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 \lambda(\tau) }
... is translated to the CAS output ...
Semantic latex: \modularlambdatau@{\tau}
Confidence: 0.90733333333333
Mathematica
Translation: ModularLambda[\[Tau]]
Information
Sub Equations
- ModularLambda[\[Tau]]
Free variables
- \[Tau]
Symbol info
- Elliptic modular function; Example: \modularlambdatau@{\tau}
Will be translated to: ModularLambda[$0] Relevant links to definitions: DLMF: http://dlmf.nist.gov/23.15#E6 Mathematica: https://reference.wolfram.com/language/ref/ModularLambda.html
Tests
Symbolic
Numeric
SymPy
Translation:
Information
Symbol info
- (LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \modularlambdatau [\modularlambdatau]
Tests
Symbolic
Numeric
Maple
Translation:
Information
Symbol info
- (LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \modularlambdatau [\modularlambdatau]
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
- Failed to parse (syntax error): {\displaystyle j(\tau) = \frac{256(1-\lambda(1-\lambda))^3}{(\lambda(1-\lambda))^2} = \frac{256(1-\lambda+\lambda^2)^3}{\lambda^2 (1-\lambda)^2} \}
Description
- function
- elliptic modular lambda function
- symmetric holomorphic function on the complex upper half-plane
- mathematics
- nome
- q-expansion
- square of the Jacobi modulus
- term of the Dedekind eta function
- term of the half-period
- relation to the j-invariant
- Hauptmodul for the group
- group
- action of the modular group
- graded character of any element
- fundamental pair of period
- theta function
- expansion
- anharmonic group
- Weierstrass 's elliptic function
- conjugacy class 4c of the monster group
- value
- monster vertex algebra
Complete translation information:
{
"id" : "FORMULA_ebf0d702b05debcea730cd26c4b5f958",
"formula" : "\\lambda(\\tau)",
"semanticFormula" : "\\modularlambdatau@{\\tau}",
"confidence" : 0.9073333333333333,
"translations" : {
"Mathematica" : {
"translation" : "ModularLambda[\\[Tau]]",
"translationInformation" : {
"subEquations" : [ "ModularLambda[\\[Tau]]" ],
"freeVariables" : [ "\\[Tau]" ],
"tokenTranslations" : {
"\\modularlambdatau" : "Elliptic modular function; Example: \\modularlambdatau@{\\tau}\nWill be translated to: ModularLambda[$0]\nRelevant links to definitions:\nDLMF: http://dlmf.nist.gov/23.15#E6\nMathematica: https://reference.wolfram.com/language/ref/ModularLambda.html"
}
},
"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" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> SymPy) No translation possible for given token: Cannot extract information from feature set: \\modularlambdatau [\\modularlambdatau]"
}
},
"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" : "",
"translationInformation" : {
"tokenTranslations" : {
"Error" : "(LaTeX -> Maple) No translation possible for given token: Cannot extract information from feature set: \\modularlambdatau [\\modularlambdatau]"
}
},
"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" : 0,
"sentence" : 0,
"word" : 10
}, {
"section" : 1,
"sentence" : 0,
"word" : 2
}, {
"section" : 1,
"sentence" : 2,
"word" : 9
} ],
"includes" : [ "\\tau", "\\lambda" ],
"isPartOf" : [ "\\lambda(\\tau) = 16q - 128q^2 + 704 q^3 - 3072q^4 + 11488q^5 - 38400q^6 + \\dots", "\\lambda(\\tau)=k^2(\\tau)", "\\lambda(\\tau) = \\Bigg(\\frac{\\sqrt{2}\\,\\eta(\\tfrac{\\tau}{2})\\eta^2(2\\tau)}{\\eta^3(\\tau)}\\Bigg)^8 = \\frac{16}{\\left(\\frac{\\eta(\\tau/2)}{\\eta(2\\tau)}\\right)^8 + 16} =\\frac{\\theta_2^4(0,\\tau)}{\\theta_3^4(0,\\tau)}", "\\frac{1}{\\big(\\lambda(\\tau)\\big)^{1/4}}-\\big(\\lambda(\\tau)\\big)^{1/4} = \\frac{1}{2}\\left(\\frac{\\eta(\\tfrac{\\tau}{4})}{\\eta(\\tau)}\\right)^4 = 2\\,\\frac{\\theta_4^2(0,\\tfrac{\\tau}{2})}{\\theta_2^2(0,\\tfrac{\\tau}{2})}", "j(\\tau) = \\frac{256(1-\\lambda(1-\\lambda))^3}{(\\lambda(1-\\lambda))^2} = \\frac{256(1-\\lambda+\\lambda^2)^3}{\\lambda^2 (1-\\lambda)^2} \\", "\\frac{16}{\\lambda(2\\tau)} - 8" ],
"definiens" : [ {
"definition" : "function",
"score" : 0.8083963513006062
}, {
"definition" : "elliptic modular lambda function",
"score" : 0.722
}, {
"definition" : "symmetric holomorphic function on the complex upper half-plane",
"score" : 0.6954080343007951
}, {
"definition" : "mathematics",
"score" : 0.6687181434333315
}, {
"definition" : "nome",
"score" : 0.552356821270491
}, {
"definition" : "q-expansion",
"score" : 0.4968133815285695
}, {
"definition" : "square of the Jacobi modulus",
"score" : 0.3522700134674619
}, {
"definition" : "term of the Dedekind eta function",
"score" : 0.35175394239749164
}, {
"definition" : "term of the half-period",
"score" : 0.35175394239749164
}, {
"definition" : "relation to the j-invariant",
"score" : 0.3515992754597499
}, {
"definition" : "Hauptmodul for the group",
"score" : 0.35159851049127155
}, {
"definition" : "group",
"score" : 0.3463967148619029
}, {
"definition" : "action of the modular group",
"score" : 0.32739553012332934
}, {
"definition" : "graded character of any element",
"score" : 0.3249086196238077
}, {
"definition" : "fundamental pair of period",
"score" : 0.2852301111990206
}, {
"definition" : "theta function",
"score" : 0.2852301111990206
}, {
"definition" : "expansion",
"score" : 0.2850746792928005
}, {
"definition" : "anharmonic group",
"score" : 0.24030441003295425
}, {
"definition" : "Weierstrass 's elliptic function",
"score" : 0.23797293143965273
}, {
"definition" : "conjugacy class 4c of the monster group",
"score" : 0.23781749953343265
}, {
"definition" : "value",
"score" : 0.14639433608097108
}, {
"definition" : "monster vertex algebra",
"score" : 0.1055593074816286
} ]
}