On some classes of irreducible polynomials

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 pol...

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Detalles Bibliográficos
Autores: Gutiérrez Gutiérrez, Jaime, Jiménez Urroz, Jorge|||0000-0002-2395-4478
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/335780
Acceso en línea:https://hdl.handle.net/2117/335780
https://dx.doi.org/10.1016/j.jsc.2019.08.005
Access Level:acceso abierto
Palabra clave:Number theory
Irreducible polynomials
Eisenstein
Stable polynomials
Nombres, Teoria dels
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descripción
Sumario: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 , then 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 over a zero characteristic field such that is irreducible over for every n-tuple of non constant one variable polynomials over . The results can also be applied to fields of positive characteristic, with some modifications.