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 \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)}

${\displaystyle \mathbf {A} _{\nu }(z)={\frac {1}{\pi }}\int _{0}^{\infty }e^{-\nu t-z\sinh t}~dt={\frac {1}{\pi }}\int _{0}^{\infty }e^{-(\nu +1)t-{\frac {ze^{t}}{2}}+{\frac {z}{2e^{t}}}}~d(e^{t})={\frac {1}{\pi }}\int _{1}^{\infty }{\frac {e^{-{\frac {zt}{2}}+{\frac {z}{2t}}}}{t^{\nu +1}}}~dt={\frac {1}{\pi }}K_{\nu }\left({\frac {z}{2}},-{\frac {z}{2}}\right)}$

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

Semantic latex: \AngerWeberA{\nu}@{z} = \frac{1}{\cpi} \int_0^\infty \expe^{-\nu t-z\sinh t} \diff{t} = \frac{1}{\cpi} \int_0^\infty \expe^{-(\nu + 1) t - \frac{z \expe^t}{2} + \frac{z}{2 \expe^t}} \diff{(} \expe^t) = \frac{1}{\cpi} \int_1^\infty \frac{\expe^{-\frac{zt}{2}+\frac{z}{2t}}}{t^{\nu+1}} \diff{t} = \frac{1}{\cpi} K_\nu(\frac{z}{2} , - \frac{z}{2})

Confidence: 0.65722105077558

Mathematica

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

SymPy

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Maple

Translation:

Information

Symbol info

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

Tests

Symbolic

Numeric

Dependency Graph Information

Includes

$K_{v}(x,y)$

$\mathbf {A} _{\nu }(z)={\frac {1}{\pi }}\int _{0}^{\infty }e^{-\nu t-z\sinh t}dt={\frac {1}{\pi }}\int _{0}^{\infty }e^{-(\nu +1)t-{\frac {ze^{t}}{2}}+{\frac {z}{2e^{t}}}}d(e^{t})={\frac {1}{\pi }}\int _{1}^{\infty }{\frac {e^{-{\frac {zt}{2}}+{\frac {z}{2t}}}}{t^{\nu +1}}}dt={\frac {1}{\pi }}K_{\nu }\left({\frac {z}{2}},-{\frac {z}{2}}\right)$

Is part of

$\mathbf {A} _{\nu }(z)={\frac {1}{\pi }}\int _{0}^{\infty }e^{-\nu t-z\sinh t}dt={\frac {1}{\pi }}\int _{0}^{\infty }e^{-(\nu +1)t-{\frac {ze^{t}}{2}}+{\frac {z}{2e^{t}}}}d(e^{t})={\frac {1}{\pi }}\int _{1}^{\infty }{\frac {e^{-{\frac {zt}{2}}+{\frac {z}{2t}}}}{t^{\nu +1}}}dt={\frac {1}{\pi }}K_{\nu }\left({\frac {z}{2}},-{\frac {z}{2}}\right)$

Complete translation information:

{
  "id" : "FORMULA_c51114e7ce154a6dd9d2d57a0a467575",
  "formula" : "\\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)",
  "semanticFormula" : "\\AngerWeberA{\\nu}@{z} = \\frac{1}{\\cpi} \\int_0^\\infty \\expe^{-\\nu t-z\\sinh t} \\diff{t} = \\frac{1}{\\cpi} \\int_0^\\infty \\expe^{-(\\nu + 1) t - \\frac{z \\expe^t}{2} + \\frac{z}{2 \\expe^t}} \\diff{(} \\expe^t) = \\frac{1}{\\cpi} \\int_1^\\infty \\frac{\\expe^{-\\frac{zt}{2}+\\frac{z}{2t}}}{t^{\\nu+1}} \\diff{t} = \\frac{1}{\\cpi} K_\\nu(\\frac{z}{2} , - \\frac{z}{2})",
  "confidence" : 0.657221050775581,
  "translations" : {
    "Mathematica" : {
      "translation" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Mathematica) No translation possible for given token: Cannot extract information from feature set: \\AngerWeberA [\\AngerWeberA]"
        }
      },
      "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: \\AngerWeberA [\\AngerWeberA]"
        }
      },
      "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" : "",
      "translationInformation" : {
        "tokenTranslations" : {
          "Error" : "(LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \\AngerWeberA [\\AngerWeberA]"
        }
      },
      "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" : [ ],
  "includes" : [ "K_v(x,y)", "\\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)" ],
  "isPartOf" : [ "\\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)" ],
  "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

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