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

By Jordi Guàrdia, Jesús Montes, Enric Nart. 2008

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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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Information Systems

View Paper: https://www.semanticscholar.org/paper/3bb99ad99124db32bc522c019db834101c1e90e2