Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields

Details Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields

2008-07-25

arxiv.org/abs/0807.4065v3

Mathematics

Number Theory

References to [HN] have been updated

Scientific paper

We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good: for a given prime number p, it computes the p-valuation of the discriminant and the factorization of p in a number field of degree 1000 in a few seconds, in a personal computer.

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