,
    "conditionallySuccessful": false
}

Numeric

SymPy

Translation: Symbol('gamma')(Symbol('alpha'), x ; b) == integrate((t)**(Symbol('alpha')- 1)* exp(- t -(b)/(t)), (t, 0, x))

Information

Sub Equations

Symbol('gamma')(Symbol('alpha'), x ; b) = integrate((t)**(Symbol('alpha')- 1)* exp(- t -(b)/(t)), (t, 0, x))

Free variables

Symbol('alpha')

Symbol('gamma')

b

x

Symbol info

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

Recognizes e with power as the exponential function. It was translated as a function.

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.

Tests

Symbolic

Numeric

Maple

Translation: gamma(alpha , x ; b) = int((t)^(alpha - 1)* exp(- t -(b)/(t)), t = 0..x)

Information

Sub Equations

gamma(alpha , x ; b) = int((t)^(alpha - 1)* exp(- t -(b)/(t)), t = 0..x)

Free variables

alpha

b

gamma

x

Symbol info

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

Recognizes e with power as the exponential function. It was translated as a function.

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.

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$\gamma (\alpha ,x;b)=\int _{0}^{x}t^{\alpha -1}e^{-t-{\frac {b}{t}}}dt$

Is part of

$\gamma (\alpha ,x;b)=\int _{0}^{x}t^{\alpha -1}e^{-t-{\frac {b}{t}}}dt$

Complete translation information:

{
  "id" : "FORMULA_2885bb5147548f6def04ae31d01def3d",
  "formula" : "\\gamma(\\alpha,x;b)=\\int_0^x t^{\\alpha-1}e^{-t-\\frac{b}{t}}~dt",
  "semanticFormula" : "\\gamma(\\alpha , x ; b) = \\int_0^x t^{\\alpha-1} \\expe^{-t-\\frac{b}{t}} \\diff{t}",
  "confidence" : 0.0,
  "translations" : {
    "Mathematica" : {
      "translation" : "\\[Gamma][\\[Alpha], x ; b] == Integrate[(t)^(\\[Alpha]- 1)* Exp[- t -Divide[b,t]], {t, 0, x}, GenerateConditions->None]",
      "translationInformation" : {
        "subEquations" : [ "\\[Gamma][\\[Alpha], x ; b] = Integrate[(t)^(\\[Alpha]- 1)* Exp[- t -Divide[b,t]], {t, 0, x}, GenerateConditions->None]" ],
        "freeVariables" : [ "\\[Alpha]", "\\[Gamma]", "b", "x" ],
        "tokenTranslations" : {
          "\\gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
          "\\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"
        }
      },
      "numericResults" : {
        "overallResult" : "SKIPPED",
        "numberOfTests" : 0,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 0,
        "wasAborted" : false,
        "crashed" : false,
        "testCalculationsGroups" : [ ]
      },
      "symbolicResults" : {
        "overallResult" : "ERROR",
        "numberOfTests" : 1,
        "numberOfFailedTests" : 0,
        "numberOfSuccessfulTests" : 0,
        "numberOfSkippedTests" : 0,
        "numberOfErrorTests" : 1,
        "crashed" : false,
        "testCalculationsGroup" : [ {
          "lhs" : "\\[Gamma]*(\\[Alpha], x ; b)",
          "rhs" : "Integrate[(t)^(\\[Alpha]- 1)* Exp[- t -Divide[b,t]], {t, 0, x}, GenerateConditions->None]",
          "testExpression" : "(\\[Gamma]*(\\[Alpha], x ; b))-(Integrate[(t)^(\\[Alpha]- 1)* Exp[- t -Divide[b,t]], {t, 0, x}, GenerateConditions->None])",
          "testCalculations" : [ {
            "result" : "ERROR",
            "testTitle" : "Simple",
            "testExpression" : null,
            "resultExpression" : null,
            "wasAborted" : false,
            "conditionallySuccessful" : false
          } ]
        } ]
      }
    },
    "SymPy" : {
      "translation" : "Symbol('gamma')(Symbol('alpha'), x ; b) == integrate((t)**(Symbol('alpha')- 1)* exp(- t -(b)/(t)), (t, 0, x))",
      "translationInformation" : {
        "subEquations" : [ "Symbol('gamma')(Symbol('alpha'), x ; b) = integrate((t)**(Symbol('alpha')- 1)* exp(- t -(b)/(t)), (t, 0, x))" ],
        "freeVariables" : [ "Symbol('alpha')", "Symbol('gamma')", "b", "x" ],
        "tokenTranslations" : {
          "\\gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
          "\\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"
        }
      }
    },
    "Maple" : {
      "translation" : "gamma(alpha , x ; b) = int((t)^(alpha - 1)* exp(- t -(b)/(t)), t = 0..x)",
      "translationInformation" : {
        "subEquations" : [ "gamma(alpha , x ; b) = int((t)^(alpha - 1)* exp(- t -(b)/(t)), t = 0..x)" ],
        "freeVariables" : [ "alpha", "b", "gamma", "x" ],
        "tokenTranslations" : {
          "\\gamma" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
          "\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
          "\\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"
        }
      }
    }
  },
  "positions" : [ ],
  "includes" : [ "\\gamma(\\alpha,x;b)=\\int_0^xt^{\\alpha-1}e^{-t-\\frac{b}{t}}dt" ],
  "isPartOf" : [ "\\gamma(\\alpha,x;b)=\\int_0^xt^{\\alpha-1}e^{-t-\\frac{b}{t}}dt" ],
  "definiens" : [ ]
}

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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