Canonical Characteristic Sets of Characterizable Differential Ideals

Details Canonical Characteristic Sets of Characterizable Differential Ideals Canonical Characteristic Sets of Characterizable Differential Ideals

2007-02-06

arxiv.org/abs/math/0702130v1

Journal of Symbolic Computation 44 (4) (2009) 333-357

Mathematics

Commutative Algebra

26 pages

Scientific paper

10.1016/j.jsc.2008.07.002

We study the concept of canonical characteristic set of a characterizable differential ideal. We propose an efficient algorithm that transforms any characteristic set into the canonical one. We prove the basic properties of canonical characteristic sets. In particular, we show that in the ordinary case for any ranking 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 a factorization-free 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.

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