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The exact length of the Euclidean algorithm in [X]

Published online by Cambridge University Press:  26 February 2010

Arnold Knopfmacher  and
John Knopfmacher
Arnold Knopfmacher
Affiliation:
Department of Computational and Applied Mathematics, University of the Witwatersrand, Johannesburg, PO Wits 2050, South Africa
John Knopfmacher
Affiliation:
Department of Mathematics, University of the Witwatersrand, Johannesburg, PO Wits 2050, South Africa
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Abstract

A study is made of the length L(h, k) of the Euclidean algorithm for determining the g.c.d. of two polynomials h, k in [X], a finite field. We obtain exact formulae for the number of pairs with a fixed length N which lie in a given range, as well as the average length and variance of the Euclidean algorithm for such pairs.

Type
Research Article
Information
Mathematika , Volume 35 , Issue 2 , December 1988 , pp. 297 - 304
Copyright
Copyright © University College London 1988

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