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.

中文翻译：

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用于麦克斯韦方程几何化的计算机代数工具

摘要

几何化麦克斯韦理论中光学器件的计算使用了众所周知的广义相对论和微分几何的形式。特别是，对于此类计算，需要知道测地方程的解析形式，这导致需要计算大量单调的数学表达式。计算机代数的目的之一是通过自动化繁琐的符号计算来促进研究人员的工作。因此，使用计算机代数系统似乎是一种相当明显的方法。考虑了广义相对论装置的符号计算的几种自由实现。给出了几何化麦克斯韦理论的符号计算的实际例子。