half.periods {elliptic}R Documentation

Calculates half periods in terms of e

Description

Calculates half periods in terms of e

Usage

half.periods(ignore=NULL, e=NULL, g=NULL, primitive)

Arguments

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.

Details

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.

Value

Returns a pair of primitive half periods

Note

Function parameters() uses function half.periods() internally, so do not use parameters() to determine e.

Author(s)

Robin K. S. Hankin

References

AMS-55

Examples


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))

[Package elliptic version 0.4-14 Index]