as.primitive: Converts basic periods to a primitive pair

In RobinHankin/elliptic: Weierstrass and Jacobi Elliptic Functions

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))

RobinHankin/elliptic documentation built on Feb. 21, 2024, 6:28 a.m.