1Function: bnrclassnolist 2Section: number_fields 3C-Name: bnrclassnolist 4Prototype: GG 5Help: bnrclassnolist(bnf,list): if list is as output by ideallist or 6 similar, gives list of corresponding ray class numbers. 7Doc: $\var{bnf}$ being as 8 output by \kbd{bnfinit}, and \var{list} being a list of moduli (with units) as 9 output by \kbd{ideallist} or \kbd{ideallistarch}, outputs the list of the 10 class numbers of the corresponding ray class groups. To compute a single 11 class number, \tet{bnrclassno} is more efficient. 12 13 \bprog 14 ? bnf = bnfinit(x^2 - 2); 15 ? L = ideallist(bnf, 100, 2); 16 ? H = bnrclassnolist(bnf, L); 17 ? H[98] 18 %4 = [1, 3, 1] 19 ? l = L[1][98]; ids = vector(#l, i, l[i].mod[1]) 20 %5 = [[98, 88; 0, 1], [14, 0; 0, 7], [98, 10; 0, 1]] 21 @eprog 22 The weird \kbd{l[i].mod[1]}, is the first component of \kbd{l[i].mod}, i.e. 23 the finite part of the conductor. (This is cosmetic: since by construction 24 the Archimedean part is trivial, I do not want to see it). This tells us that 25 the ray class groups modulo the ideals of norm 98 (printed as \kbd{\%5}) have 26 respectively order $1$, $3$ and $1$. Indeed, we may check directly: 27 \bprog 28 ? bnrclassno(bnf, ids[2]) 29 %6 = 3 30 @eprog 31