On 01/23/2017 05:37 AM, Waldek Hebisch wrote:
Martin Baker wrote:
Patch is here:
https://github.com/martinbaker/fricasAlgTop/blob/master/permgrps1.patch
I have tried it now. AFAICS it is _extremally_ inefficient:
coerce(symmetricGroup(4))@GroupPresentation crashes due to
running out of memory (tested on sbcl with default 1GB limit),
coerce(dihedralGroup(7))@GroupPresentation works but takes
a lot of time and produces large presentation.
Waldek,
Thank you for looking at this. I did not find a published algorithm for
this so I just worked out a simple algorithm myself, I did not think
much about efficiency I was just happy to hit on a method that worked.
The main issue is finding the relations. It seems to me that each
relation corresponds to a loop in the Cayley graph.
So I just wrote an algorithm that found all the relations (loops) by
doing a tree search of the Cayley graph. Obviously this finds a lot of
redundant rules (loops).
Am I correct in thinking that the algorithm that you are proposing is
more efficient because it uses a stabilizer chain (sequence of
subgroups, each containing the next and each stabilizing one more
point). So when we work out the loops in the subgroup we implicitly
encode information about the loops in the cosets so we consider less loops?
Martin B
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