[R] Farey sequences

From: Robin Hankin <r.hankin_at_soc.soton.ac.uk>
Date: Sat 05 Mar 2005 - 01:06:02 EST


Hi

has anyone coded up Farey sequences?

[
The Farey sequence of order "n" is the set of rational numbers i/j with (i,j)=1 such that 0 <= i,j <= n; the sequence is ordered from lowest to highest.
Thus

Farey_4 = {0/1 , 1/4 , 1/3 , 1/2 , 2/3 , 3/4 , 1/1} ]

My motivation is unimodular transformations: I need to systematically generate 2-by-2 integer matrices with determinant 1, and Farey sequences seem to be the best way to do this.

--
Robin Hankin
Uncertainty Analyst
Southampton Oceanography Centre
European Way, Southampton SO14 3ZH, UK
  tel  023-8059-7743

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Received on Sat Mar 05 03:49:01 2005

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