Translator Disclaimer
2022 Square-free OM computation of global integral bases
Jordi Guàrdia, Enric Nart
Algebra Number Theory 16(6): 1327-1376 (2022). 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[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.

Citation

Download Citation

Jordi Guàrdia. Enric Nart. "Square-free OM computation of global integral bases." Algebra Number Theory 16 (6) 1327 - 1376, 2022. https://doi.org/10.2140/ant.2022.16.1327

Information

Received: 26 July 2018; Revised: 8 August 2021; Accepted: 5 October 2021; Published: 2022
First available in Project Euclid: 2 October 2022

Digital Object Identifier: 10.2140/ant.2022.16.1327

Subjects:
Primary: 11R04
Secondary: 11Y40

Keywords: Integral basis , Newton polygons , OM algorithm

Rights: Copyright © 2022 Mathematical Sciences Publishers

JOURNAL ARTICLE
50 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.16 • No. 6 • 2022
MSP
Back to Top