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 \Lambda(q)}
... is translated to the CAS output ...
Semantic latex: \Lambda(q)
Confidence: 0
Mathematica
Translation: \[CapitalLambda][q]
Information
Sub Equations
- \[CapitalLambda][q]
Free variables
- \[CapitalLambda]
- q
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
SymPy
Translation: Symbol('Lambda')(q)
Information
Sub Equations
- Symbol('Lambda')(q)
Free variables
- Symbol('Lambda')
- q
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Maple
Translation: Lambda(q)
Information
Sub Equations
- Lambda(q)
Free variables
- Lambda
- q
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- Müller
- limit of the Mathieu equation
- Lamé equation
- expression
- expression of the Mathieu case
- term
- asymptotic expansion
- boundary condition
- eigenvalue
- Ince
- odd integer
Complete translation information:
{
"id" : "FORMULA_cae7522a33ea5933915a51694b87ec9f",
"formula" : "\\Lambda(q)",
"semanticFormula" : "\\Lambda(q)",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "\\[CapitalLambda][q]",
"translationInformation" : {
"subEquations" : [ "\\[CapitalLambda][q]" ],
"freeVariables" : [ "\\[CapitalLambda]", "q" ],
"tokenTranslations" : {
"\\Lambda" : "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" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"SymPy" : {
"translation" : "Symbol('Lambda')(q)",
"translationInformation" : {
"subEquations" : [ "Symbol('Lambda')(q)" ],
"freeVariables" : [ "Symbol('Lambda')", "q" ],
"tokenTranslations" : {
"\\Lambda" : "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" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
},
"Maple" : {
"translation" : "Lambda(q)",
"translationInformation" : {
"subEquations" : [ "Lambda(q)" ],
"freeVariables" : [ "Lambda", "q" ],
"tokenTranslations" : {
"\\Lambda" : "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" : "SKIPPED",
"numberOfTests" : 0,
"numberOfFailedTests" : 0,
"numberOfSuccessfulTests" : 0,
"numberOfSkippedTests" : 0,
"numberOfErrorTests" : 0,
"crashed" : false,
"testCalculationsGroup" : [ ]
}
}
},
"positions" : [ {
"section" : 2,
"sentence" : 5,
"word" : 2
} ],
"includes" : [ "\\Lambda", "q" ],
"isPartOf" : [ "\\begin{align}\\Lambda(q) = {} & q\\kappa - \\frac{1}{2^3}(1+k^2)(q^2+1) - \\frac{q}{2^6\\kappa}\\{(1+k^2)^2(q^2+3) - 4k^2(q^2+5)\\} \\\\[6pt]& {} -\\frac{1}{2^{10}\\kappa^2} \\Big\\{(1+k^2)^3(5q^4+34q^2+9) - 4k^2(1+k^2)(5q^4+34q^2+9) \\\\[6pt]& {} - 384\\Omega^2k^4(q^2+1)\\Big\\} - \\cdots ,\\end{align}", "\\begin{align}\\Lambda_{\\pm}(q) \\simeq {} & \\Lambda(q_0) + (q-q_0)\\left(\\frac{\\partial \\Lambda}{\\partial q} \\right)_{q_0} + \\cdots \\\\[6pt]= {} & \\Lambda(q_0) +(q-q_0)\\kappa \\left[1 - \\frac{q_0(1+k^2)}{2^2\\kappa} - \\frac{1}{2^6\\kappa^2}\\{3(1+k^2)^2(q^2_0+1)-4k^2(q^2_0+2q_0+5)\\}+ \\cdots\\right] \\\\[6pt]\\simeq {} & \\Lambda(q_0) \\mp 2\\kappa\\sqrt{\\frac{2}{\\pi}} \\left( \\frac{1+k}{1-k} \\right)^{-\\kappa/k} \\left( \\frac{8\\kappa}{1-k^2}\\right)^{q_0/2} \\frac{1}{[(q_0-1)/2]!} \\Big[ 1 - \\frac{1}{2^5\\kappa}(1+k^2)(3q^2_0+8q_0+3) \\\\[6pt]& {} + \\frac{1}{3.2^{11}\\kappa^2}\\{3(1+k^2)^2(9q^4_0+8q^3_0-78q^2_0-88q_0-87) \\\\[6pt]& {} + 128k^2(2q^3_0+9q^2_0+10q_0+15)\\} - \\cdots\\Big].\\end{align}" ],
"definiens" : [ {
"definition" : "Müller",
"score" : 0.6787567335176542
}, {
"definition" : "limit of the Mathieu equation",
"score" : 0.6601229053380933
}, {
"definition" : "Lamé equation",
"score" : 0.5730317852477183
}, {
"definition" : "expression",
"score" : 0.5243095238095238
}, {
"definition" : "expression of the Mathieu case",
"score" : 0.5243095238095238
}, {
"definition" : "term",
"score" : 0.522304278200167
}, {
"definition" : "asymptotic expansion",
"score" : 0.416579329930231
}, {
"definition" : "boundary condition",
"score" : 0.416579329930231
}, {
"definition" : "eigenvalue",
"score" : 0.416579329930231
}, {
"definition" : "Ince",
"score" : 0.416579329930231
}, {
"definition" : "odd integer",
"score" : 0.416579329930231
} ]
}