Square-free OM computation of global integral bases

Guàrdia, Jordi; Nart, Enric

doi:10.2140/ant.2022.16.1327

Download this article
	For screen
	For printing

Recent Issues

The Journal

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

This article is available for purchase or by subscription. See below.

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 $f$ .

PDF Access Denied

We have not been able to recognize your IP address 18.117.186.92 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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