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 x}
... is translated to the CAS output ...
Semantic latex: x
Confidence: 0
Mathematica
Translation: x
Information
Sub Equations
- x
Free variables
- x
Tests
Symbolic
Numeric
SymPy
Translation: x
Information
Sub Equations
- x
Free variables
- x
Tests
Symbolic
Numeric
Maple
Translation: x
Information
Sub Equations
- x
Free variables
- x
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
Description
- erf
- erfi
- Dawson function
- term of the real error function
- entire complex plane
- imaginary error function
- ix
- error function erf
- asymptotic expansion
- series expansion
- term
- Gaussian function
- origin
- one-sided Fourier -- Laplace sine
- Faddeeva function
- derivative
- Hilbert
- differential equation
- p.v.
- extrema
- trivial inflection point
- Inflection point
- distribution
- exponential representation
- Fourier representation
- function
- principal value
- real axis
- respect
- Gaussian
- result
- Cauchy principal value
Complete translation information:
{
"id" : "FORMULA_9dd4e461268c8034f5c8564e155c67a6",
"formula" : "x",
"semanticFormula" : "x",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "x",
"translationInformation" : {
"subEquations" : [ "x" ],
"freeVariables" : [ "x" ]
},
"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" : "x",
"translationInformation" : {
"subEquations" : [ "x" ],
"freeVariables" : [ "x" ]
},
"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" : "x",
"translationInformation" : {
"subEquations" : [ "x" ],
"freeVariables" : [ "x" ]
},
"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" : 4,
"word" : 32
}, {
"section" : 1,
"sentence" : 7,
"word" : 16
}, {
"section" : 2,
"sentence" : 2,
"word" : 40
}, {
"section" : 2,
"sentence" : 2,
"word" : 50
} ],
"includes" : [ ],
"isPartOf" : [ "D_+(x) = {\\sqrt{\\pi} \\over 2} e^{-x^2} \\operatorname{erfi} (x) = - {i \\sqrt{\\pi} \\over 2 }e^{-x^2} \\operatorname{erf} (ix)", "D_+(x) = e^{-x^2} \\int_0^x e^{t^2}\\,dt", "x) = -i", "F(x)", "D_-(x) = e^{x^2} \\int_0^x e^{-t^2}\\,dt.", "D_-(x) = \\frac{\\sqrt{\\pi}}{2} e^{x^2} \\operatorname{erf}(x)", "D_+(x) = F(x) = \\frac{\\sqrt{\\pi}}{2} \\operatorname{Im}[ w(x) ]", "D_+(x) = \\frac12 \\int_0^\\infty e^{-t^2/4}\\,\\sin(xt)\\,dt", "D(x)", "D_-(x) = i F(-ix) = -\\frac{\\sqrt{\\pi}}{2} \\left[ e^{x^2} - w(-ix) \\right]", "x|", "F(x) \\approx x", "F(x) \\approx 1/(2x)", "F(x) = \\sum_{k=0}^\\infty \\frac{(-1)^k \\, 2^k}{(2k+1)!!} \\, x^{2k+1} = x - \\frac{2}{3} x^3 + \\frac{4}{15} x^5 - \\cdots", "F(x) = \\sum_{k=0}^{\\infty} \\frac{(2k-1)!!}{2^{k+1} x^{2k+1}} = \\frac{1}{2 x} + \\frac{1}{4 x^3} + \\frac{3}{8 x^5} + \\cdots", "F(x) = \\frac{1}{2 x}", "x= \\pm0.92413887... (", "F(x) = \\pm0.54104422... (", "F(x) = \\frac{x}{2 x^2 - 1}", "x= \\pm1.50197526... (", "F(x) = \\pm0.42768661... (", "x= 0,F(x) = 0.)", "H(y) = \\pi^{-1} \\operatorname{P.V.} \\int_{-\\infty}^\\infty \\frac{e^{-x^2}}{y-x} \\, dx", "1/u=1/(y-x)", "\\pi H(y) = \\operatorname{Im} \\int_0^\\infty dk \\,\\exp[-k^2/4+iky] \\int_{-\\infty}^\\infty dx \\, \\exp[-(x+ik/2)^2]", "x^{2n}e^{-x^2}", "H_n = \\pi^{-1} \\operatorname{P.V.} \\int_{-\\infty}^\\infty \\frac{x^{2n}e^{-x^2}}{y-x} \\, dx", "H_a = \\pi^{-1} \\operatorname{P.V.} \\int_{-\\infty}^\\infty {e^{-ax^2} \\over y-x} \\, dx", "{\\partial^nH_a \\over \\partial a^n} = (-1)^n\\pi^{-1} \\operatorname{P.V.} \\int_{-\\infty}^\\infty \\frac{x^{2n}e^{-ax^2}}{y-x} \\, dx" ],
"definiens" : [ {
"definition" : "erf",
"score" : 0.8058868265640047
}, {
"definition" : "erfi",
"score" : 0.7953886760431328
}, {
"definition" : "Dawson function",
"score" : 0.691024763752936
}, {
"definition" : "term of the real error function",
"score" : 0.6596087687157589
}, {
"definition" : "entire complex plane",
"score" : 0.6185699173880385
}, {
"definition" : "imaginary error function",
"score" : 0.5939385827348387
}, {
"definition" : "ix",
"score" : 0.5939385827348387
}, {
"definition" : "error function erf",
"score" : 0.5672486918673748
}, {
"definition" : "asymptotic expansion",
"score" : 0.5225904761904762
}, {
"definition" : "series expansion",
"score" : 0.5225904761904762
}, {
"definition" : "term",
"score" : 0.5225904761904762
}, {
"definition" : "Gaussian function",
"score" : 0.5131889866817476
}, {
"definition" : "origin",
"score" : 0.4864990958142838
}, {
"definition" : "one-sided Fourier -- Laplace sine",
"score" : 0.44666515548327657
}, {
"definition" : "Faddeeva function",
"score" : 0.4390545455768667
}, {
"definition" : "derivative",
"score" : 0.40170360744940814
}, {
"definition" : "Hilbert",
"score" : 0.3949402339269477
}, {
"definition" : "differential equation",
"score" : 0.36472730811035264
}, {
"definition" : "p.v.",
"score" : 0.3507165558821447
}, {
"definition" : "extrema",
"score" : 0.3491796734631687
}, {
"definition" : "trivial inflection point",
"score" : 0.34195572775317623
}, {
"definition" : "Inflection point",
"score" : 0.3170812444090436
}, {
"definition" : "distribution",
"score" : 0.3145950988780003
}, {
"definition" : "exponential representation",
"score" : 0.3145950988780003
}, {
"definition" : "Fourier representation",
"score" : 0.3145950988780003
}, {
"definition" : "function",
"score" : 0.3145950988780003
}, {
"definition" : "principal value",
"score" : 0.3145950988780003
}, {
"definition" : "real axis",
"score" : 0.3145950988780003
}, {
"definition" : "respect",
"score" : 0.3145950988780003
}, {
"definition" : "Gaussian",
"score" : 0.27479123517494514
}, {
"definition" : "result",
"score" : 0.2747603935835178
}, {
"definition" : "Cauchy principal value",
"score" : 0.22753405541557728
} ]
}