as.primitive {elliptic} R Documentation

## Converts basic periods to a primitive pair

### Description

Given a pair of basic periods, returns a primitive pair and (optionally) the unimodular transformation used.

### Usage

as.primitive(p, n = 3, tol = 1e-05, give.answers = FALSE)
is.primitive(p, n = 3, tol = 1e-05)


### Arguments

 p Two element vector containing the two basic periods n Maximum magnitude of matrix entries considered tol Numerical tolerance used to determine reality of period ratios give.answers Boolean, with TRUE meaning to return extra information (unimodular matrix and the magnitudes of the primitive periods) and default FALSE meaning to return just the primitive periods

### Details

Primitive periods are not unique. This function follows Chandrasekharan and others (but not, of course, Abramowitz and Stegun) in demanding that the real part of p1, and the imaginary part of p2, are nonnegative.

### Value

If give.answers is TRUE, return a list with components

 M The unimodular matrix used p The pair of primitive periods mags The magnitudes of the primitive periods

### Note

Here, “unimodular” includes the case of determinant minus one.

### Author(s)

Robin K. S. Hankin

### References

K. Chandrasekharan 1985. Elliptic functions, Springer-Verlag

### Examples

as.primitive(c(3+5i,2+3i))
as.primitive(c(3+5i,2+3i),n=5)

##Rounding error:
is.primitive(c(1,1i))

## Try
is.primitive(c(1,1.001i))



[Package elliptic version 1.4-0 Index]