Fine costs for Euclid's algorithm on polynomials and Farey maps

This paper studies digit-cost functions for the Euclid algorithm on polynomials with coefficients in a finite field, in terms of the number of operations performed on the finite field Fq. The usual bit-complexity is defined with respect to the degree of the quotients; we focus here on a notion of ‘f...

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Bibliographic Details
Published in:	Advances in applied mathematics Vol. 54; pp. 27 - 65
Main Authors:	Berthé, Valérie, Nakada, Hitoshi, Natsui, Rie, Vallée, Brigitte
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 01.03.2014 Elsevier
Subjects:	Algorithms Asymptotic properties Bit-complexity Bivariate generating functions Combinatorial analysis Computational Complexity Computer Science Continued fractions Cost function Costs Data Structures and Algorithms Ergodic processes Farey map Finite field Functions (mathematics) Laurent formal power series Mathematical analysis Polynomials Finite field 68W40 Bit-complexity Bivariate generating functions Farey map 11J70 Continued fractions 11K50 11A05 Laurent formal power series 62E20 Cost function 11T55 Combinatorial analysis
ISSN:	0196-8858, 1090-2074
Online Access:	Get full text
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