Computing super-irreducible forms of systems of linear differential equations via moser-reduction: a new approach

Authors:
Moulay A. Barkatou;Eckhard Pflügel
Affiliations:
Université de Limoges, Limoges, France;Kingston University, Kingston upon Thames, Surrey, United Kingdom
Venue:
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Year:
2007

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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].