| half.periods {elliptic} | R Documentation |
Calculates half periods in terms of e
half.periods(ignore=NULL, e=NULL, g=NULL, primitive)
e |
e |
g |
g |
ignore |
Formal argument present to ensure that e or
g is named (ignored) |
primitive |
Boolean, with default TRUE meaning to return
primitive periods and FALSE to return the direct result of
Legendre's iterative scheme |
Parameter e=c(e1,e2,e3) are the values of the
Weierstrass P function at the periods:
e1=P(omega1), e2=P(omega2), e3=p(omega3)
where omega1+omega2+omega3=0.
Also, e is given by the roots of the cubic equation x^3-g2*x-g3=0, but the problem is finding which root corresponds to which of the three elements of e.
Returns a pair of primitive half periods
Function parameters() uses function half.periods()
internally, so do not use parameters()
to determine e.
Robin K. S. Hankin
M. Abramowitz and I. A. Stegun 1965. Handbook of Mathematical Functions. New York, Dover.
half.periods(g=c(8,4)) ## Example 6, p665, LHS u <- half.periods(g=c(-10,2)) massage(c(u[1]-u[2] , u[1]+u[2])) ## Example 6, p665, RHS half.periods(g=c(10,2)) ## Example 7, p665, LHS u <- half.periods(g=c(7,6)) massage(c(u[1],2*u[2]+u[1])) ## Example 7, p665, RHS half.periods(g=c(1,1i, 1.1+1.4i)) half.periods(e=c(1,1i, 2, 1.1+1.4i))