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TitleUniversal characteristic decomposition of radical differential ideals
Author(s) Oleg D. Golubitsky
TypeArticle in Journal
AbstractWe call a differential ideal universally characterizable, if it is characterizable w.r.t. any ranking on partial derivatives. We propose a factorization-free algorithm that represents a radical differential ideal as a finite intersection of universally characterizable ideals. The algorithm also constructs a universal characteristic set for each universally characterizable component, i.e., a finite set of differential polynomials that contains a characterizing set of the ideal w.r.t. any ranking. As a part of the proposed algorithm, the following problem of satisfiability by a ranking is efficiently solved: given a finite set of differential polynomials with a derivative selected in each polynomial, determine whether there exists a ranking w.r.t. which the selected derivatives are leading derivatives and, if so, construct such a ranking.
KeywordsDifferential algebra, Radical differential ideals, Factorization-free algorithms, Characteristic decomposition, Universal characteristic sets, Differential rankings
URL http://www.sciencedirect.com/science/article/pii/S0747717107000971
JournalJournal of Symbolic Computation
Pages27 - 45
Translation No
Refereed No