Guàrdia, JordiMontes, JesúsNart, Enric2018-09-262018-09-2620131615-3375https://hdl.handle.net/2445/124824Let $K$ 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.34 p.application/pdfeng(c) Springer Verlag, 2013Teoria de nombresTeoria de la computacióAritmètica computacionalNumber theoryTheory of computationComputer arithmeticinfo:eu-repo/semantics/article6174852018-09-26info:eu-repo/semantics/openAccess