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

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
References to [HN] have been updated

Keywords

Number Theory, 11Y40; 11R04; 11R29

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/172875

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.4065
 http://arxiv.org/abs/0807.4065

Collections

arXiv