Refined algorithms to compute syzygies. (May 2016)

• Record Type: Journal Article
• Authors: Eröcal, Burçin; Motsak, Oleksandr; Schreyer, Frank-Olaf; Steenpaß, Andreas
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 308
• Page End: 327
• Publication Date: 2016-05
• Subjects: 14Q99 -- 13D02 -- 13P20; Syzygies -- Schreyer Algorithm; 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.2015.07.004
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: Based on Schreyer's algorithm (Schreyer, 1980, 1991; Berkesch and Schreyer, 2014 ), we present two refined algorithms for the computation of syzygies. The two main ideas of the first algorithm, calledLiftHybrid, are the following: First, we may leave out certain terms of module elements during the computation which do not contribute to the result. These terms are called "lower order terms", see Definition 4.2. Second, we do not need to order the remaining terms of these module elements during the computation. This significantly reduces the number of monomial comparisons for the arithmetic operations. For the second algorithm, calledLiftTree, we additionally cache some partial results and reuse them at the remaining steps.