Vol. 16, No. 6, 2022

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Square-free OM computation of global integral bases

Jordi Guàrdia and Enric Nart

Vol. 16 (2022), No. 6, 1327–1376

For a prime p, the OM algorithm finds the p-adic factorization of an irreducible polynomial f [x] in polynomial time. This may be applied to construct p-integral bases in the number field K defined by f. In this paper, we adapt the OM techniques to work with a positive integer N instead of p. As an application, we obtain an algorithm to compute global integral bases in K, which does not require a previous factorization of the discriminant of f.

integral basis, Newton polygons, OM algorithm
Mathematical Subject Classification 2010
Primary: 11R04
Secondary: 11Y40
Received: 26 July 2018
Revised: 8 August 2021
Accepted: 5 October 2021
Published: 27 September 2022
Jordi Guàrdia
Departament de Matemàtiques
Escola Politècnica Superior d’Enginyeria de Vilanova i la Geltrú
Vilanova i la Geltrú
Enric Nart
Departament de Matemàtiques
Universitat Autònoma de Barcelona
Cerdanyola del Vallès