as.primitive: 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
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
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.
References
K. Chandrasekharan 1985. Elliptic functions, Springer-Verlag