OreMorphisms : A Homological Algebraic Package for Factoring, Reducing and Decomposing Linear Functional Systems

The purpose of this paper is to demonstrate the symbolic package OREMORPHISMS which is dedicated to the implementation of different algorithms and heuristic methods for the study of the factorization, reduction and decomposition problems of general linear functional systems (e.g., systems of partial differential or difference equations, differential time-delay systems). In particular, we explicitly show how to decompose a differential timedelay system (a string with an interior mass [15]) formed by 4 equations in 6 unknowns and prove that it is equivalent to a simple equation in 3 unknowns. We finally give a list of reductions of classical systems of differential time-delay equations and partial differential equations coming from control theory and mathematical physics.