Computer Algebra Tools for Geometrization of Maxwell’s Equations

Calculations of optical devices in the geometrized Maxwell’s theory use well-known formalisms of general theory of relativity and differential geometry. In particular, for such calculations it is required to know the analytical form of the geodesic equations, which leads to the need to calculate a l...

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Bibliographic Details
Published inProgramming and computer software Vol. 49; no. 4; pp. 366 - 371
Main Authors Korol’kova, A. V., Gevorkyan, M. N., Kulyabov, D. S., Sevast’yanov, L. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.08.2023
Springer Nature B.V
Subjects
Algebra
Artificial Intelligence
Computer algebra
Computer Science
Differential geometry
Inverse problems
Investigations
Libraries
Mathematical analysis
Maxwell's equations
Numerical analysis
Operating Systems
Permeability
Relativity
Software
Software Engineering
Software Engineering/Programming and Operating Systems
Theory of relativity
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Summary:Calculations of optical devices in the geometrized Maxwell’s theory use well-known formalisms of general theory of relativity and differential geometry. In particular, for such calculations it is required to know the analytical form of the geodesic equations, which leads to the need to calculate a large number of monotonous mathematical expressions. One of the purposes of computer algebra is to facilitate the researcher’s work by automating cumbersome symbolic computations. Thus, the use of computer algebra systems seems to be quite an obvious way. Several free implementations of symbolic computations for the apparatus of general relativity are considered. A practical example of symbolic computations for the geometrized Maxwell’s theory is given.
ISSN:0361-7688
1608-3261
DOI:10.1134/S0361768823020111