[GAP Forum] [GAP Support] I think I found a bug.

[Lisette Brillemans]

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
> > > > Support at gap-system.org
> > > > http://mail.gap-system.org/mailman/listinfo/support
> > > 
> > 
> > 
>