# pari

##### 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

##### 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*