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A new computational approach to ideal theory in number fields
dc.contributor.author | Guàrdia Rubies, Jordi |
dc.contributor.author | Montes Peral, Jesús |
dc.contributor.author | Nart Vinyals, Enric |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2015-06-05T14:02:14Z |
dc.date.available | 2015-06-05T14:02:14Z |
dc.date.created | 2013 |
dc.date.issued | 2013 |
dc.identifier.citation | Guàrdia, 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.issn | 1615-3375 |
dc.identifier.uri | http://hdl.handle.net/2117/28201 |
dc.description.abstract | Let 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.extent | 34 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra |
dc.subject.lcsh | Algorithms |
dc.title | A new computational approach to ideal theory in number fields |
dc.type | Article |
dc.subject.lemac | Algorismes |
dc.contributor.group | Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
dc.rights.access | Open Access |
local.identifier.drac | 15831713 |
dc.description.version | Postprint (author’s final draft) |
local.citation.author | Guàrdia, J.; Montes, J.; Nart, E. |
local.citation.publicationName | Foundations of computational mathematics |
local.citation.volume | 13 |
local.citation.number | 5 |
local.citation.startingPage | 729 |
local.citation.endingPage | 762 |
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