On Fri, Apr 18, 2014 at 09:17:16AM -0700, Volker Braun wrote:
> The problem is that we don't have an algorithm to find out that the group
> is finite (short of generating all elements). So it is placed in the
> "Groups" category instead of "FiniteGroups", and that doesn't have an
> iterator. There should be an in-between category of finitely generated
> groups which provides the iterator. In any case, a workaround is:
> sage: list(TransitiveIdeal(lambda x:[g*x for g in G4.gens()], [G4.one()]))
> [ [1 0] [ w 0] [ 1 -w - 1] [ w 1] [ 0 -w - 1]
> [ [0 1], [w + 1 1], [ 0 w], [w + 1 0], [ -1 w],
> [-w - 1 w] [ 1 -w] [ w w + 1] [-w - 1 -1]
> [ w w + 1], [ 0 -w - 1], [w + 1 -w], [ w 0],
> [ -w 0] [ 0 1] [ 0 w] [ w + 1 -w] [ -w -1]
> [-w - 1 -1], [-1 0], [ -1 w + 1], [ -w -w - 1], [-w - 1 0],
> [ -1 w + 1] [ 0 w + 1] [-w - 1 0] [ -w -w - 1]
> [ 0 -w], [ 1 -w], [ w 1], [-w - 1 w],
> [w + 1 1] [ -1 w] [ 0 -1] [w + 1 0] [-1 0]
> [ -w 0], [ 0 w + 1], [ 1 0], [ -w -1], [ 0 -1],
> [ 0 -w] ]
> [ 1 -w - 1] ]
If you know your group is finite, you should be able to do (not tested):
sage: G4._refine_category(FiniteGroups())
We should probably add a "category" optional argument to MatrixGroup,
so that we can specify this when we build the group.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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