Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-07-06T19:11:22.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Algorithmes des fractions continues et de Jacobi-Perron

Published online by Cambridge University Press:  17 April 2009

Brigitte Adam  and
Georges Rhin
Brigitte Adam
Affiliation:
URA CNRS 399, Département de Mathématiques et InformatiqueUFR MIM, Université de Metz, Ile du Saulcy57045 Metz Cedex 01France
Georges Rhin
Affiliation:
URA CNRS 399, Département de Mathématiques et InformatiqueUFR MIM, Université de Metz, Ile du Saulcy57045 Metz Cedex 01France
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give an algorithm by which one can compute, using only rational numbers, the continued fraction and more generally the Jacobi-Perron algorithm expansion of real algebraic numbers.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 2 , April 1996 , pp. 341 - 350
Copyright
Copyright © Australian Mathematical Society 1996

References

Bibliographie

[1]Akritas, A.G., Elements of computer algebra with applications (Wiley Interscience, New York, 1989).Google Scholar
[2]Bombieri, E. et van der Poorten, A.J., ‘Continued fractions of algebraic numbers’, in Computational algebra and number theory, Sydney 1992, (Bosnia, Wieb and Van Der Poorten, Alf, Editors) (Kluwer Academic Publishing, 1995), pp. 138–154.Google Scholar
[3]Brualdi, R., Combinatorial matrix theory (Cambridge University Press, Cambridge, 1991).CrossRefGoogle Scholar
[4]Cantor, G., Galyean, P. and Zimmer, G., ‘A continued fraction algorithm for real algebraic numbers’, Math. Comp. 26 (1972), 785–791.CrossRefGoogle Scholar
[5]Karlin, S., Initiation aux processus aléatoires (Dunod.).Google Scholar
[6]Lang, S. et Trotter, A., ‘Continued fractions for some algebraic numbers’, J. für Math. 255 (1972), 112–134.Google Scholar
[7]Mignotte, M., ‘Mathématiques pour le calcul formel’, PUF, p. 208.Google Scholar
[8]Perron, O., ‘Grundlagen für eine Theorie des Jacobischen Kettenbruchalgorithmus’, Math. Ann. 64 (1907), 1–76.CrossRefGoogle Scholar
[9]Zassenhaus, H., On the continued fraction development of real irrational algebraic numbers, (unpublished) (Ohio State University, Columbus, Oh., 1968).Google Scholar