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
- positive real number
- value
- number of prime number
- special function
- good approximation to the prime-counting function
- integral representation
- mathematics
- integral logarithm li
- logarithmic integral function
- logarithmic integral
- Siegel-Walfisz
- function li
- Cauchy principal value
- equation
- incomplete gamma function
- series representation of li
- convergent series by Ramanujan
- asymptotic behavior
- full asymptotic expansion
- accurate asymptotic behaviour
- large value
- bracket li
- prime number theorem state
- function
- singularity
- exponential integral ei
- e.g.
- example
- number of prime
- identity
- reasonable approximation
- Riemann hypothesis
- series
- asymptotic expansion
- finite number of term
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" : 0,
"sentence" : 2,
"word" : 36
}, {
"section" : 1,
"sentence" : 0,
"word" : 13
}, {
"section" : 5,
"sentence" : 4,
"word" : 34
}, {
"section" : 6,
"sentence" : 1,
"word" : 23
} ],
"includes" : [ ],
"isPartOf" : [ "x)", "\\operatorname{li}(x) = \\int_0^x \\frac{dt}{\\ln t}", "x > 1", "\\operatorname{li}(x) = \\lim_{\\varepsilon \\to 0+} \\left( \\int_0^{1-\\varepsilon} \\frac{dt}{\\ln t} + \\int_{1+\\varepsilon}^x \\frac{dt}{\\ln t} \\right)", "\\operatorname{Li}(x) = \\int_2^x \\frac{dt}{\\ln t} = \\operatorname{li}(x) - \\operatorname{li}(2)", "x\\approx 1.45136 92348 83381 05028 39684 85892 02744 94930..", "\\Gamma\\left(a,x\\right)", "\\hbox{li}(x)=\\hbox{Ei}(\\ln x) , \\,", "x> 0", "\\operatorname{li}(x) = \\gamma + \\ln \\ln x + \\sqrt{x} \\sum_{n=1}^\\infty \\frac{ (-1)^{n-1} (\\ln x)^n} {n! \\, 2^{n-1}} \\sum_{k=0}^{\\lfloor (n-1)/2 \\rfloor} \\frac{1}{2k+1}", "x\\rightarrow \\infty", "\\operatorname{li}(x) = O \\left( {x\\over \\ln x} \\right) \\;", "\\operatorname{li}(x) \\sim \\frac{x}{\\ln x} \\sum_{k=0}^\\infty \\frac{k!}{(\\ln x)^k}", "\\frac{\\operatorname{li}(x)}{x/\\ln x} \\sim 1 + \\frac{1}{\\ln x} + \\frac{2}{(\\ln x)^2} + \\frac{6}{(\\ln x)^3} + \\cdots", "\\operatorname{li}(x) - {x\\over \\ln x} = O \\left( {x\\over \\ln^2 x} \\right) \\;", "1+\\frac{1}{\\ln x} < \\operatorname{li}(x) \\frac{\\ln x}{x} < 1+\\frac{1}{\\ln x}+\\frac{3}{(\\ln x)^2}", "\\ln x \\ge 11", "\\pi(x)\\sim\\operatorname{Li}(x)", "\\pi(x)", "\\operatorname{Li}(x)-\\pi(x) = O(\\sqrt{x}\\log x)" ],
"definiens" : [ {
"definition" : "positive real number",
"score" : 0.722
}, {
"definition" : "value",
"score" : 0.722
}, {
"definition" : "number of prime number",
"score" : 0.6185699173880385
}, {
"definition" : "special function",
"score" : 0.5939385827348387
}, {
"definition" : "good approximation to the prime-counting function",
"score" : 0.5713127376286706
}, {
"definition" : "integral representation",
"score" : 0.5672486918673748
}, {
"definition" : "mathematics",
"score" : 0.5672486918673748
}, {
"definition" : "integral logarithm li",
"score" : 0.5274147515363676
}, {
"definition" : "logarithmic integral function",
"score" : 0.5274147515363676
}, {
"definition" : "logarithmic integral",
"score" : 0.48015757177699975
}, {
"definition" : "Siegel-Walfisz",
"score" : 0.4774026636766875
}, {
"definition" : "function li",
"score" : 0.4471423749538429
}, {
"definition" : "Cauchy principal value",
"score" : 0.4415501731786472
}, {
"definition" : "equation",
"score" : 0.35069096040271575
}, {
"definition" : "incomplete gamma function",
"score" : 0.3414396566832059
}, {
"definition" : "series representation of li",
"score" : 0.3412843203980455
}, {
"definition" : "convergent series by Ramanujan",
"score" : 0.34128422571819655
}, {
"definition" : "asymptotic behavior",
"score" : 0.3412842248511015
}, {
"definition" : "full asymptotic expansion",
"score" : 0.34128422477727527
}, {
"definition" : "accurate asymptotic behaviour",
"score" : 0.34128422477700016
}, {
"definition" : "large value",
"score" : 0.3412842247769864
}, {
"definition" : "bracket li",
"score" : 0.3412842247769857
}, {
"definition" : "prime number theorem state",
"score" : 0.3412842247769857
}, {
"definition" : "function",
"score" : 0.32776916222080826
}, {
"definition" : "singularity",
"score" : 0.32776916222080826
}, {
"definition" : "exponential integral ei",
"score" : 0.31459958002652344
}, {
"definition" : "e.g.",
"score" : 0.31459433390952196
}, {
"definition" : "example",
"score" : 0.31459433390952196
}, {
"definition" : "number of prime",
"score" : 0.31459433390952196
}, {
"definition" : "identity",
"score" : 0.27476048919957446
}, {
"definition" : "reasonable approximation",
"score" : 0.27476039357851534
}, {
"definition" : "Riemann hypothesis",
"score" : 0.27476039357851473
}, {
"definition" : "series",
"score" : 0.22806989713198664
}, {
"definition" : "asymptotic expansion",
"score" : 0.17878095238095298
}, {
"definition" : "finite number of term",
"score" : 0.17878095238095298
} ]
}