Title:
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A new computational approach to ideal theory in number fields
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Author:
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Guàrdia, Jordi; Montes, Jesús; Nart, Enric
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Other authors:
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Universitat de Barcelona |
Abstract:
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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 the defining equation $f(x)$. 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. |
Subject(s):
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-Teoria de nombres -Teoria de la computació -Aritmètica computacional -Number theory -Theory of computation -Computer arithmetic |
Rights:
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(c) Springer Verlag, 2013
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Document type:
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Article Article - Accepted version |
Published by:
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Springer Verlag
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