Calculates half periods in terms of e
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 |
primitive |
Boolean, with default |
Parameter e=c(e1,e2,e3) are the values of the Weierstrass
P function at the half 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)) g.fun(half.periods(g=c(8,4))) ## should be c(8,4)
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