fpp {elliptic} | R Documentation |
Reduce z=x+iy
to a congruent value within the
fundamental period parallelogram (FPP). Function mn()
gives
(real, possibly noninteger) m
and n
such that
z=m\cdot p_1+n\cdot p_2
.
fpp(z, p, give=FALSE)
mn(z, p)
z |
Primary complex argument |
p |
Vector of length two with first element the first period and
second element the second period. Note that |
give |
Boolean, with |
Function fpp()
is fully vectorized.
Use function mn()
to determine the “coordinates” of a
point.
Use floor(mn(z,p)) %*% p
to give the complex value of
the (unique) point in the same period parallelogram as z
that
is congruent to the origin.
Robin K. S. Hankin
p <- c(1.01+1.123i, 1.1+1.43i)
mn(z=1:10,p) %*% p ## should be close to 1:10
#Now specify some periods:
p2 <- c(1+1i,1-1i)
#Define a sequence of complex numbers that zooms off to infinity:
u <- seq(from=0,by=pi+1i*exp(1),len=2007)
#and plot the sequence, modulo the periods:
plot(fpp(z=u,p=p2))
#and check that the resulting points are within the qpp:
polygon(c(-1,0,1,0),c(0,1,0,-1))