%0 Journal Article
%T Newton polygons of higher order in algebraic number theory
%A Jordi Guardia
%A Jesus Montes
%A Enric Nart
%J Mathematics
%D 2008
%I arXiv
%X We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible factors. This carries out a program suggested by \O{}. Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number fields.
%U http://arxiv.org/abs/0807.2620v2