Using Two Types of Computer Algebra Systems to Solve Maxwell Optics Problems

TL;DR

This paper explores the use of two different computer algebra systems, Cadabra and FORM, at different stages of modeling Maxwell optics problems, focusing on tensor and vector analysis for system synthesis.

Contribution

It introduces a dual-system approach for Maxwell optics modeling, distinguishing between model development and usage stages with specific algebra tools.

Findings

Cadabra is effective for tensor analysis during model development.

FORM is suitable for executing stereotyped operations in model usage.

The approach streamlines Maxwell optics system synthesis.

Abstract

To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number of simple stereotyped operations, which are adequately supported by computer algebra systems. In this paper, we distinguish between two stages of working with a mathematical model: model development and model usage. Each of these stages implies its own computer algebra system. As a model problem, we consider the problem of geometrization of Maxwell's equations. Two computer algebra systems---Cadabra and FORM---are selected for use at different stages of investigation.