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

DOI:
https://doi.org/10.1090/S0025-5718-1972-0330118-4

MathSciNet review:
0330118

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Abstract | References | Similar Articles | Additional Information

Abstract: Let a denote a real algebraic number that is a root of a polynomial . The purpose of this paper is to state an algorithm for finding the simple continued fraction expansion of . 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**, https://doi.org/10.1007/BF02165312**[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 (Unpublished.)**[6]**Hans Zassenhaus,*A real root calculus*, Computational Problems in Abstract Algebra (Proc.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**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0330118-4

Keywords:
Continued fraction expansion,
algorithm,
discrimination of roots,
irrational real algebraic numbers,
*PV* numbers,
binary search procedure,
sign determination,
mean value theorem

Article copyright:
© Copyright 1972
American Mathematical Society