Computing super-irreducible forms of systems of linear differential equations via moser-reduction

Abstract

The notion of irreducible forms of systems of linear differential equations as defined by Moser [14 ] and its generalisation, the super-irreducible forms introduced by Hilali/Wazner in [9 ] are important concepts in the context of the symbolic resolution of systems of linear differential equations [3,15,16 ]. In this paper, we give a new algorithm for computing, given an arbitrary linear differential system with formal power series coefficients as input, an equivalent system which is super-irreducible. Our algorithm is optimal in the sense that it computes transformation matrices which obtain a maximal reduction of rank in each step of the algorithm. This distinguishes it from the algorithms in [9,14,2] and generalises [7].