LaTeX to CAS translator
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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 z\log \Gamma(z)-\log G(1+z)}
... is translated to the CAS output ...
Semantic latex: z \log \EulerGamma@{z} - \log \BarnesG@{1 + z}
Confidence: 0.79480005735187
Mathematica
Translation:
Information
Symbol info
- (LaTeX -> Mathematica) Error while translating DLMF/DRMF Macro: Unable to retrieve correct number of arguments for the macro \EulerGamma [\EulerGamma]
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \EulerGamma [\EulerGamma]
Tests
Symbolic
Numeric
Maple
Translation:
Information
Symbol info
- (LaTeX -> Maple) Error while translating DLMF/DRMF Macro: Unable to retrieve correct number of arguments for the macro \EulerGamma [\EulerGamma]
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- proof
- gamma function
- logarithm of the Weierstrass product form
- Adamchik
- Barnes G-function
- Euler -- Mascheroni
- logarithmic difference of the gamma function
- parametric loggamma
- Ref
- result
- term of the Barnes G-function
- Barnes function
- evaluation
- interval
- little simplification
- re-ordering of term
- series expansion
Complete translation information:
{
"id" : "FORMULA_398a8b32942d3fdfe7dc3e8cfa99d7a2",
"formula" : "z\\log \\Gamma(z)-\\log G(1+z)",
"semanticFormula" : "z \\log \\EulerGamma@{z} - \\log \\BarnesG@{1 + z}",
"confidence" : 0.7948000573518728,
"translations" : {
"Mathematica" : {
"translation" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> Mathematica) Error while translating DLMF/DRMF Macro: Unable to retrieve correct number of arguments for the macro \\EulerGamma [\\EulerGamma]"
}
},
"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: \\EulerGamma [\\EulerGamma]"
}
},
"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) Error while translating DLMF/DRMF Macro: Unable to retrieve correct number of arguments for the macro \\EulerGamma [\\EulerGamma]"
}
},
"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" : 8,
"sentence" : 0,
"word" : 53
} ],
"includes" : [ "\\,\\Gamma(x)", "z", "G" ],
"isPartOf" : [ "\\int_0^z \\log \\Gamma(x)\\,dx=\\frac{z(1-z)}{2}+\\frac{z}{2}\\log 2\\pi +z\\log\\Gamma(z) -\\log G(1+z)", "\\begin{align}& z\\log \\Gamma(z)-\\log G(1+z)=-z \\log\\left(\\frac{1}{\\Gamma (z)}\\right)-\\log G(1+z) \\\\[5pt]= {} & {-z} \\left[ \\log z+\\gamma z +\\sum_{k=1}^\\infty \\Bigg\\{ \\log\\left(1+\\frac{z}{k} \\right) -\\frac{z}{k} \\Bigg\\} \\right] \\\\[5pt]& {} -\\left[ \\frac{z}{2}\\log 2\\pi -\\frac{z}{2}-\\frac{z^2}{2} -\\frac{z^2 \\gamma}{2} + \\sum_{k=1}^\\infty \\Bigg\\{k\\log\\left(1+\\frac{z}{k}\\right) +\\frac{z^2}{2k} -z \\Bigg\\} \\right]\\end{align}" ],
"definiens" : [ {
"definition" : "proof",
"score" : 0.9038750523143215
}, {
"definition" : "gamma function",
"score" : 0.7972168260265916
}, {
"definition" : "logarithm of the Weierstrass product form",
"score" : 0.7972168260265916
}, {
"definition" : "Adamchik",
"score" : 0.6629879847031728
}, {
"definition" : "Barnes G-function",
"score" : 0.6629879847031728
}, {
"definition" : "Euler -- Mascheroni",
"score" : 0.6629879847031728
}, {
"definition" : "logarithmic difference of the gamma function",
"score" : 0.6629879847031728
}, {
"definition" : "parametric loggamma",
"score" : 0.6629879847031728
}, {
"definition" : "Ref",
"score" : 0.6629879847031728
}, {
"definition" : "result",
"score" : 0.6629879847031728
}, {
"definition" : "term of the Barnes G-function",
"score" : 0.6629879847031728
}, {
"definition" : "Barnes function",
"score" : 0.6375030048324222
}, {
"definition" : "evaluation",
"score" : 0.6375030048324222
}, {
"definition" : "interval",
"score" : 0.6375030048324222
}, {
"definition" : "little simplification",
"score" : 0.6375030048324222
}, {
"definition" : "re-ordering of term",
"score" : 0.6375030048324222
}, {
"definition" : "series expansion",
"score" : 0.6375030048324222
} ]
}