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{ber}(x) = 1 + \sum_{k \geq 1} \frac{(-1)^k}{[(2k)!]^2} \left(\frac{x}{2} \right )^{4k}}
... is translated to the CAS output ...
Semantic latex: \mathrm{ber}(x) = 1 + \sum_{k \geq 1} \frac{(-1)^k}{[(2k)!]^2}(\frac{x}{2})^{4k}
Confidence: 0
Mathematica
Translation: ber[x] == 1 + Sum[Divide[(- 1)^(k),((2*k)!)^(2)]*(Divide[x,2])^(4*k), {k, 1, Infinity}, GenerateConditions->None]
Information
Sub Equations
- ber[x] = 1 + Sum[Divide[(- 1)^(k),((2*k)!)^(2)]*(Divide[x,2])^(4*k), {k, 1, 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: (ber[x])-(1 + Sum[Divide[(- 1)^(k),((2*k)!)^(2)]*(Divide[x,2])^(4*k), {k, 1, Infinity}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: ber(x) == 1 + Sum(((- 1)**(k))/((factorial(2*k))**(2))*((x)/(2))**(4*k), (k, 1, oo))
Information
Sub Equations
- ber(x) = 1 + Sum(((- 1)**(k))/((factorial(2*k))**(2))*((x)/(2))**(4*k), (k, 1, 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: ber(x) = 1 + sum(((- 1)^(k))/((factorial(2*k))^(2))*((x)/(2))^(4*k), k = 1..infinity)
Information
Sub Equations
- ber(x) = 1 + sum(((- 1)^(k))/((factorial(2*k))^(2))*((x)/(2))^(4*k), k = 1..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
Complete translation information:
{
"id" : "FORMULA_3c95140dd4db7e899faae6bfd0c9d443",
"formula" : "\\mathrm{ber}(x) = 1 + \\sum_{k \\geq 1} \\frac{(-1)^k}{[(2k)!]^2} \\left(\\frac{x}{2} \\right )^{4k}",
"semanticFormula" : "\\mathrm{ber}(x) = 1 + \\sum_{k \\geq 1} \\frac{(-1)^k}{[(2k)!]^2}(\\frac{x}{2})^{4k}",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "ber[x] == 1 + Sum[Divide[(- 1)^(k),((2*k)!)^(2)]*(Divide[x,2])^(4*k), {k, 1, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "ber[x] = 1 + Sum[Divide[(- 1)^(k),((2*k)!)^(2)]*(Divide[x,2])^(4*k), {k, 1, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"ber" : "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" : "ber[x]",
"rhs" : "1 + Sum[Divide[(- 1)^(k),((2*k)!)^(2)]*(Divide[x,2])^(4*k), {k, 1, Infinity}, GenerateConditions->None]",
"testExpression" : "(ber[x])-(1 + Sum[Divide[(- 1)^(k),((2*k)!)^(2)]*(Divide[x,2])^(4*k), {k, 1, Infinity}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "ber(x) == 1 + Sum(((- 1)**(k))/((factorial(2*k))**(2))*((x)/(2))**(4*k), (k, 1, oo))",
"translationInformation" : {
"subEquations" : [ "ber(x) = 1 + Sum(((- 1)**(k))/((factorial(2*k))**(2))*((x)/(2))**(4*k), (k, 1, oo))" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"ber" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
},
"Maple" : {
"translation" : "ber(x) = 1 + sum(((- 1)^(k))/((factorial(2*k))^(2))*((x)/(2))^(4*k), k = 1..infinity)",
"translationInformation" : {
"subEquations" : [ "ber(x) = 1 + sum(((- 1)^(k))/((factorial(2*k))^(2))*((x)/(2))^(4*k), k = 1..infinity)" ],
"freeVariables" : [ "x" ],
"tokenTranslations" : {
"ber" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary)."
}
}
}
},
"positions" : [ {
"section" : 1,
"sentence" : 1,
"word" : 18
} ],
"includes" : [ "x", "x)" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "series expansion",
"score" : 0.722
}, {
"definition" : "asymptotic series",
"score" : 0.7125985104912714
}, {
"definition" : "special case",
"score" : 0.6859086196238077
} ]
}