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Right now in for group cosets resorts to iterating over the coset, which is very inefficient.
We should provide a custom method for this. I would not dispatch to GAP's, but instead implement this "directly": i.e. to test g in Hx, test if g/x in H and similar for g in xH (so that we avoid creating GapObj for those).
Speaking of iterators, the iterate implementation for GroupCoset currently directly wraps a GAP coset iterator. But (a) this requires creating a GapObj (with extra overhead for left cosets). And furthermore on the GAP side, the iterator is a wrapper for an enumerator.
Instead, the Julia iterator for a coset C could be based on the group iterator for C.H.
Right now
in
for group cosets resorts to iterating over the coset, which is very inefficient.We should provide a custom method for this. I would not dispatch to GAP's, but instead implement this "directly": i.e. to test
g in Hx
, test ifg/x in H
and similar forg in xH
(so that we avoid creatingGapObj
for those).Speaking of iterators, the
iterate
implementation forGroupCoset
currently directly wraps a GAP coset iterator. But (a) this requires creating aGapObj
(with extra overhead for left cosets). And furthermore on the GAP side, the iterator is a wrapper for an enumerator.Instead, the Julia iterator for a coset
C
could be based on the group iterator forC.H
.Lastly, contrast
versus
I suggest we use something like this:
And then I assume similar for
GroupDoubleCoset
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