Ok here is the setting. It is rather specific.
I have a group G (W(E8) in this example) and a left G equivariant
equivalence relation R on it. R is not known directly, but for any g in G
and any subset S of G I can efficiently check (complexity O(1)) if g is
equivalent to any element in S. I want to find representatives for G/R.
Of course this is equivalent to determining the subgroup H={h in G | h ~ 1}
and a set of representatives for G/H.
So what I do is I start with H={1}, S={1} and iterate over representatives
of g of G/H. If g is not equivalent to any element in S then I add g to S.
If g is equivalent to an element s in S then h=g^-1 s ~ 1 and I replace H
with the subgroup generated by H and h and repeat.
The algorithm stops when |H| |S|=|G|. It works very efficiently, as long
as G/R is not too big (even if G itself is big).
Best,
Michel
On Thursday, February 5, 2026 at 4:33:15 PM UTC+1 wrote:
In case you just want a permutation action of W on the cosets of G, you can
avoid dealing with cosets all together.
sage: f=libgap(W).FactorCosetAction(libgap(G)).Image()
sage: f.OrbitLength(1)
138240
In fact, libgap(W).FactorCosetAction(libgap(G)) is a proper group
homomorphism, so you can go back and forth between W and f.
If you explain what you wanted to do with your coset representatives, I
can say more...
Dima
On Thursday, February 5, 2026 at 6:15:17 AM UTC-6 wrote:
Hmm I have to retract this last post.Using
for i in range(0, len(R)):
w = W(R[i])
still triggers the bug.
Best,
Michel
On Thursday, February 5, 2026 at 12:57:16 PM UTC+1 Michel VAN DEN BERGH
wrote:
On Thursday, February 5, 2026 at 12:15:21 PM UTC+1 wrote:
As a workaround, I think that explicitly converting the gap list returned
by libgap.RightTransversal(W, G) into a python list helps. I.e.,
list(libgap.RightTransversal(W, G))
Martin
I use this initially also for G=trivial (basically I am trying to
incrementally build the stabilizer of something by iterating over the
cosets of a stabilizing group already found) so constructing a list of
which only a small part will be consumed is a bit inconvenient. However
your issue suggests to use
for i in range(0, len(R)):
w = W(R[i])
This seems to work perfectly!
I must say that I am mildly surprised that this works. I was guessing that
the coset representatives would be found on the fly in some way.
In any case: thanks for investigating and filing the issue!
Best,
Michel
On Thursday, 5 February 2026 at 11:16:52 UTC+1 Martin R wrote:
That's a huge example.
sage: len(libgap.RightTransversal(W, G))
138240
I think it is a gap bug, I am checking right now.
On Thursday, 5 February 2026 at 07:46:47 UTC+1 wrote:
> This is very strange code - you are attempting to change the variable of
a loop inside a loop.
>
> What do you mean to do here?
>
> Dima
Well that's not the point. Writing v=W(w) gives the same bug...
Best,
Michel
PS. This was just some quick test code, but this being said, I think
assigning to a loop variable is fine. This does not influence the state of
the iterator. A quick test confirms this.
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