On some classes of irreducible polynomials. (July 2021)
- Record Type:
- Journal Article
- Title:
- On some classes of irreducible polynomials. (July 2021)
- Main Title:
- On some classes of irreducible polynomials
- Authors:
- Gutierrez, Jaime
Jiménez Urroz, Jorge - 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.
- Is Part Of:
- Journal of symbolic computation. Volume 105(2021)
- Journal:
- Journal of symbolic computation
- Issue:
- Volume 105(2021)
- Issue Display:
- Volume 105, Issue 2021 (2021)
- Year:
- 2021
- Volume:
- 105
- Issue:
- 2021
- Issue Sort Value:
- 2021-0105-2021-0000
- 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 - Journal URLs:
- http://www.sciencedirect.com/science/journal/07477171 ↗
http://www.elsevier.com/journals ↗ - DOI:
- 10.1016/j.jsc.2019.08.005 ↗
- Languages:
- English
- ISSNs:
- 0747-7171
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 5067.900000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 15399.xml