Triangular systems and a generalization of primitive polynomials. (May 2015)

• Record Type: Journal Article
• Authors: Angermüller, Gerhard
• Is Part Of: Journal of symbolic computation. Volume 68:Part 1(2015)
• Page Start: 316
• Page End: 325
• Publication Date: 2015-05
• Subjects: Polynomial system -- Primitive polynomial -- Regular chain -- Saturation ideal -- Triangular set; 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.2014.09.022
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: A well-known generalization of the notion of primitive polynomials over factorial domains to arbitrary commutative rings is analyzed and applied to triangular systems. In particular, we clarify when a triangular system generates its saturation ideal, thus correcting a criterion published first in 2008.