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 q}
... is translated to the CAS output ...
Semantic latex: q
Confidence: 0
Mathematica
Translation: q
Information
Sub Equations
- q
Free variables
- q
Tests
Symbolic
Numeric
SymPy
Translation: q
Information
Sub Equations
- q
Free variables
- q
Tests
Symbolic
Numeric
Maple
Translation: q
Information
Sub Equations
- q
Free variables
- q
Tests
Symbolic
Numeric
Dependency Graph Information
Is part of
Description
- term
- boundary condition
- Müller
- calculation for Mathieu function
- asymptotic expansion
- eigenvalue
- Ince
- odd integer
- oblate spheroidal wave function
- ellipsoidal wave
- period
- prime meaning
- quarter period
- prolate spheroidal wave
- limit of the Mathieu equation
- Lamé equation
- expression
- expression of the Mathieu case
Complete translation information:
{
"id" : "FORMULA_7694f4a66316e53c8cdd9d9954bd611d",
"formula" : "q",
"semanticFormula" : "q",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "q",
"translationInformation" : {
"subEquations" : [ "q" ],
"freeVariables" : [ "q" ]
},
"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" : "q",
"translationInformation" : {
"subEquations" : [ "q" ],
"freeVariables" : [ "q" ]
},
"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" : "q",
"translationInformation" : {
"subEquations" : [ "q" ],
"freeVariables" : [ "q" ]
},
"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" : 1,
"word" : 13
}, {
"section" : 2,
"sentence" : 2,
"word" : 8
} ],
"includes" : [ ],
"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}", "\\operatorname{Ec}^{q_0}_n, \\operatorname{Es}^{q_0+1}_n, \\operatorname{Ec}^{q_0-1}_n, \\operatorname{Es}^{q_0}_n", "q_0=1,3,5, \\ldots", "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]", "\\Lambda(q)", "q_0", "\\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" : "term",
"score" : 0.884731929146429
}, {
"definition" : "boundary condition",
"score" : 0.7997184989433743
}, {
"definition" : "Müller",
"score" : 0.7389129837124012
}, {
"definition" : "calculation for Mathieu function",
"score" : 0.6584627369697272
}, {
"definition" : "asymptotic expansion",
"score" : 0.657257825973014
}, {
"definition" : "eigenvalue",
"score" : 0.657257825973014
}, {
"definition" : "Ince",
"score" : 0.657257825973014
}, {
"definition" : "odd integer",
"score" : 0.657257825973014
}, {
"definition" : "oblate spheroidal wave function",
"score" : 0.6317728461022634
}, {
"definition" : "ellipsoidal wave",
"score" : 0.5927925509888069
}, {
"definition" : "period",
"score" : 0.5927925509888069
}, {
"definition" : "prime meaning",
"score" : 0.5927925509888069
}, {
"definition" : "quarter period",
"score" : 0.5927925509888069
}, {
"definition" : "prolate spheroidal wave",
"score" : 0.5919389057712561
}, {
"definition" : "limit of the Mathieu equation",
"score" : 0.41371425056515165
}, {
"definition" : "Lamé equation",
"score" : 0.32662313047477654
}, {
"definition" : "expression",
"score" : 0.27790086903658207
}, {
"definition" : "expression of the Mathieu case",
"score" : 0.27790086903658207
} ]
}