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Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
2011
Journal de Théorie des Nombres de Bordeaux
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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.
doi:10.5802/jtnb.782
fatcat:3e773mn4qnatvozn3xewyh6qku