Newton polygons of higher order in algebraic number theory
Jordi Guàrdia, Jesús Sanz Montes, Enric Nart · arXiv (Cornell University) · 2008
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 Ø. Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number fields.