| as.primitive {elliptic} | R Documentation |
Given a pair of basic periods, returns a primitive pair and (optionally) the unimodular transformation used.
as.primitive(p, n = 3, tol = 1e-05, give.answers = FALSE) is.primitive(p, n = 3, tol = 1e-05)
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 |
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.
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 |
Here, “unimodular” includes the case of determinant minus one.
Robin K. S. Hankin
K. Chandrasekharan 1985. Elliptic functions, Springer-Verlag
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))