# pari

0th

Percentile

##### Wrappers for PARI functions

Wrappers for the three elliptic functions of PARI

Keywords
math
##### Usage
P.pari(z,Omega,pari.fun="ellwp",numerical=TRUE)
##### Arguments
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 $\wp$ 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

##### Details

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

##### Value

Returns an object with the same attributes as z.

##### Note

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.

##### References

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

• pari
• PARI
• P.pari
• gp
• GP
• Gp
##### Examples
# 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"))

# }

Documentation reproduced from package elliptic, version 1.4-0, License: GPL-2

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