On Thursday, 19 July 2012 08:13:04 UTC+8, Rob Beezer wrote: > > 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. >
It looks like a hack. IMHO representations and groups themselves should not be mixed in one glass. Moreover, your approach does not go far enough, as representations of Z_n might be quite exotic thing, as soon as n is divisible by the characteristic of the field R, or when R isn't a field any more... (and even in characteristic 0, when your field does not contain the splitting field of the group, things are rather nontrivial, IMHO) Dima > > 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
