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.
CitacióGuardia, J.; Montes, J.; Nart, E. Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields. "Journal de théorie des nombres de Bordeaux", 01 Desembre 2011, vol. 23, núm. 3, p. 667-696.