Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
Journal de Théorie des Nombres de Bordeaux, Volume 23 (2011) no. 3, pp. 667-696.

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.

Nous présentons un algorithme pour calculer le discriminant et la décomposition des idéaux d’un corps de nombres en produit d’idéaux premiers. L’algorithme est un raffinement d’une méthode de factorisation p-adique qui utilise polygones de Newton d’ordre supérieur. L’exigence de mémoire et les temps d’exécution sont très bons.

Received:
Published online:
DOI: 10.5802/jtnb.782
Jordi Guàrdia 1; Jesús Montes 2; Enric Nart 3

1 Departament de Matemàtica Aplicada IV Escola Politècnica Superior d’Enginyera de Vilanova i la Geltrú Av. Víctor Balaguer s/n. E-08800 Vilanova i la Geltrú, Catalonia
2 Departament de Ciències Econòmiques i Empresarials Facultat de Ciències Socials, Universitat Abat Oliba CEU Bellesguard 30 E-08022 Barcelona, Catalonia, Spain Departament de Matemàtica Econòmica, Financera i Actuarial Facultat d’Economia i Empresa, Universitat de Barcelona Av. Diagonal 690 E-08034 Barcelona, Catalonia, Spain
3 Departament de Matemàtiques Universitat Autònoma de Barcelona Edifici C E-08193 Bellaterra, Barcelona, Catalonia, Spain
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Jordi Guàrdia; Jesús Montes; Enric Nart. Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields. Journal de Théorie des Nombres de Bordeaux, Volume 23 (2011) no. 3, pp. 667-696. doi : 10.5802/jtnb.782. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.782/

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