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}
}
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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