The spring layout is "accidentally" finding the normal subgroup
{+/-1}. If we look at a smaller subgraph, the problem should be
apparent.
G= SL(2, ZZ)
S, T= G.gens(); ST= S*T
L= [S^i*ST^j for i in range(4) for j in range(3)]
els= Set([ a*b for a in L for b in L])
gr= G.cayley_graph(generators = [S, ST], elements= els)
gr.plot(color_by_label= True, iterations= 500, vertex_labels=False,
vertex_size= 1, scale=10 ) #for example
On Tue, Mar 13, 2012 at 1:27 PM, Pierre <pierre.guil...@gmail.com> wrote:
> Dear Tom,
>
> Thanks for your answer! I get the empty set, too. I really wonder what
> is going on with the picture though... if one cannot "rely on the
> picture", then it pretty much defeats the purpose when it comes to
> Cayley graphs, doesn't it?
>
> and i mean, there *is* a double arrow on some edges.
>
> thanks again,
> pierre
>
> On 13 mar, 13:50, Tom Boothby <tomas.boot...@gmail.com> wrote:
>> Pierre,
>>
>> Don't rely on the picture!
>>
>> sage: U = set(gr.edges())
>> sage: V = set(gr.reverse().edges())
>> sage: U.intersection(V) #for me, this is the empty set
>>
>>
>>
>>
>>
>>
>>
>> On Tue, Mar 13, 2012 at 3:26 AM, Pierre <pierre.guil...@gmail.com> wrote:
>> > Hi,
>>
>> > I've been playing with Cayley graphs in Sage (thanks to whoever
>> > implemented this!) I got funny results on one example, and I'd like to
>> > understand.
>>
>> > I've tried SL(2, ZZ):
>>
>> > sage: G= SL(2, ZZ)
>> > sage: S, T= G.gens(); ST= S*T
>> > sage: L= [S^i*ST^j for i in range(4) for j in range(3)] #S has order
>> > 4, ST has order 3
>> > sage: els= Set([ a*b*c*d for a in L for b in L for c in L for d in L])
>> > sage: gr= G.cayley_graph(generators = [S, ST], elements= els)
>> > sage: gr.show(color_by_label= True, iterations= 500, vertex_labels=
>> > False, vertex_size= 1, dpi= 800)) #for example
>>
>> > I don't know how to attach a picture to this message, so I'll have to
>> > describe the result as very close to the Cayley graph of PSL(2, ZZ)
>> > rather than SL(2, ZZ)!! it looks as if one of my generators has order
>> > 2!!
>>
>> > does anyone know what is going on?
>>
>> > thanks!
>> > Pierre
>>
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