Details:
Title  An improvement of RosenfeldGr\"obner algorithm.  Author(s)  Amir Hashemi, Zahra Touraji  Type  Book, Chapter in Book, Conference Proceeding  Abstract  In their paper Boulier et al. (2009) described the RosenfeldGröbner 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 deltapolynomial 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 RosenfeldGröbner algorithm and our refined version on the same platform in Maple and compare them via a set of benchmarks.  Keywords  Differential algebra, RosenfeldGröbner, Buchberger first criterion  ISBN  9783662441985/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F9783662441992_70 
Language  English  Pages  466471  Publisher  Berlin: Springer  Year  2014  Edition  0  Translation 
No  Refereed 
No 
