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 \theta(\tau)= \sum_{n=-\infty}^\infty e^{\pi i n^2\tau}.}
... is translated to the CAS output ...
Semantic latex: \theta(\tau) = \sum_{n=-\infty}^\infty \expe^{\cpi \iunit n^2 \tau}
Confidence: 0
Mathematica
Translation: \[Theta][\[Tau]] == Sum[Exp[Pi*I*(n)^(2)* \[Tau]], {n, - Infinity, Infinity}, GenerateConditions->None]
Information
Sub Equations
- \[Theta][\[Tau]] = Sum[Exp[Pi*I*(n)^(2)* \[Tau]], {n, - Infinity, Infinity}, GenerateConditions->None]
Free variables
- \[Tau]
- \[Theta]
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Pi was translated to: Pi
- Recognizes e with power as the exponential function. It was translated as a function.
- Imaginary unit was translated to: I
Tests
Symbolic
Test expression: (\[Theta]*(\[Tau]))-(Sum[Exp[Pi*I*(n)^(2)* \[Tau]], {n, - Infinity, Infinity}, GenerateConditions->None])
ERROR:
{
"result": "ERROR",
"testTitle": "Simple",
"testExpression": null,
"resultExpression": null,
"wasAborted": false,
"conditionallySuccessful": false
}
Numeric
SymPy
Translation: Symbol('theta')(Symbol('tau')) == Sum(exp(pi*I*(n)**(2)* Symbol('tau')), (n, - oo, oo))
Information
Sub Equations
- Symbol('theta')(Symbol('tau')) = Sum(exp(pi*I*(n)**(2)* Symbol('tau')), (n, - oo, oo))
Free variables
- Symbol('tau')
- Symbol('theta')
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Pi was translated to: pi
- Recognizes e with power as the exponential function. It was translated as a function.
- Imaginary unit was translated to: I
Tests
Symbolic
Numeric
Maple
Translation: theta(tau) = sum(exp(Pi*I*(n)^(2)* tau), n = - infinity..infinity)
Information
Sub Equations
- theta(tau) = sum(exp(Pi*I*(n)^(2)* tau), n = - infinity..infinity)
Free variables
- tau
- theta
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Pi was translated to: Pi
- Recognizes e with power as the exponential function. It was translated as a function.
- Imaginary unit was translated to: I
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Description
- term of Jacobi 's theta function
- Mellin
- Riemann zeta function
Complete translation information:
{
"id" : "FORMULA_ab1abc010fb845bcdd8c5d54f98c39d1",
"formula" : "\\theta(\\tau)= \\sum_{n=-\\infty}^\\infty e^{\\pi i n^2\\tau}",
"semanticFormula" : "\\theta(\\tau) = \\sum_{n=-\\infty}^\\infty \\expe^{\\cpi \\iunit n^2 \\tau}",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "\\[Theta][\\[Tau]] == Sum[Exp[Pi*I*(n)^(2)* \\[Tau]], {n, - Infinity, Infinity}, GenerateConditions->None]",
"translationInformation" : {
"subEquations" : [ "\\[Theta][\\[Tau]] = Sum[Exp[Pi*I*(n)^(2)* \\[Tau]], {n, - Infinity, Infinity}, GenerateConditions->None]" ],
"freeVariables" : [ "\\[Tau]", "\\[Theta]" ],
"tokenTranslations" : {
"\\theta" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\cpi" : "Pi was translated to: Pi",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I"
}
},
"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" : "\\[Theta]*(\\[Tau])",
"rhs" : "Sum[Exp[Pi*I*(n)^(2)* \\[Tau]], {n, - Infinity, Infinity}, GenerateConditions->None]",
"testExpression" : "(\\[Theta]*(\\[Tau]))-(Sum[Exp[Pi*I*(n)^(2)* \\[Tau]], {n, - Infinity, Infinity}, GenerateConditions->None])",
"testCalculations" : [ {
"result" : "ERROR",
"testTitle" : "Simple",
"testExpression" : null,
"resultExpression" : null,
"wasAborted" : false,
"conditionallySuccessful" : false
} ]
} ]
}
},
"SymPy" : {
"translation" : "Symbol('theta')(Symbol('tau')) == Sum(exp(pi*I*(n)**(2)* Symbol('tau')), (n, - oo, oo))",
"translationInformation" : {
"subEquations" : [ "Symbol('theta')(Symbol('tau')) = Sum(exp(pi*I*(n)**(2)* Symbol('tau')), (n, - oo, oo))" ],
"freeVariables" : [ "Symbol('tau')", "Symbol('theta')" ],
"tokenTranslations" : {
"\\theta" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\cpi" : "Pi was translated to: pi",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I"
}
}
},
"Maple" : {
"translation" : "theta(tau) = sum(exp(Pi*I*(n)^(2)* tau), n = - infinity..infinity)",
"translationInformation" : {
"subEquations" : [ "theta(tau) = sum(exp(Pi*I*(n)^(2)* tau), n = - infinity..infinity)" ],
"freeVariables" : [ "tau", "theta" ],
"tokenTranslations" : {
"\\theta" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\cpi" : "Pi was translated to: Pi",
"\\expe" : "Recognizes e with power as the exponential function. It was translated as a function.",
"\\iunit" : "Imaginary unit was translated to: I"
}
}
}
},
"positions" : [ {
"section" : 16,
"sentence" : 0,
"word" : 20
} ],
"includes" : [ "n", "2" ],
"isPartOf" : [ ],
"definiens" : [ {
"definition" : "term of Jacobi 's theta function",
"score" : 0.722
}, {
"definition" : "Mellin",
"score" : 0.6460746792928004
}, {
"definition" : "Riemann zeta function",
"score" : 0.6460746792928004
} ]
}