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

Abstract

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

References in corpus (1)

• Newton polygons of higher order in algebraic number theory

Cited by in corpus (4)

• Newton polygons of higher order in algebraic number theory
• A new computational approach to ideal theory in number fields
• Arithmetic in big number fields: the '+Ideals' package
• Explicit Factorization of Prime Integers in Quartic Number Fields defined by $X^4+aX+b$