A continued fraction algorithm for real algebraic numbers-Reference-Cited by-同舟云学术

A continued fraction algorithm for real algebraic numbers

Published:1972 Issue:119 Volume:26 Page:785-791
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Cantor David G.,Galyean Paul H.,Zimmer Horst G.

Abstract

Let a denote a real algebraic number that is a root of a polynomial f ( x ) ∈ Z [ x ] f(x) \in {\text {Z}}[x] . The purpose of this paper is to state an algorithm for finding the simple continued fraction expansion of α \alpha . Furthermore, an application of the algorithm to sign determination in real algebraic number fields is given.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1972-26-119/S0025-5718-1972-0330118-4/S0025-5718-1972-0330118-4.pdf

Reference6 articles.

1. On sign determinations in real algebraic number fields;Kempfert, H.;Numer. Math.,1968

2. J. Lagrange, “Sur la résolution des équations numériques,” Oeuvres. Vol. 2, pp. 560-578.

3. D. L. Smith, The Calculation of Simple Continued Fraction Expansions of Real Algebraic Numbers, Master Thesis, Ohio State University, Columbus, Ohio, 1969.

4. J. V. Uspensky, Theory of Equations, McGraw-Hill, New York-Toronto-London, 1948.

5. H. Zassenhaus, On the Continued Fraction Development of Real Irrational Algebraic Numbers, Ohio State University, Columbus, Ohio, 1968. (Unpublished.)

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