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 \kappa }
... is translated to the CAS output ...
Semantic latex: \kappa
Confidence: 0
Mathematica
Translation: \[Kappa]
Information
Sub Equations
- \[Kappa]
Free variables
- \[Kappa]
Tests
Symbolic
Numeric
SymPy
Translation: Symbol('kappa')
Information
Sub Equations
- Symbol('kappa')
Free variables
- Symbol('kappa')
Tests
Symbolic
Numeric
Maple
Translation: kappa
Information
Sub Equations
- kappa
Free variables
- kappa
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
Description
- constant
- ellipsoidal equation
- ellipsoidal wave equation
- elliptic modulus of the Jacobian elliptic function
- general form of Lamé 's equation
- equation
- Mathieu equation
- elliptic sine function
- integer
- case
- elliptic modulus
- meromorphic function
- solution
- whole complex plane
- important case
- term
- boundary condition
- Müller
- ellipsoidal wave
- period
- prime meaning
- quarter period
- Asymptotic expansion of periodic ellipsoidal wave function
- asymptotic expansion
- eigenvalue
- Ince
- odd integer
- calculation for Mathieu function
- Lamé function
- large value
- oblate spheroidal wave function
- prolate spheroidal wave
- limit of the Mathieu equation
- Lamé equation
- expression
- expression of the Mathieu case
Complete translation information:
{
"id" : "FORMULA_269cb4a8704d5fb203ad10436efe52d1",
"formula" : "\\kappa",
"semanticFormula" : "\\kappa",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "\\[Kappa]",
"translationInformation" : {
"subEquations" : [ "\\[Kappa]" ],
"freeVariables" : [ "\\[Kappa]" ]
},
"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('kappa')",
"translationInformation" : {
"subEquations" : [ "Symbol('kappa')" ],
"freeVariables" : [ "Symbol('kappa')" ]
},
"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" : "kappa",
"translationInformation" : {
"subEquations" : [ "kappa" ],
"freeVariables" : [ "kappa" ]
},
"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" : 46
}, {
"section" : 2,
"sentence" : 0,
"word" : 19
}, {
"section" : 2,
"sentence" : 2,
"word" : 10
} ],
"includes" : [ ],
"isPartOf" : [ "\\kappa^2 = n(n+1)k^2", "B\\weierp(x) = - \\kappa^2 \\operatorname{sn}^2x", "\\frac{d^2y}{dx^2} + (\\Lambda - \\kappa^2 \\operatorname{sn}^2x - \\Omega^2k^4 \\operatorname{sn}^4x)y = 0", "\\Omega = 0, k = 0, \\kappa = 2h, \\Lambda -2h^2 = \\lambda, x= z \\pm \\frac{\\pi}{2}", "\\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}", "q-q_0 = \\mp 2\\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]!} \\left[ 1 - \\frac{3(q^2_0+1)(1+k^2)}{2^5\\kappa} + \\cdots \\right]", "\\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" : "constant",
"score" : 0.6831291227361694
}, {
"definition" : "ellipsoidal equation",
"score" : 0.6564392318687055
}, {
"definition" : "ellipsoidal wave equation",
"score" : 0.6564392318687055
}, {
"definition" : "elliptic modulus of the Jacobian elliptic function",
"score" : 0.6564392318687055
}, {
"definition" : "general form of Lamé 's equation",
"score" : 0.6564392318687055
}, {
"definition" : "equation",
"score" : 0.5652840660170346
}, {
"definition" : "Mathieu equation",
"score" : 0.5652840660170346
}, {
"definition" : "elliptic sine function",
"score" : 0.5112243608314074
}, {
"definition" : "integer",
"score" : 0.5112243608314074
}, {
"definition" : "case",
"score" : 0.4845344699639436
}, {
"definition" : "elliptic modulus",
"score" : 0.4845344699639436
}, {
"definition" : "meromorphic function",
"score" : 0.4845344699639436
}, {
"definition" : "solution",
"score" : 0.4845344699639436
}, {
"definition" : "whole complex plane",
"score" : 0.4845344699639436
}, {
"definition" : "important case",
"score" : 0.4447005296329364
}, {
"definition" : "term",
"score" : 0.4268720227737233
}, {
"definition" : "boundary condition",
"score" : 0.41695665106201213
}, {
"definition" : "Müller",
"score" : 0.39058376108402415
}, {
"definition" : "ellipsoidal wave",
"score" : 0.339350440523076
}, {
"definition" : "period",
"score" : 0.339350440523076
}, {
"definition" : "prime meaning",
"score" : 0.339350440523076
}, {
"definition" : "quarter period",
"score" : 0.339350440523076
}, {
"definition" : "Asymptotic expansion of periodic ellipsoidal wave function",
"score" : 0.3151166185587035
}, {
"definition" : "asymptotic expansion",
"score" : 0.3133012110353723
}, {
"definition" : "eigenvalue",
"score" : 0.3133012110353723
}, {
"definition" : "Ince",
"score" : 0.3133012110353723
}, {
"definition" : "odd integer",
"score" : 0.3133012110353723
}, {
"definition" : "calculation for Mathieu function",
"score" : 0.3127851399654019
}, {
"definition" : "Lamé function",
"score" : 0.27528267822769625
}, {
"definition" : "large value",
"score" : 0.27528267822769625
}, {
"definition" : "oblate spheroidal wave function",
"score" : 0.2729511996343947
}, {
"definition" : "prolate spheroidal wave",
"score" : 0.22569401987502682
}, {
"definition" : "limit of the Mathieu equation",
"score" : 0.22553935293728508
}, {
"definition" : "Lamé equation",
"score" : 0.131629278985302
}, {
"definition" : "expression",
"score" : 0.09328116088548116
}, {
"definition" : "expression of the Mathieu case",
"score" : 0.09328116088548116
} ]
}