We develop a theory of arithmetic Newton polygons of higher
order, that provides the factorization of a separable polynomial over a p-adic
eld, together with relevant arithmetic information about the elds generated
by the irreducible factors. This carries out a program suggested by . Ore.
As an application, we obtain fast algorithms to compute discriminants, prime
ideal decomposition and integral bases of number elds.
Guardia, J.; Montes, J.; Nart, E. Newton polygons of higher order in algebraic number theory. "Transactions of the American Mathematical Society", 10 Gener 2012, vol. 364, núm. 1, p. 361-416.