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Computer Algebra Tools for Geometrization of Maxwell’s Equations

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Abstract

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.

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Notes

  1. Here \(n: = n(x,y,z)\)

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Funding

This work was supported by the program of strategic academic leadership of the Peoples’ Friendship University of Russia (RUDN University).

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia (RUDN University), 117198, Moscow, Russia

    A. V. Korol’kova, M. N. Gevorkyan, D. S. Kulyabov & L. A. Sevast’yanov

  2. Joint Institute for Nuclear Research, 141980, Dubna, Moscow oblast, Russia

    D. S. Kulyabov & L. A. Sevast’yanov

Authors
  1. A. V. Korol’kova
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  2. M. N. Gevorkyan
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  3. D. S. Kulyabov
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  4. L. A. Sevast’yanov
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Corresponding authors

Correspondence to A. V. Korol’kova, M. N. Gevorkyan, D. S. Kulyabov or L. A. Sevast’yanov.

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The authors declare that they have no conflicts of interest.

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Translated by A. Klimontovich

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Korol’kova, A.V., Gevorkyan, M.N., Kulyabov, D.S. et al. Computer Algebra Tools for Geometrization of Maxwell’s Equations. Program Comput Soft 49, 366–371 (2023). https://doi.org/10.1134/S0361768823020111

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  • DOI: https://doi.org/10.1134/S0361768823020111

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