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
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad de Cantabria (UC)
Repositorio:UCrea Repositorio Abierto de la Universidad de Cantabria
Idioma:inglés
OAI Identifier:oai:repositorio.unican.es:10902/31237
Acceso en línea:https://hdl.handle.net/10902/31237
Access Level:acceso abierto
Palabra clave:Irreducible polynomials
Eisenstein
Stable polynomials
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 F(x,y)=f1(x)f2(y)-f2(x)f1(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(x1,---,xn)E K[x1,...,xn] over a zero characteristic field K such that p(h1(x1),..,hn(xn)) is irreducible over K for every n-tuple h1(x1),...,hn(xn) of non constant one variable polynomials over K. The results can also be applied to fields of positive characteristic, with some modifications.