A continued fraction algorithm for real algebraic numbers
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- by David G. Cantor, Paul H. Galyean and Horst G. Zimmer PDF
- Math. Comp. 26 (1972), 785-791 Request permission
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.References
- H. Kempfert, On sign determinations in real algebraic number fields, Numer. Math. 11 (1968), 170–174. MR 225762, DOI 10.1007/BF02165312 J. Lagrange, “Sur la résolution des équations numériques,” Oeuvres. Vol. 2, pp. 560-578. D. L. Smith, The Calculation of Simple Continued Fraction Expansions of Real Algebraic Numbers, Master Thesis, Ohio State University, Columbus, Ohio, 1969. J. V. Uspensky, Theory of Equations, McGraw-Hill, New York-Toronto-London, 1948. H. Zassenhaus, On the Continued Fraction Development of Real Irrational Algebraic Numbers, Ohio State University, Columbus, Ohio, 1968. (Unpublished.)
- Hans Zassenhaus, A real root calculus, Computational Problems in Abstract Algebra (Proc. Conf., Oxford, 1967) Pergamon, Oxford, 1970, pp. 383–392. MR 0276205
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Math. Comp. 26 (1972), 785-791
- MSC: Primary 12D10; Secondary 10F20
- DOI: https://doi.org/10.1090/S0025-5718-1972-0330118-4
- MathSciNet review: 0330118