parameters {elliptic}  R Documentation 
Calculates the invariants g_2
and g_3
,
the evalues e_1,e_2,e_3
, and the half periods
\omega_1,\omega_2
, from any one of them.
parameters(Omega=NULL, g=NULL, description=NULL)
Omega 
Vector of length two, containing the half
periods 
g 
Vector of length two:

description 
string containing “equianharmonic”, “lemniscatic”, or “pseudolemniscatic”, to specify one of A and S's special cases 
Returns a list with the following items:
Omega 
A complex vector of length 2 giving the fundamental half
periods The relevant periods are made unique by the further requirement that
Note Different definitions exist for 
q 
The nome. Here,

g 
Complex vector of length 2 holding the invariants 
e 
Complex vector of length 3. Here
where Note that the 
Delta 
The quantity 
Eta 
Complex vector of length 3 often denoted
Note that the name of this element is capitalized to avoid confusion
with function 
is.AnS 
Boolean, with 
given 
character string indicating which parameter was supplied.
Currently, one of “ 
Robin K. S. Hankin
## Example 6, p665, LHS
parameters(g=c(10,2+0i))
## Example 7, p665, RHS
a < parameters(g=c(7,6)) ; attach(a)
c(omega2=Omega[1],omega2dash=Omega[1]+Omega[2]*2)
## verify 18.3.37:
Eta[2]*Omega[1]Eta[1]*Omega[2] #should be close to pi*1i/2
## from Omega to g and and back;
## following should be equivalentto c(1,1i):
parameters(g=parameters(Omega=c(1,1i))$g)$Omega