Please use this identifier to cite or link to this item:
http://hdl.handle.net/2445/124824
Title: | A new computational approach to ideal theory in number fields |
Author: | Guàrdia, Jordi Montes, Jesús Nart, Enric |
Keywords: | Teoria de nombres Teoria de la computació Aritmètica computacional Number theory Theory of computation Computer arithmetic |
Issue Date: | 2013 |
Publisher: | Springer Verlag |
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 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1007/s10208-012-9137-5 |
It is part of: | Foundations of Computational Mathematics, 2013, vol. 13, num. 5, p. 729-762 |
URI: | http://hdl.handle.net/2445/124824 |
Related resource: | https://doi.org/10.1007/s10208-012-9137-5 |
ISSN: | 1615-3375 |
Appears in Collections: | Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial) |
Files in This Item:
File | Description | Size | Format | |
---|---|---|---|---|
617485.pdf | 496.41 kB | Adobe PDF | View/Open |
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.