Dear Max, Yes! Thank you very much! Now I see why the output is correct. Super.
Greetings, Lisette > Dear Lisette, > > I think the "logic" comes from the orbit algorithm. It works about as > follows: > > l := [a]; > i := 1; > while i <= Length(l) do > for g in gens do > if not(l[i]^g in l) then > Add(l,l[i]^g); > fi; > od; > i := i + 1; > od; > > Of course the GAP library has an optimised version of this, but this > basically should explain the order of the things in the list you see. > > I think SymmetricGroup(9) will have > (1,2,3,4,5,6,7,8,9) and (1,2) > as generators, so the output you sent is exactly what I would expect > from the above algorithm. > > Cheers, > Max. > > On Tue, Jul 13, 2010 at 03:21:42PM +0200, Lisette Brillemans wrote: > > Dear Max, > > > > You're right. If you look at it this way you can say the answer given is > > of course entirely correct. However I am still wondering why the > > ordering of the second line in my example is somehow "unlogical" > > compared to the other lines. Is there some inconsistency in the > > algorithm? (I mean, why only when a = 2?) > > But if that's not the case then I apologize. > > > > Best regards, > > > > Lisette > > > > > > > Dear Lisette, > > > > > > as far as I see there is nothing incorrect. The documentation of > > > "Orbit" says that the result is the *list of all images* and not the > > > *set of all images*. Therefore it is OK that the list is not sorted. > > > The order of the elements you see depends on the starting point and > > > the generators of your group in general. Also, it is not guaranteed by > > > the documentation. > > > > > > If you need the orbit as a set just use > > > Set(Orbit(S,a)) > > > instead. > > > > > > I hope this is useful, if there are any other questions please do not > > > hesitate to ask again. > > > > > > Best regards, > > > Max Neunhoeffer > > > > > > On Tue, Jul 13, 2010 at 01:28:43PM +0200, Lisette Brillemans wrote: > > > > LS > > > > > > > > > > > > I'm using the latest version of GAP on linux and have read all the > > > > bugfixes but didn't find this one: > > > > > > > > If you type this: > > > > > > > > > > > > S:=SymmetricGroup(9); > > > > for a in [1..9] do > > > > Print(Orbit(S,a),"\n"); > > > > od; > > > > > > > > The output is as follows: > > > > > > > > [1,2,3,4,5,6,7,8,9] > > > > [2,3,1,4,5,6,7,8,9] > > > > [3,4,5,6,7,8,9,1,2] > > > > [4,5,6,7,8,9,1,2,3] > > > > [5,6,7,8,9,1,2,3,4] > > > > [6,7,8,9,1,2,3,4,5] > > > > [7,8,9,1,2,3,4,5,6] > > > > [8,9,1,2,3,4,5,6,7] > > > > [9,1,2,3,4,5,6,7,8] > > > > > > > > The problem is the second line: > > > > > > > > [2,3,1,4,5,6,7,8,9] > > > > > > > > Which, according to me, is incorrect. > > > > > > > > But apart from that GAP is a splendid program which possibilities still > > > > surprise me everyday. > > > > > > > > With regards. > > > > > > > > Lisette Brillemans > > > > Rotterdam, Holland > > > > > > > > > > > > _______________________________________________ > > > > Support mailing list > > > > [email protected] > > > > http://mail.gap-system.org/mailman/listinfo/support > > > > > > > > _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
