I'm working (along with a summer research student) to expand the collection of small groups (and their representations) in Sage. A question about matrix groups, as built by GAP for Sage.
For small, not-very-sophisticated groups, such as a Dihedral group, is it preferable to concoct generators in Sage and use the generic MatrixGroup() constructor or use a GAP routine to build the group? A simple example: GAP: Wrap - "CyclicGroup( IsMatrixGroup, GF(2), 12 )" will build a matrix group of order 12 with matrices of size 12, over a few different types of fields. This is about as much freedom as GAP allows. Python: Mythical - CyclicMatrixGroup(n, R, dimension=None) to build a cyclic group of order n over R, but where "dimension" could default to n, or be sum of invariants, or sum of prime powers, or 1 over the cyclotomic field. Then an appropriate matrix could be created and sent to the MatrixGroup() (ideally as part of a class providing a sensible repr, etc.) The second approach allows for a lot more flexibility in providing representations of different dimensions. My question: is much lost by building the generators and computing the GAP group from those, versus using the built-in GAP named constructions? Again, I'm just interested right now about simpler matrix groups, not the classical groups like GL(), PSL(), etc. Thanks, Rob -- -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
