A continued fraction algorithm for real algebraic numbers

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

doi:10.1090/S0025-5718-1972-0330118-4

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Browser Compatibility Info Help
ISSN 1088-6842(online) ISSN 0025-5718(print)

A continued fraction algorithm for real algebraic numbers

Authors: David G. Cantor, Paul H. Galyean and Horst G. Zimmer
Journal: Math. Comp. 26 (1972), 785-791
MSC: Primary 12D10; Secondary 10F20
MathSciNet review: 0330118
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

[1] H. Kempfert, On sign determinations in real algebraic number fields, Numer. Math. 11 (1968), 170–174. MR 0225762 (37 #1355)
[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 (Unpublished.)
[6] Hans Zassenhaus, A real root calculus, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 383–392. MR 0276205 (43 #1953)

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|

Bibliography