At 02:13 PM 9/30/02 +0200, you wrote: >Dear Gap-forum, and Christopher Jefferson, > > > I am dealing with a problem where I have a permutation group G defined > over > > the integers 1...n, generated by a set of generators S > > > > I want to find orbit(1), orbit(2) in "stabilizer of 1", orbit(3) in > > "stabilizer of 1 and stabilizer of 2", etc. > >OrbitList:=function(S,n) > local g,i,l; > g:=Group(S); l:=; > for i in [1..n] do > Append(l,[Orbit(g,i)]); > g:=Stabilizer(g,i); > od; > return l; >end; > >For example: >gap> OrbitList([(1,2,3),(2,4)],4); >[ [ 1, 2, 3, 4 ], [ 2, 4, 3 ], [ 3, 4 ], [ 4 ] ] > >Best regards, > > Jan
Thank you, this algorithm returns exactly what I want, and seems to do it
at lightening speed for any group I care to give it :)
However, for "neatness" of my paper, it would be nice to be able to write
that this took polynomial time in n and the number of generators of S I
give... could anyone tell me if I can indeed write this, or where I could
start looking to find out if I can write this?
Thank you all for lots of useful replies!