Computing the bound of an Ore polynomial. Applications to factorization. (May 2019)

• Record Type: Journal Article
• Authors: Gómez-Torrecillas, José; Lobillo, F.J.; Navarro, Gabriel
• Is Part Of: Journal of symbolic computation. Volume 92(2019)
• Page Start: 269
• Page End: 297
• Publication Date: 2019-05
• Subjects: 16S36 -- 16Z05 -- 68W30; Ore polynomial -- Bound -- Skew polynomial -- Irreducible polynomial -- Factorization; 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.2018.04.018
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We develop two algorithms for computing a bound of an Ore polynomial over a skew field, under mild conditions. As an application, we state a criterion for deciding whether a bounded Ore polynomial is irreducible, and we discuss a factorization algorithm. The asymptotic time complexity in the degree of the given Ore polynomial is studied.