Factoring bivariate sparse (lacunary) polynomials

We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input...

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Detalles Bibliográficos
Autores: Avendaño, Martín, Krick, Teresa Elena Genoveva, Sombra, Martín
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/117850
Acceso en línea:http://hdl.handle.net/11336/117850
Access Level:acceso abierto
Palabra clave:HEIGHT OF POINTS
LACUNARY (SPARSE) POLYNOMIALS
LEHMER'S PROBLEM
POLYNOMIAL FACTORIZATION
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:We present a deterministic algorithm for computing all irreducible factors of degree ≤ d of a given bivariate polynomial f ∈ K [x, y] over an algebraic number field K and their multiplicities, whose running time is polynomial over the rationals, in the bit length of the sparse encoding of the input and in d. Moreover, we show that the factors over over(Q, -) of degree ≤ d which are not binomials can also be computed in time polynomial in the sparse length of the input and in d. © 2006 Elsevier Inc. All rights reserved.