Square-free OM computation of global integral bases

Guàrdia, Jordi; Nart, Enric

doi:10.2140/ant.2022.16.1327

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Square-free OM computation of global integral bases

Jordi Guàrdia and Enric Nart

Vol. 16 (2022), No. 6, 1327–1376

DOI: 10.2140/ant.2022.16.1327

Abstract

For a prime $p$ , the OM algorithm finds the $p$ -adic factorization of an irreducible polynomial $f \in ℤ [x]$ 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 $f$ .

Keywords

integral basis, Newton polygons, OM algorithm

Mathematical Subject Classification 2010

Primary: 11R04

Secondary: 11Y40

Milestones

Received: 26 July 2018

Revised: 8 August 2021

Accepted: 5 October 2021

Published: 27 September 2022

Authors

Jordi Guàrdia
Departament de Matemàtiques Escola Politècnica Superior d’Enginyeria de Vilanova i la Geltrú Vilanova i la Geltrú Spain

Enric Nart
Departament de Matemàtiques Universitat Autònoma de Barcelona Cerdanyola del Vallès Spain

Vol. 16, No. 6, 2022