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TitleAlgebraic transformation of differential characteristic decompositions from one ranking to another
Author(s) Oleg D. Golubitsky, Marina Kondratieva, Alexey Ovchinnikov
TypeArticle in Journal
AbstractWe propose an algorithm for transforming a characteristic decomposition of a radical differential ideal from one ranking into another. The algorithm is based on a new bound: 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. Applying this bound, the algorithm determines the number of times one needs to differentiate the given differential polynomials, so that a characteristic decomposition w.r.t. the target ranking could be computed by a purely algebraic algorithm (that is, without further differentiations). We also 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. This algorithm is not restricted to the ordinary case and is applicable for an arbitrary ranking.
KeywordsDifferential algebra, Canonical characteristic sets, Radical differential ideals, Bounds for orders
URL http://www.sciencedirect.com/science/article/pii/S0747717108001065
JournalJournal of Symbolic Computation
Pages333 - 357
Translation No
Refereed No