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TitleAn improvement of Rosenfeld-Gr\"obner algorithm.
Author(s) Amir Hashemi, Zahra Touraji
TypeBook, Chapter in Book, Conference Proceeding
AbstractIn their paper Boulier et al. (2009) described the Rosenfeld-Gröbner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of polynomial differential equations, ordinary or with partial derivatives. In order to enhance the efficiency of this algorithm, they proposed their analog of Buchberger’s criteria to avoid useless reductions to zero. For example, they showed that if p and q are two differential polynomials which are linear, homogeneous, in one differential indeterminate, with constant coefficients and with leaders θu and ϕu, respectively so that θ and ϕ are disjoint then the delta-polynomial of p and q reduces to zero w.r.t. the set {p,q}. In this paper we generalize this result showing that it remains true if p and q are products of differential polynomials which are linear, homogeneous, in the same differential indeterminate, with constant coefficients and θ and ϕ are disjoint where θu and ϕu are leaders of p and q, respectively. We have implemented the Rosenfeld-Gröbner algorithm and our refined version on the same platform in Maple and compare them via a set of benchmarks.
KeywordsDifferential algebra, Rosenfeld-Gröbner, Buchberger first criterion
ISBN978-3-662-44198-5/pbk
URL http://link.springer.com/chapter/10.1007%2F978-3-662-44199-2_70
LanguageEnglish
Pages466--471
PublisherBerlin: Springer
Year2014
Edition0
Translation No
Refereed No
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