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dc.contributor.authorGuàrdia Rubies, Jordi
dc.contributor.authorMontes Peral, Jesús
dc.contributor.authorNart Vinyals, Enric
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV
dc.date.accessioned2015-06-05T14:02:14Z
dc.date.available2015-06-05T14:02:14Z
dc.date.created2013
dc.date.issued2013
dc.identifier.citationGuàrdia, J.; Montes, J.; Nart, E. A new computational approach to ideal theory in number fields. "Foundations of computational mathematics", 2013, vol. 13, núm. 5, p. 729-762.
dc.identifier.issn1615-3375
dc.identifier.urihttp://hdl.handle.net/2117/28201
dc.description.abstractLet K be the number field determined by a monic irreducible polynomial f(x) with integer coefficients. In previous papers we parameterized the prime ideals of K in terms of certain invariants attached to Newton polygons of higher order of f(x). In this paper we show how to carry out the basic operations on fractional ideals of K in terms of these constructive representations of the prime ideals. From a computational perspective, these results facilitate the manipulation of fractional ideals of K avoiding two heavy tasks: the construction of the maximal order of K and the factorization of the discriminant of f(x). The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime ideals
dc.format.extent34 p.
dc.language.isoeng
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject.lcshAlgorithms
dc.titleA new computational approach to ideal theory in number fields
dc.typeArticle
dc.subject.lemacAlgorismes
dc.contributor.groupUniversitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres
dc.rights.accessOpen Access
local.identifier.drac15831713
dc.description.versionPostprint (author’s final draft)
local.citation.authorGuàrdia, J.; Montes, J.; Nart, E.
local.citation.publicationNameFoundations of computational mathematics
local.citation.volume13
local.citation.number5
local.citation.startingPage729
local.citation.endingPage762


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