pari: Wrappers for PARI functions
In elliptic: Weierstrass and Jacobi Elliptic Functions

Description Usage Arguments Details Value Note Author(s) References Examples

Wrappers for the three elliptic functions of PARI

1	P.pari(z,Omega,pari.fun="ellwp",numerical=TRUE)

`z`	Complex argument
`Omega`	Half periods
`pari.fun`	String giving the name of the function passed to PARI. Values of `ellwp`, `ellsigma`, and `ellzeta`, are acceptable here for the Weierstrass P function, the sigma function, and the zeta function respectively
`numerical`	Boolean with default `TRUE` meaning to return the complex value returned by PARI, and `FALSE` meaning to return the ascii string returned by PARI

This function calls PARI via an R system() call.

Returns an object with the same attributes as z.

Function translates input into, for example, “ellwp([1+1*I,2+3*I],1.111+5.1132*I)” and pipes this string directly into gp.

The PARI system clearly has more powerful syntax than the basic version that I'm using here, but I can't (for example) figure out how to vectorize any of the calls.

Robin K. S. Hankin

http://www.parigp-home.de/

## Not run:  #this in a dontrun environment because it requires pari/gp 
z  <- seq(from=1,to=3+2i,len=34)
p <- c(1,1i)
plot(abs(P.pari(z=z,Omega=p) - P(z=z,Omega=p)))
plot(zeta(z=z,params=parameters(Omega=p))- P.pari(z=z,Omega=c(p),pari.fun="ellzeta"))


## End(Not run)