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

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606514-X

MathSciNet review:
606514

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Abstract | References | Similar Articles | Additional Information

Abstract: We present an alternative expression of the Jacobi-Perron algorithm on a set of 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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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1981-0606514-X

Keywords:
Jacobi-Perron algorithm,
multiprecision arithmetic,
continued fractions,
fundamental unit,
cubic fields

Article copyright:
© Copyright 1981
American Mathematical Society