# name
A new computational approach to ideal theory in number fields

# metadata.dc.description.abstract[].value
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.

# metadata.dc.relation.ispartof[].value
Foundations of Computational Mathematics, 2013, vol. 13, num. 5, p. 729-762

# metadata.dc.source[].value
Articles publicats en revistes (Matemàtica Econòmica, Financera i Actuarial)

# metadata.dc.title[].value
A new computational approach to ideal theory in number fields