bnrclassnolist

Function: bnrclassnolist
Section: number_fields
C-Name: bnrclassnolist
Prototype: GG
Help: bnrclassnolist(bnf,list): if list is as output by ideallist or
 similar, gives list of corresponding ray class numbers.
Doc: $\var{bnf}$ being as
 output by \kbd{bnfinit}, and \var{list} being a list of moduli (with units) as
 output by \kbd{ideallist} or \kbd{ideallistarch}, outputs the list of the
 class numbers of the corresponding ray class groups. To compute a single
 class number, \tet{bnrclassno} is more efficient.

 \bprog
 ? bnf = bnfinit(x^2 - 2);
 ? L = ideallist(bnf, 100, 2);
 ? H = bnrclassnolist(bnf, L);
 ? H[98]
 %4 = [1, 3, 1]
 ? l = L[1][98]; ids = vector(#l, i, l[i].mod[1])
 %5 = [[98, 88; 0, 1], [14, 0; 0, 7], [98, 10; 0, 1]]
 @eprog
 The weird \kbd{l[i].mod[1]}, is the first component of \kbd{l[i].mod}, i.e.
 the finite part of the conductor. (This is cosmetic: since by construction
 the Archimedean part is trivial, I do not want to see it). This tells us that
 the ray class groups modulo the ideals of norm 98 (printed as \kbd{\%5}) have
 respectively order $1$, $3$ and $1$. Indeed, we may check directly:
 \bprog
 ? bnrclassno(bnf, ids[2])
 %6 = 3
 @eprog