Algorithms for computing symbolic representations of basic e-sums and their application to composites

The main goal of the paper is to present an algorithm to realize the theoretical method by Berlyand and Mityushev, 2001 and Berlyand and Mityushev, 2005 for computations of the effective conductivity of fibrous composites expressed in therms of the linear combinations of the basic e-sums. Algorithms are presented in Mathematical Pseudo-language with examples in Mathematica®. A method for simplifying the basic e-sums by reducing mirror terms is presented. Developed algorithms are applied to the optimal packing problem of disks in the plane.