WeierstrassP {elliptic} | R Documentation |
Weierstrass elliptic function and its derivative, Weierstrass sigma function, and the Weierstrass zeta function
P(z, g=NULL, Omega=NULL, params=NULL, use.fpp=TRUE, give.all.3=FALSE, ...)
Pdash(z, g=NULL, Omega=NULL, params=NULL, use.fpp=TRUE, ...)
sigma(z, g=NULL, Omega=NULL, params=NULL, use.theta=TRUE, ...)
zeta(z, g=NULL, Omega=NULL, params=NULL, use.fpp=TRUE, ...)
z |
Primary complex argument |
g |
Invariants |
Omega |
Half periods |
params |
Object with class “ |
use.fpp |
Boolean, with default |
give.all.3 |
Boolean, with default |
use.theta |
Boolean, with default |
... |
Extra parameters passed to |
In this package, function sigma()
is the Weierstrass sigma
function. For the number theoretic divisor function also known as
“sigma”, see divisor()
.
Robin K. S. Hankin
R. K. S. Hankin. Introducing Elliptic, an R package for Elliptic and Modular Functions. Journal of Statistical Software, Volume 15, Issue 7. February 2006.
## Example 8, p666, RHS:
P(z=0.07 + 0.1i,g=c(10,2))
## Example 8, p666, RHS:
P(z=0.1 + 0.03i,g=c(-10,2))
## Right answer!
## Compare the Laurent series, which also gives the Right Answer (tm):
P.laurent(z=0.1 + 0.03i,g=c(-10,2))
## Now a nice little plot of the zeta function:
x <- seq(from=-4,to=4,len=100)
z <- outer(x,1i*x,"+")
view(x,x,limit(zeta(z,c(1+1i,2-3i))),nlevels=6,scheme=1)
#now figure 18.5, top of p643:
p <- parameters(Omega=c(1+0.1i,1+1i))
n <- 40
f <- function(r,i1,i2=1)seq(from=r+1i*i1, to=r+1i*i2,len=n)
g <- function(i,r1,r2=1)seq(from=1i*i+r1,to=1i*i+2,len=n)
solid.lines <-
c(
f(0.1,0.5),NA,
f(0.2,0.4),NA,
f(0.3,0.3),NA,
f(0.4,0.2),NA,
f(0.5,0.0),NA,
f(0.6,0.0),NA,
f(0.7,0.0),NA,
f(0.8,0.0),NA,
f(0.9,0.0),NA,
f(1.0,0.0)
)
dotted.lines <-
c(
g(0.1,0.5),NA,
g(0.2,0.4),NA,
g(0.3,0.3),NA,
g(0.4,0.2),NA,
g(0.5,0.0),NA,
g(0.6,0.0),NA,
g(0.7,0.0),NA,
g(0.8,0.0),NA,
g(0.9,0.0),NA,
g(1.0,0.0),NA
)
plot(P(z=solid.lines,params=p),xlim=c(-4,4),ylim=c(-6,0),type="l",asp=1)
lines(P(z=dotted.lines,params=p),xlim=c(-4,4),ylim=c(-6,0),type="l",lty=2)