Finding normal integral bases of cyclic number fields of prime degree
type: Item
instance of: scholarly article
title: Finding normal integral bases of cyclic number fields of prime degree
zbMATH Open document ID: 0977.11047
author: Vincenzo Acciaro
author: Claus Fieker
published in: Journal of Symbolic Computation
publication date: 2002-01-22T00:00:00Z
review text: Let \(L\) be a cyclic number field of prime degree \(p\). The authors give an efficient algorithm to calculate normal integral bases in \(L\). The method avoids computations in large extension fields of \(L\). The problem is reduced to finding the generator of a principal ideal in the \(p\)-th cyclotomic field. The procedure is implemented in the algebraic number theory package KASH developed in Berlin. To illustrate the algorithm the authors computed normal bases in the first 1000 fields of E. Lehmer's parametric family of cyclic quintic fields.
Mathematics Subject Classification ID: 11R04
Mathematics Subject Classification ID: 11Y40
Mathematics Subject Classification ID: 11-04
zbMATH DE Number: 1513053
zbMATH Keywords: normal integral bases
zbMATH Keywords: cyclic fields
zbMATH Keywords: efficient algorithm
reviewed by: István Gaál
describes a project that uses: KANT/KASH
MaRDI profile type: Publication
full work available at URL: jsco.1999.0335
OpenAlex ID: W2034333936
cites work: Computing automorphisms of abelian number fields
cites work: KANT V4
cites work: Note on a Polynomial of Emma Lehmer
cites work: Power integral bases in a parametric family of totally real cyclic quintics
cites work: Q5287502
cites work: Connection Between Gaussian Periods and Cyclic Units
cites work: Polynomial cycles in algebraic number fields
cites work: Q4692759
cites work: Algorithms to construct normal bases of cyclic number fields
cites work: Quintic Polynomials and Real Cyclotomic Fields with Large Class Number
DOI: 10.1006/JSCO.1999.0335
description: scientific article; zbMATH DE number 1513053