Vol. 16, No. 6, 2022

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 8, 1777–2003
Issue 7, 1547–1776
Issue 6, 1327–1546
Issue 5, 1025–1326
Issue 4, 777–1024
Issue 3, 521–775
Issue 2, 231–519
Issue 1, 1–230

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
 
Other MSP Journals
Square-free OM computation of global integral bases

Jordi Guàrdia and Enric Nart

Vol. 16 (2022), No. 6, 1327–1376
Abstract

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.

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