elliptic (version 1.2-2)

farey: Farey sequences

Description

Returns the Farey sequence of order $n$

Usage

farey(n, print=FALSE, give.series = FALSE)

Arguments

n

Order of Farey sequence

print

Boolean, with TRUE meaning to print out the text version of the Farey sequence in human-readable form. Default value of FALSE means not to print anything

give.series

Boolean, with TRUE meaning to return the series explicitly, and default FALSE meaning to return a 3 dimensional array as detailed below

Details

If give.series takes its default value of FALSE, return a matrix a of dimension c(2,u) where u is a (complicated) function of n. If v <- a[i,], then v[1]/v[2] is the $i^{\mathrm th}$ term of the Farey sequence. Note that det(a[(n):(n+1),])== -1

If give.series is TRUE, then return a matrix a of size c(4,u-1). If v <- a[i,], then v[1]/v[2] and v[3]/v[4] are successive pairs of the Farey sequence. Note that det(matrix(a[,i],2,2))== -1

References

G. H. Hardy and E. M. Wright 1985. An introduction to the theory of numbers, Oxford University Press (fifth edition)

See Also

unimodular

Examples

farey(3)