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 \gamma}
... is translated to the CAS output ...
Semantic latex: \EulerConstant
Confidence: 0
Mathematica
Translation: EulerGamma
Information
Sub Equations
- EulerGamma
Symbol info
- Euler-Mascheroni constant was translated to: EulerGamma
Tests
Symbolic
Numeric
SymPy
Translation: EulerGamma
Information
Sub Equations
- EulerGamma
Symbol info
- Euler-Mascheroni constant was translated to: EulerGamma
Tests
Symbolic
Numeric
Maple
Translation: gamma
Information
Sub Equations
- gamma
Symbol info
- Euler-Mascheroni constant was translated to: gamma
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
Description
- Euler -- Mascheroni
- different cosine
- integral definition
- series
- definition
- series expansion
- hyperbolic cosine integral
- case of imaginary argument
- real part
- auxiliary function
- error
- formula
- integral
- Padé
- rational function
- Rowe et al.
- integro-exponential function
- many term for high precision
Complete translation information:
{
"id" : "FORMULA_ae539dfcc999c28e25a0f3ae65c1de79",
"formula" : "\\gamma",
"semanticFormula" : "\\EulerConstant",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "EulerGamma",
"translationInformation" : {
"subEquations" : [ "EulerGamma" ],
"tokenTranslations" : {
"\\EulerConstant" : "Euler-Mascheroni constant was translated to: 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" : "EulerGamma",
"translationInformation" : {
"subEquations" : [ "EulerGamma" ],
"tokenTranslations" : {
"\\EulerConstant" : "Euler-Mascheroni constant was translated to: 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" : "gamma",
"translationInformation" : {
"subEquations" : [ "gamma" ],
"tokenTranslations" : {
"\\EulerConstant" : "Euler-Mascheroni constant was translated to: gamma"
}
},
"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" : 2,
"sentence" : 0,
"word" : 11
}, {
"section" : 4,
"sentence" : 0,
"word" : 8
} ],
"includes" : [ ],
"isPartOf" : [ "\\operatorname{Ci}(x) = -\\int_x^\\infty \\frac{\\cos t}{t}\\operatorname{d}t = \\gamma + \\ln x - \\int_0^x \\frac{1 - \\cos t}{t}\\operatorname{d}t\\qquad\\text{ for }\\left|\\operatorname{Arg}(x)\\right| < \\pi", "\\operatorname{Ci}(x) = \\gamma + \\ln x - \\operatorname{Cin}(x)", "\\operatorname{Chi}(x) = \\gamma+\\ln x + \\int_0^x\\frac{\\;\\cosh t-1\\;}{t}\\operatorname{d}t \\qquad\\text{ for }\\left| \\operatorname{Arg}(x) \\right| < \\pi", "\\operatorname{Chi}(x) = \\gamma + \\ln(x) + \\frac {x^2}{4} + \\frac {x^4}{96} + \\frac {x^6}{4320} + \\frac {x^8}{322560} + \\frac{x^{10}}{36288000} + O(x^{12})", "\\operatorname{Ci}(x)= \\gamma+\\ln x+\\sum_{n=1}^{\\infty}\\frac{(-1)^{n}x^{2n}}{2n(2n)!}=\\gamma+\\ln x-\\frac{x^2}{2!\\cdot2}+\\frac{x^4}{4! \\cdot4}\\mp\\cdots", "\\int_1^\\infty \\cos(ax)\\frac{\\ln x}{x} \\, dx =-\\frac{\\pi^2}{24}+\\gamma\\left(\\frac{\\gamma}{2}+\\ln a\\right)+\\frac{\\ln^2a}{2}+\\sum_{n\\ge 1} \\frac{(-a^2)^n}{(2n)!(2n)^2}", "\\int_1^\\infty e^{iax}\\frac{\\ln x}{x} \\, \\operatorname{d}x = -\\frac{\\pi^2}{24} + \\gamma\\left(\\frac{\\gamma}{2}+\\ln a\\right)+\\frac{\\ln^2 a}{2} -\\frac{\\pi}{2}i\\left(\\gamma+\\ln a\\right) + \\sum_{n\\ge 1}\\frac{(ia)^n}{n!n^2}", "\\int_1^\\infty e^{iax}\\frac{\\ln x}{x^2}\\, \\operatorname{d}x = 1 + ia\\left[ -\\frac{\\;\\pi^2}{24} + \\gamma \\left( \\frac{\\gamma}{2} + \\ln a - 1 \\right) + \\frac{\\ln^2 a}{2} - \\ln a + 1 \\right]+ \\frac{\\pi a}{2} \\Bigl( \\gamma+\\ln a - 1 \\Bigr) + \\sum_{n\\ge 1}\\frac{(ia)^{n+1}}{(n+1)!n^2}", "\\begin{array}{rcl}\\operatorname{Si}(x) &\\approx & x \\cdot \\left( \\frac{\\begin{array}{l}1 -4.54393409816329991\\cdot 10^{-2} \\cdot x^2 + 1.15457225751016682\\cdot 10^{-3} \\cdot x^4 - 1.41018536821330254\\cdot 10^{-5} \\cdot x^6 \\\\+ 9.43280809438713025 \\cdot 10^{-8} \\cdot x^8 - 3.53201978997168357 \\cdot 10^{-10} \\cdot x^{10} + 7.08240282274875911 \\cdot 10^{-13} \\cdot x^{12} \\\\- 6.05338212010422477 \\cdot 10^{-16} \\cdot x^{14}\\end{array}}{\\begin{array}{l}1 + 1.01162145739225565 \\cdot 10^{-2} \\cdot x^2 + 4.99175116169755106 \\cdot 10^{-5} \\cdot x^4 + 1.55654986308745614 \\cdot 10^{-7} \\cdot x^6 \\\\+ 3.28067571055789734 \\cdot 10^{-10} \\cdot x^8 + 4.5049097575386581 \\cdot 10^{-13} \\cdot x^{10} + 3.21107051193712168 \\cdot 10^{-16} \\cdot x^{12}\\end{array}}\\right)\\\\&&\\\\\\operatorname{Ci}(x) &\\approx & \\gamma + \\ln(x) +\\\\&& x^2 \\cdot \\left(\\frac{\\begin{array}{l}-0.25 + 7.51851524438898291 \\cdot 10^{-3} \\cdot x^2 - 1.27528342240267686 \\cdot 10^{-4} \\cdot x^4 + 1.05297363846239184 \\cdot 10^{-6} \\cdot x^6 \\\\-4.68889508144848019 \\cdot 10^{-9} \\cdot x^8 + 1.06480802891189243 \\cdot 10^{-11} \\cdot x^{10} - 9.93728488857585407 \\cdot 10^{-15} \\cdot x^{12} \\\\\\end{array}}{\\begin{array}{l}1 + 1.1592605689110735 \\cdot 10^{-2} \\cdot x^2 + 6.72126800814254432 \\cdot 10^{-5} \\cdot x^4 + 2.55533277086129636 \\cdot 10^{-7} \\cdot x^6 \\\\+ 6.97071295760958946 \\cdot 10^{-10} \\cdot x^8 + 1.38536352772778619 \\cdot 10^{-12} \\cdot x^{10} + 1.89106054713059759 \\cdot 10^{-15} \\cdot x^{12} \\\\+ 1.39759616731376855 \\cdot 10^{-18} \\cdot x^{14} \\\\\\end{array}}\\right)\\end{array}" ],
"definiens" : [ {
"definition" : "Euler -- Mascheroni",
"score" : 0.722
}, {
"definition" : "different cosine",
"score" : 0.6687181434333315
}, {
"definition" : "integral definition",
"score" : 0.6288842031023242
}, {
"definition" : "series",
"score" : 0.4378404520233745
}, {
"definition" : "definition",
"score" : 0.42517456802546916
}, {
"definition" : "series expansion",
"score" : 0.3610308415964304
}, {
"definition" : "hyperbolic cosine integral",
"score" : 0.35175394239749164
}, {
"definition" : "case of imaginary argument",
"score" : 0.35159851049127144
}, {
"definition" : "real part",
"score" : 0.35159851049127144
}, {
"definition" : "auxiliary function",
"score" : 0.3249086196238076
}, {
"definition" : "error",
"score" : 0.3249086196238076
}, {
"definition" : "formula",
"score" : 0.3249086196238076
}, {
"definition" : "integral",
"score" : 0.3249086196238076
}, {
"definition" : "Padé",
"score" : 0.3249086196238076
}, {
"definition" : "rational function",
"score" : 0.3249086196238076
}, {
"definition" : "Rowe et al.",
"score" : 0.3249086196238076
}, {
"definition" : "integro-exponential function",
"score" : 0.28507467929280045
}, {
"definition" : "many term for high precision",
"score" : 0.23781749953372208
} ]
}