Algorithm for computing formal invariants of linear differential systems

Abstract

This paper deals with the system of n linear differential equations (*) y'(x) = A(x)y where A(x) is a matrix with formal series coefficients. A sequence of formal invariants related to (*) is defined. An algorithm which reduces (*) by means of meromorphic transformations to a “super-irreducible” form is given. The computation of these invariants follows directly from this form. This algorithm is implemented in Reduce.