On some classes of irreducible polynomials. (July 2021)

• Record Type: Journal Article
• Authors: Gutierrez, Jaime; Jiménez Urroz, Jorge
• Is Part Of: Journal of symbolic computation. Volume 105(2021)
• Page Start: 64
• Page End: 70
• Publication Date: 2021-07
• Subjects: Irreducible polynomials -- Eisenstein -- Stable polynomials; 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.2019.08.005
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: One of the fundamental tasks of Symbolic Computation is the factorization of polynomials into irreducible factors. The aim of the paper is to produce new families of irreducible polynomials, generalizing previous results in the area. One example of our general result is that for a near-separated polynomial, i.e., polynomials of the form F ( x, y ) = f 1 ( x ) f 2 ( y ) − f 2 ( x ) f 1 ( y ), then F ( x, y ) + r is always irreducible for any constant r different from zero. We also provide the biggest known family of HIP polynomials in several variables. These are polynomials p ( x 1, …, x n ) ∈ K [ x 1, …, x n ] over a zero characteristic field K such that p ( h 1 ( x 1 ), …, h n ( x n ) ) is irreducible over K for every n -tuple h 1 ( x 1 ), …, h n ( x n ) of non constant one variable polynomials over K . The results can also be applied to fields of positive characteristic, with some modifications.