# A New Computational Approach to Ideal Theory in Number Fields

```@article{Gurdia2013ANC,
title={A New Computational Approach to Ideal Theory in Number Fields},
author={Jordi Gu{\`a}rdia and Jes{\'u}s Montes and Enric Nart},
journal={Foundations of Computational Mathematics},
year={2013},
volume={13},
pages={729-762}
}```
• Published 7 May 2010
• Mathematics
• Foundations of Computational Mathematics
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…
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