On the computation of units and class numbers by a generalization of Lagrange's algorithm
type: Item
instance of: scholarly article
title: On the computation of units and class numbers by a generalization of Lagrange's algorithm
zbMATH Open document ID: 0615.12001
DOI: 10.1016/0022-314X(87)90092-8
published in: Journal of Number Theory
publication date: 1987-01-01T00:00:00Z
review text: The author describes an algorithm which allows one to compute a fundamental system of units, a cycle of reduced ideals and the class number of any order \({\mathfrak O}\) of an arbitrary algebraic number field F. His algorithm is a number geometric generalization of Lagrange's continued fraction algorithm and leads to a fundamental system of units of F in \(O(RD^{\epsilon})\) binary operations, for any \(\epsilon >0\); here R is the regulator of F, D is the absolute value of the discriminant of F, and the big O-constant depends only on the degree n of F over \({\mathbb{Q}}\). Examples involving 20 totally real quartic fields are given.
reviewed by: Claude Levesque
Mathematics Subject Classification ID: 12-04
Mathematics Subject Classification ID: 11J70
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R52
Mathematics Subject Classification ID: 11R16
zbMATH DE Number: 3995815
zbMATH Keywords: class number of order
zbMATH Keywords: algorithm
zbMATH Keywords: fundamental system of units
zbMATH Keywords: cycle of reduced ideals
zbMATH Keywords: Lagrange's continued fraction algorithm
zbMATH Keywords: totally real quartic fields
author: Johannes Buchmann
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3995815