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 \mathrm{bei}(x) = \sum_{k \geq 0} \frac{(-1)^k }{[(2k+1)!]^2} \left(\frac{x}{2} \right )^{4k+2}}
... is translated to the CAS output ...
Semantic latex: \mathrm{bei}(x) = \sum_{k \geq 0} \frac{(-1)^k }{[(2k+1)!]^2}(\frac{x}{2})^{4k+2}
Confidence: 0
Mathematica
Translation: bei[x] == Sum[Divide[(- 1)^(k),((2*k + 1)!)^(2)]*(Divide[x,2])^(4*k + 2), {k, 0, Infinity}, GenerateConditions->None]
Information
Sub Equations
- bei[x] = Sum[Divide[(- 1)^(k),((2*k + 1)!)^(2)]*(Divide[x,2])^(4*k + 2), {k, 0, Infinity}, GenerateConditions->None]
Free variables
- x
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Test expression: (bei[x])-(Sum[Divide[(- 1)^(k),((2*k + 1)!)^(2)]*(Divide[x,2])^(4*k + 2), {k, 0, Infinity}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: bei(x) == Sum(((- 1)**(k))/((factorial(2*k + 1))**(2))*((x)/(2))**(4*k + 2), (k, 0, oo))
Information
Sub Equations
- bei(x) = Sum(((- 1)**(k))/((factorial(2*k + 1))**(2))*((x)/(2))**(4*k + 2), (k, 0, oo))
Free variables
- x
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Maple
Translation: bei(x) = sum(((- 1)^(k))/((factorial(2*k + 1))^(2))*((x)/(2))^(4*k + 2), k = 0..infinity)
Information
Sub Equations
- bei(x) = sum(((- 1)^(k))/((factorial(2*k + 1))^(2))*((x)/(2))^(4*k + 2), k = 0..infinity)
Free variables
- x
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- series expansion
- asymptotic series
- special case
- ber
- bei
Complete translation information:
{
"id" : "FORMULA_346957d01ea3e434d0c25c4a45086e6a",
"formula" : "\\mathrm{bei}(x) = \\sum_{k \\geq 0} \\frac{(-1)^k }{[(2k+1)!]^2} \\left(\\frac{x}{2} \\right )^{4k+2}",
"semanticFormula" : "\\mathrm{bei}(x) = \\sum_{k \\geq 0} \\frac{(-1)^k }{[(2k+1)!]^2}(\\frac{x}{2})^{4k+2}",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "bei[x] == Sum[Divide[(- 1)^(k),((2*k + 1)!)^(2)]*(Divide[x,2])^(4*k + 2), {k, 0, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "bei[x] = Sum[Divide[(- 1)^(k),((2*k + 1)!)^(2)]*(Divide[x,2])^(4*k + 2), {k, 0, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"bei" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
},
"numericResults" : {
"overallResult" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"wasAborted" : false,
"crashed" : false,
"testCalculationsGroups" : [ ]
},
"symbolicResults" : {
"overallResult" : "ERROR",
"numberOfTests" : 1,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 1,
"crashed" : false,
"testCalculationsGroup" : [ {
"lhs" : "bei[x]",
"rhs" : "Sum[Divide[(- 1)^(k),((2*k + 1)!)^(2)]*(Divide[x,2])^(4*k + 2), {k, 0, Infinity}, GenerateConditions->None]",
"testExpression" : "(bei[x])-(Sum[Divide[(- 1)^(k),((2*k + 1)!)^(2)]*(Divide[x,2])^(4*k + 2), {k, 0, Infinity}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "bei(x) == Sum(((- 1)**(k))/((factorial(2*k + 1))**(2))*((x)/(2))**(4*k + 2), (k, 0, oo))",
"translationInformation" : {
"subEquations" : [ "bei(x) = Sum(((- 1)**(k))/((factorial(2*k + 1))**(2))*((x)/(2))**(4*k + 2), (k, 0, oo))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"bei" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
},
"Maple" : {
"translation" : "bei(x) = sum(((- 1)^(k))/((factorial(2*k + 1))^(2))*((x)/(2))^(4*k + 2), k = 0..infinity)",
"translationInformation" : {
"subEquations" : [ "bei(x) = sum(((- 1)^(k))/((factorial(2*k + 1))^(2))*((x)/(2))^(4*k + 2), k = 0..infinity)" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"bei" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
}
},
"positions" : [ {
"section" : 2,
"sentence" : 1,
"word" : 18
} ],
"includes" : [ "x", "x)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "series expansion",
"score" : 0.722
}, {
"definition" : "asymptotic series",
"score" : 0.6954080343007951
}, {
"definition" : "special case",
"score" : 0.6687181434333315
}, {
"definition" : "ber",
"score" : 0.6288842031023242
}, {
"definition" : "bei",
"score" : 0.5816270233429564
} ]
}