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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>p</mml:mi> </mml:math> -adic factorization method based on Newton polygons of higher order. The running-time and memory requirements of the algorithm appear to be very good.