[R] Farey sequences

[Greg Snow]

This sequence of commands replicates your example, could you expand this
to do what you want?

> tmp <- c( outer( 0:4, 1:4, "/") )
> tmp <- tmp[tmp <= 1]
> tmp <- unique(tmp)
> tmp <- sort(tmp)
> library(MASS)
> fractions(tmp)
[1]   0 1/4 1/3 1/2 2/3 3/4   1


Greg Snow, Ph.D.
Statistical Data Center
greg.snow at ihc.com
(801) 408-8111

>>> Robin Hankin <r.hankin at soc.soton.ac.uk> 03/04/05 07:06AM >>>
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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