The Jacobi-Perron algorithm in integer form-Reference-Cited by-同舟云学术

The Jacobi-Perron algorithm in integer form

Published:1981 Issue:154 Volume:36 Page:565-574
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Hendy M. D.,Jeans N. S.

Abstract

We present an alternative expression of the Jacobi-Perron algorithm on a set of n − 1 n - 1 independent numbers of an algebraic number field of degree n, where computation of real valued (nonrational) numbers is avoided. In some instances this saves the need to compute with high levels of precision. We also demonstrate a necessary and sufficient condition for the algorithm to cycle. The paper is accompanied by several numerical examples.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1981-36-154/S0025-5718-1981-0606514-X/S0025-5718-1981-0606514-X.pdf

Reference10 articles.

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3. A 3-dimensional periodic Jacobi-Perron algorithm of period length 8;Bernstein, Leon;J. Number Theory,1972

4. G. Chrystal, Algebra, Part II, 2nd ed., A. and C. Black Ltd., London, 1931.

5. Applications of a continued fraction algorithm to some class number problems;Hendy, M. D.;Math. Comp.,1974

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