Function: idealprincipalunits
Section: number_fields
C-Name: idealprincipalunits
Prototype: GGL
Help: idealprincipalunits(nf,pr,k): returns the structure [no, cyc, gen]
 of the multiplicative group (1 + pr) / (1 + pr^k).
Doc: given a prime ideal in \tet{idealprimedec} format,
 returns the multiplicative group $(1 + \var{pr}) / (1 + \var{pr}^{k})$ as an
 abelian group. This function is much faster than \tet{idealstar} when the
 norm of \var{pr} is large, since it avoids (useless) work in the
 multiplicative group of the residue field.
 \bprog
 ? K = nfinit(y^2+1);
 ? P = idealprimedec(K,2)[1];
 ? G = idealprincipalunits(K, P, 20);
 ? G.cyc
 %4 = [512, 256, 4]   \\ Z/512 x Z/256 x Z/4
 ? G.gen
 %5 = [[-1, -2]~, 1021, [0, -1]~] \\ minimal generators of given order
 @eprog
