On Computation of Canonical Characteristic Sets in Differential Algebra

Abstract:
We discuss the concept of canonical characteristic set for a characterizable differential ideal and study factorization-free algorithms for their computation. We show the basic properties of canonical characteristic sets. In particular, we demonstrate that in the ordinary case the order of each element of the canonical characteristic set of a characterizable differential ideal is bounded by the order of the ideal. Finally, we propose an algorithm for computing the canonical characteristic set of a characterizable differential ideal represented as a radical ideal by a set of generators. The algorithm is not restricted to the ordinary case and is applicable for an arbitrary ranking.

This is a joint research work with Oleg Golubitsky (Queen's University, Kingston, Canada) and Marina V. Kondratieva (Moscow State University, Moscow, Russia).