# farey: Farey sequences In elliptic: Weierstrass and Jacobi Elliptic Functions

## Description

Returns the Farey sequence of order n

## Usage

 `1` ```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-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`

## Author(s)

Robin K. S. Hankin

## References

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

`unimodular`
 `1` ```farey(3) ```