Faster class group computations using norm relations Examples : Kummer fields Q(ζn, a 1/n 1 , . . . , a 1/n k ) : ? pol = kummer(3,[2,3,5]); ? abbnf = abelianbnfinit(pol); cpu time = 4,549 ms. ? getcyc(abbnf) % = [6, 6, 3]