On the equivalence problem of linear differential systems and its application for factoring completely reducible systems

Abstract

Given two linear di erential systems with rational function coe cients, we give an algorithm to decide whether these two systems are equivalent and to compute the corresponding transformation matrices. In the second part of the paper, we use this for computing factorizations of completely reducible systems. In 20 algorithms for solving these problems in the case of scalar di erential equations have been given. They are based upon the local analysis of the singularities of the equation. Our method uses local methods as well, but it avoids converting to the scalar case. The algorithms are implemented and available 1 .