Details:
Title | Universal characteristic decomposition of radical differential ideals | Author(s) | Oleg D. Golubitsky | Type | Article in Journal | Abstract | We 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. | Keywords | Differential algebra, Radical differential ideals, Factorization-free algorithms, Characteristic decomposition, Universal characteristic sets, Differential rankings | ISSN | 0747-7171 |
URL |
http://www.sciencedirect.com/science/article/pii/S0747717107000971 |
Language | English | Journal | Journal of Symbolic Computation | Volume | 43 | Number | 1 | Pages | 27 - 45 | Year | 2008 | Edition | 0 | Translation |
No | Refereed |
No |
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