Niveau: Supérieur, Doctorat, Bac+8
Factoring Partial Differential Systems in Posi- tive Characteristic M. A. Barkatou, T. Cluzeau, J.-A. Weil with an appendix by M. van der Put: Classification of Partial Differential Modules in Positive Characteristic Abstract. An algorithm for factoring differential systems in characteristic p has been given by Cluzeau in [Cl03]. It is based on both the reduction of a matrix called p-curvature and eigenring techniques. In this paper, we gener- alize this algorithm to factor partial differential systems in characteristic p. We show that this factorization problem reduces effectively to the problem of simultaneous reduction of commuting matrices. In the appendix, van der Put shows how to extend his classification of differ- ential modules, used in the work of Cluzeau, to partial differential systems in positive characteristic. Mathematics Subject Classification (2000). 68W30; 16S32; 15A21; 16S50; 35G05. Keywords. Computer Algebra, Linear Differential Equations, Partial Differ- ential Equations, D-Finite Systems, Modular Algorithms, p-Curvature, Fac- torization, Simultaneous Reduction of Commuting Matrices. Introduction The problem of factoring D-finite partial differential systems in characteristic zero has been recently studied by Li, Schwarz and Tsarev in [LST02, LST03] (see also [Wu05]). In these articles, the authors show how to adapt Beke's algorithm (which factors ordinary differential systems, see [CH04] or [PS03, 4.2.1] and references therein) to the partial differential case.
- positive characteristic
- partial differential
- partial differ- ential system
- zero-dimensional poly- nomial
- ential equations
- differential system
- system over