# coqueraux

From elliptic v1.4-0
by Robin K S Hankin

##### Fast, conceptually simple, iterative scheme for Weierstrass P functions

Fast, conceptually simple, iterative scheme for Weierstrass \(\wp\) functions, following the ideas of Robert Coqueraux

- Keywords
- math

##### Usage

`coqueraux(z, g, N = 5, use.fpp = FALSE, give = FALSE)`

##### Arguments

- z
Primary complex argument

- g
Invariants; if an object of type

`parameters`

is supplied, the invariants will be extracted appropriately- N
Number of iterations to use

- use.fpp
Boolean, with default

`FALSE`

meaning to*not*reduce`z`

to the fpp. Setting to`TRUE`

reduces`z`

to the fpp via`parameters()`

: this is more accurate (see example) but slower- give
Boolean, with

`TRUE`

meaning to return an estimate of the error, and`FALSE`

meaning to return just the value

##### References

R. Coqueraux, 1990. *Iterative method for calculation of the
Weierstrass elliptic function*, IMA Journal of Numerical Analysis,
volume 10, pp119-128

##### Examples

```
# NOT RUN {
z <- seq(from=1+1i,to=30-10i,len=55)
p <- P(z,c(0,1))
c.true <- coqueraux(z,c(0,1),use.fpp=TRUE)
c.false <- coqueraux(z,c(0,1),use.fpp=FALSE)
plot(1:55,abs(p-c.false))
points(1:55,abs(p-c.true),pch=16)
# }
```

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

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