A new algorithm for computing staggered linear bases. (July 2023)

• Record Type: Journal Article
• Authors: Hashemi, Amir; Michael Möller, H.
• Is Part Of: Journal of symbolic computation. Volume 117(2023)
• Page Start: 1
• Page End: 14
• Publication Date: 2023-07
• Subjects: 13P10 -- 68W30; Polynomial ideals -- Gröbner bases -- Buchberger's algorithm -- Buchberger's criteria -- Staggered linear bases; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.11.003
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Considering a multivariate polynomial ideal over a given field as a vector space, we investigate for such an ideal a particular linear basis, a so-called staggered linear basis, which contains a Gröbner basis as well. In this paper, we present a simple and efficient algorithm to compute a staggered linear basis. The new framework is equipped with some novel criteria (including both Buchberger's criteria) to detect superfluous reductions. The proposed algorithm has been implemented in Maple, and we provide an illustrative example to show how it works. Finally, the efficiency of this algorithm compared to the existing methods is discussed via a set of benchmark polynomials.