On 01/26/2017 09:04 PM, Kurt Pagani wrote:
Hi Martin
I've also tried your code and must confirm Waldek's statements. I guess there
are some pitfalls which are known for some time.
Did you read "Implementation and Analysis of the Todd-Coxeter Algorithm"
by Cannon et al.? Old but still beneficial.
http://staff.itee.uq.edu.au/havas/1973cdhw.pdf
Maybe you should alo have a look at sympy:
http://docs.sympy.org/dev/modules/combinatorics/fp_groups.html
where the article above is also cited.
Otherwise I see much progress.
Kurt
Hi Kurt,
Yes, lots more to do but I'm encouraged by progress so far.
I had not seen the Cannon et al. paper. This looks very useful
especially for thinking about variations in the algorithm and what its
ultimate limitations might be. Mostly for Todd-Coxeter Algorithm I
looked at this paper by Akos Seress:
http://www.ams.org/notices/199706/seress.pdf
because it has a worked example.
For the other direction (PermutationGroup to GroupPresentation) I did
not find a published algorithm for this so I just did a tree search for
loops in the Cayley graph.
Initially a was just happy to find algorithms that worked in each
direction albeit for small groups. However now, of course, I am keen to
get these implementations to scale up as much as possible.
Before I look at the above paper in more detail I think I need to get
the basics right and to absorb the information that Waldek posted about
cosets and strong generators and to modify the code to remove
'coincidences'.
By the way, I think the posts from Waldek about GroupPresentation are
very useful. I think it would be good if all that information could be
put together somewhere where it can be found by potential developers in
the future.
Martin B
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