Im<-                    Manipulate real or imaginary components of an
                        object
J                       Various modular functions
K.fun                   quarter period K
P.laurent               Laurent series for elliptic and related
                        functions
WeierstrassP            Weierstrass P and related functions
amn                     matrix a on page 637
as.primitive            Converts basic periods to a primitive pair
ck                      Coefficients of Laurent expansion of
                        Weierstrass P function
congruence              Solves mx+by=1 for x and y
coqueraux               Fast, conceptually simple, iterative scheme for
                        Weierstrass P functions
divisor                 Number theoretic functions
e16.28.1                Numerical verification of equations 16.28.1 to
                        16.28.5
e18.10.9                Numerical checks of equations 18.10.9-11, page
                        650
e1e2e3                  Calculate e1, e2, e3 from the invariants
elliptic-package        Weierstrass and Jacobi Elliptic Functions
equianharmonic          Special cases of the Weierstrass elliptic
                        function
eta                     Dedekind's eta function
farey                   Farey sequences
fpp                     Fundamental period parallelogram
g.fun                   Calculates the invariants g2 and g3
half.periods            Calculates half periods in terms of e
latplot                 Plots a lattice of periods on the complex plane
lattice                 Lattice of complex numbers
limit                   Limit the magnitude of elements of a vector
massage                 Massages numbers near the real line to be real
mob                     Moebius transformations
myintegrate             Complex integration
near.match              Are two vectors close to one another?
newton_raphson          Newton Raphson iteration to find roots of
                        equations
nome                    Nome in terms of m or k
p1.tau                  Does the right thing when calling g2.fun() and
                        g3.fun()
parameters              Parameters for Weierstrass's P function
pari                    Wrappers for PARI functions
sn                      Jacobi form of the elliptic functions
sqrti                   Generalized square root
theta                   Jacobi theta functions 1-4
theta.neville           Neville's form for the theta functions
theta1.dash.zero        Derivative of theta1
theta1dash              Derivatives of theta functions
unimodular              Unimodular matrices
view                    Visualization of complex functions

## Example 8, p666, RHS:
 P(z=0.07 + 0.1i, 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,"+")
 par(pty="s")
 view(x,x,limit(zeta(z,c(1+1i,2-3i))),nlevels=3,scheme=1)
 view(x,x,P(z*3,params=equianharmonic()),real=FALSE)

     ## Some number theory:
 mobius(1:10)
 plot(divisor(1:300,k=1),type="s",xlab="n",ylab="divisor(n,1)")

    ## Primitive periods:
 as.primitive(c(3+4.01i , 7+10i))
 as.primitive(c(3+4.01i , 7+10i),n=10)   # Note difference

    ## Now some contour integration:
 f <- function(z){1/z}
 u <- function(x){exp(2i*pi*x)}
 udash <- function(x){2i*pi*exp(2i*pi*x)}
 integrate.contour(f,u,udash) - 2*pi*1i


 x <- seq(from=-10,to=10,len=200)
 z <- outer(x,1i*x,"+")
 view(x,x,P(z,params=lemniscatic()),real=FALSE)
 view(x,x,P(z,params=pseudolemniscatic()),real=FALSE)
 view(x,x,P(z,params=equianharmonic()),real=FALSE)