Factorization of differential systems in characteristic p

Authors:
Thomas Cluzeau
Affiliations:
Laboratoire d'Arithmétique, Calcul formel et Optimisation (LACO), Limoges-Cedex, France
Venue:
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Year:
2003

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Abstract

We present an algorithm for factoring differential systems with coefficients in Fp(z). Such an algorithm has already been given by van der Put in [20], [24, 13.1] and [22]. We recast his ideas to handle systems directly and we add some comparisons of strategies, an implementation in Maple1 and a complexity analysis. The central tool for factoring in characteristic p is the p curvature. We prove the links between the p-curvature and the eigenring and we show how to use these to obtain another algorithm following the exposition of Barkatou in [1].