Algebraic computations with continued fractions
type: Item
instance of: scholarly article
title: Algebraic computations with continued fractions
zbMATH Open document ID: 0929.11066
author: Pierre Liardet
author: Pierre Stambul
published in: Journal of Number Theory
publication date: 2000-02-02T00:00:00Z
review text: The authors describe several algorithms, in terms of transducers, which perform algebraic computations with continued fractions. In particular, they come up with an efficient formal algorithm which produces consecutive partial quotients of \((a\omega+ b)/c\omega+d)\), with \(a,b,c,d \in\mathbb{Z}\) and \((ad-bc)\neq 0\), by reading the consecutive partial quotients of the irrational number \(\omega\). Other nice new results are obtained as well.
reviewed by: Claude Levesque
Mathematics Subject Classification ID: 11Y65
Mathematics Subject Classification ID: 11A55
Mathematics Subject Classification ID: 11K50
zbMATH DE Number: 1268047
zbMATH Keywords: consecutive partial quotients of irrational number
zbMATH Keywords: algorithms
zbMATH Keywords: transducers
zbMATH Keywords: algebraic computations
zbMATH Keywords: continued fractions
MaRDI profile type: Publication
full work available at URL: jnth.1998.2274
OpenAlex ID: W2021235833
cites work: Algorithmes des fractions continues et de Jacobi-Perron
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cites work: A generalization of Perron's theorem about Hurwitzian numbers
cites work: Q5792555
DOI: 10.1006/JNTH.1998.2274
description: scientific article; zbMATH DE number 1268047