sopsku <rrburns@...> writes: > > Dear Forum, > > How do I define the group of units of Z_n[i] in GAP? In particular I > ultimately want to determine isomorphism classes of these groups. I assume > that once I have properly defined the group of units I can then just use > StructureDescription, but any help in actually defining the isomorphism > would be appreciated. > > Thank you for your help. > > Ron >
After some thought I tried working the polynomial ring isomorphic to Z_n[i]. Below is is what I have come up with. Is there a better way to do this in gap (aside from my simplistic coding)? n:=7; x:=Indeterminate(GF(n),"x"); r:=PolynomialRing(GF(n)); p:=x^2+1; i:=Ideal(r,[p]); q:=r/i; List(last); g:=Units(q); ele:=List(g); ord:=Length(ele); gorders:=Collected(List(ele,Order)); asg:=AllSmallGroups(ord);; ordersasg:=List([1..Length(asg)],x->Collected(List(asg[x],Order))); pos:=Position(List(ordersasg,x->x=gorders),true); StructureDescription(asg[pos]); Again thanks for any help given. Ron _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
