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Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart, Enric
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. TN - Teoria de Nombres
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística
Polygons
Polígons
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/submittedVersion
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