On 08/10/16 12:54, Waldek Hebisch wrote:
Some statements there look wrong. For example:
+We can generate a subgroup by either removing a generator or
+adding a relation.
By adding a relation you form _quotient_ group. Maybe you
think about kernel of quotient map, which indeed is a
subgroup. But it requires nontrivial computation to
find presentation of the kernel. In general, to get a
subgroup you specify new generators which are words in
terms of generators of larger group. Another way is to
specify a predicate so that the subgroup consists of
elements satisfying the predicate. Again, it may be
tricky to find presentation of such subgroup. And
one needs to use appropriate predicate, otherwise
elements satisfying the predicate do not form a
subgroup.
BTW: You can get arbitrary quotient by adding relations
(possibly infintely many relations).
Well my thinking went like this:
1) I want conversions between PermutationGroup and GroupPresentation.
2) To do this I want to implement Todd–Coxeter algorithm.
3) To do that I need to enumerate the cosets.
4) To implement cosets I need a subgroup.
But I have not had time to study Todd–Coxeter algorithm. Until I
investigate it I don't really know what I want.
Would it be possible to commit the patch without the suspect words? Then
I can take longer to investigate.
Martin B
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