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Mathematics of Computation

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The Jacobi-Perron algorithm in integer form

Authors: M. D. Hendy and N. S. Jeans
Journal: Math. Comp. 36 (1981), 565-574
MSC: Primary 10A30; Secondary 12A45
MathSciNet review: 606514
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Abstract: We present an alternative expression of the Jacobi-Perron algorithm on a set of $ 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.

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Keywords: Jacobi-Perron algorithm, multiprecision arithmetic, continued fractions, fundamental unit, cubic fields
Article copyright: © Copyright 1981 American Mathematical Society

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