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 L(\lambda, \alpha, s)}
... is translated to the CAS output ...
Semantic latex: L(\lambda, \alpha, s)
Confidence: 0
Mathematica
Translation: L[\[Lambda], \[Alpha], s]
Information
Sub Equations
- L[\[Lambda], \[Alpha], s]
Free variables
- \[Alpha]
- \[Lambda]
- s
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
SymPy
Translation: L(Symbol('lambda'), Symbol('alpha'), s)
Information
Sub Equations
- L(Symbol('lambda'), Symbol('alpha'), s)
Free variables
- Symbol('alpha')
- Symbol('lambda')
- s
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
Maple
Translation: L(lambda , alpha , s)
Information
Sub Equations
- L(lambda , alpha , s)
Free variables
- alpha
- lambda
- s
Symbol info
- Function without DLMF-Definition. We keep it like it is (but delete prefix \ if necessary).
- Could be the second Feigenbaum constant.
But this system doesn't know how to translate it as a constant. It was translated as a general letter.
Tests
Symbolic
Numeric
Dependency Graph Information
Includes
Is part of
Description
- finite sum over the Hurwitz zeta-function
- root of unity
- summand
- special case
- last formula
- Hurwitz zeta function
- Lipschitz formula
- Lerch zeta function
Complete translation information:
{
"id" : "FORMULA_053a98124485559a12edcc8176574789",
"formula" : "L(\\lambda, \\alpha, s)",
"semanticFormula" : "L(\\lambda, \\alpha, s)",
"confidence" : 0.0,
"translations" : {
"Mathematica" : {
"translation" : "L[\\[Lambda], \\[Alpha], s]",
"translationInformation" : {
"subEquations" : [ "L[\\[Lambda], \\[Alpha], s]" ],
"freeVariables" : [ "\\[Alpha]", "\\[Lambda]", "s" ],
"tokenTranslations" : {
"L" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : "L(Symbol('lambda'), Symbol('alpha'), s)",
"translationInformation" : {
"subEquations" : [ "L(Symbol('lambda'), Symbol('alpha'), s)" ],
"freeVariables" : [ "Symbol('alpha')", "Symbol('lambda')", "s" ],
"tokenTranslations" : {
"L" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : "L(lambda , alpha , s)",
"translationInformation" : {
"subEquations" : [ "L(lambda , alpha , s)" ],
"freeVariables" : [ "alpha", "lambda", "s" ],
"tokenTranslations" : {
"L" : "Function without DLMF-Definition. We keep it like it is (but delete prefix \\ if necessary).",
"\\alpha" : "Could be the second Feigenbaum constant.\nBut this system doesn't know how to translate it as a constant. It was translated as a general letter.\n"
}
},
"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" : 4,
"sentence" : 0,
"word" : 14
} ],
"includes" : [ "\\lambda", "s" ],
"isPartOf" : [ "\\,\\Phi(e^{2\\pi i\\lambda}, s,\\alpha)=L(\\lambda, \\alpha,s)", "\\,\\zeta(s,\\alpha)=L(0, \\alpha,s)=\\Phi(1,s,\\alpha)", "L(\\lambda, \\alpha, s) = \\sum_{n=0}^\\infty\\frac { e^{2\\pi i\\lambda n}} {(n+\\alpha)^s}", "\\Phi(e^{i\\varphi},s,a)=L\\big(\\tfrac{\\varphi}{2\\pi},a,s\\big)= \\frac{1}{a^s} + \\frac{1}{2\\Gamma(s)}\\int_{0}^{\\infty}\\frac{t^{s-1}e^{-at}\\big(e^{i\\varphi}-e^{-t}\\big)}{\\cosh{t}-\\cos{\\varphi}}\\,dt" ],
"definiens" : [ {
"definition" : "finite sum over the Hurwitz zeta-function",
"score" : 0.6859086196238077
}, {
"definition" : "root of unity",
"score" : 0.6859086196238077
}, {
"definition" : "summand",
"score" : 0.6460746792928004
}, {
"definition" : "special case",
"score" : 0.3902770819198429
}, {
"definition" : "last formula",
"score" : 0.3766844353679306
}, {
"definition" : "Hurwitz zeta function",
"score" : 0.3635871910523791
}, {
"definition" : "Lipschitz formula",
"score" : 0.34999454450046674
}, {
"definition" : "Lerch zeta function",
"score" : 0.3420991914353436
} ]
}