The Jacobi-Perron algorithm in integer form

Hendy, M. D.; Jeans, N. S.

doi:10.1090/S0025-5718-1981-0606514-X

The Jacobi-Perron algorithm in integer form
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by M. D. Hendy and N. S. Jeans PDF

Math. Comp. 36 (1981), 565-574 Request permission

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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