farey {elliptic} | R Documentation |
Returns the Farey sequence of order n
farey(n, print=FALSE, give.series = FALSE)
n |
Order of Farey sequence |
print |
Boolean, with |
give.series |
Boolean, with |
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
Robin K. S. Hankin
G. H. Hardy and E. M. Wright 1985. An introduction to the theory of numbers, Oxford University Press (fifth edition)
farey(3)