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[sage-devel] Re: Fwd: [sage-combinat-devel] permutation group perspectives Rob Beezer Sun May 30 18:00:11 2010

On May 30, 2:46 pm, Mike Hansen <[EMAIL PROTECTED]> wrote:
> I've been working on this over the next few days, cleaning up the
> code, and making permutation groups act over an "arbitrary" domain.
> I'll be posting these in the next few days.

Mike H - thanks for your work on this!

Mike O'S - that's a great wish list.  I'd like to see lots of that
happen.  Another item on my wish list is to build a quotient group and
have its elements (optionally) actually be cosets.  Right now for
permutation groups you get back a new permutation group:

sage: D=DihedralGroup(7)
sage: H=D.subgroup([D((1,2,3,4,5,6,7))])
sage: Q=D.quotient(H)
sage: Q.list()
[(), (1,2)]

Maybe with a new "coset" class and Mike's arbitrary domains this would
be easy to implement?

I've brought this one up before.  How do folks feel about having the
named permutation groups available like graphs are?  In other words,
rather than each family of permutation groups being a new class, there
is a single system-wide object ("groups", or "perm_groups") whose
methods produce instances of permutation groups (or more generally,
just groups).  So for example,

D=groups.DihedralGroup(7)

would replace the above syntax.  Advantages - namespace is less
cluttered, and tab-completion (groups.<tab>) gives precise one-stop
shopping for examples of specific groups.

Rob

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