Is there a reason you can't use finite cyclotomic fields? These exist in Sage and are reasonably well optimized. And GAP supports matrix groups over them, though as David Joyner mentioned, I don't think that functionality is wrapped from Sage. Defining matrix groups over finite cyclotomic fields and wrapping some Gap functionality for them would be cool. David
On Sat, Oct 16, 2010 at 17:12, Christian Stump <christian.st...@gmail.com>wrote: > > This would be an infinite group which I think is not implemented in Sage > or GAP. > > I can't even imagine a way that GAP could help, but it can't hurt to > > ask in the GAP support list. Maybe there is an "approximation" someone > could > > think of that might help. Please be as specific as possible when > formulating > > your question though. > > Sorry if my question and explanation is not exact enough! I don't want > the group of all matrices over the cyclotomics, but only a matrix > group with some generators: E.g., I would like the following for UCF > being the universal cyclotomic field: > > M = matrix( UCF, 1, [ E(3) ] ) > G = MatrixGroup( [ M ] ) > > or, a little more interesting: > > gens = [ matrix( UCF, 2, [ E(3), 0, 0, E(4) ] ), matrix( UCF, 2, [ - > E(3), 0, 0, -1 ] ) ] > G = MatrixGroup( gens ) > > The same is already possible in gap: > > gap> G := GroupWithGenerators( [ [[E(3)]] ] ); > Group([ [ [ E(3) ] ] ]) > gap> Number( Elements( G ) ); > 3 > gap> G := GroupWithGenerators( [ [[E(3),0],[0,E(4)]], [[-E(3),0], > [0,-1]] ] ); > Group([ [ [ E(3), 0 ], [ 0, E(4) ] ], [ [ -E(3), 0 ], [ 0, -1 ] ] ]) > gap> > Number( Elements( G ) ); > 24 > > I thought, having UCF in sage available, this would be nice to have as > well. > > Thanks, Christian > > -- > To post to this group, send an email to sage-devel@googlegroups.com > To unsubscribe from this group, send an email to > sage-devel+unsubscr...@googlegroups.com<sage-devel%2bunsubscr...@googlegroups.com> > For more options, visit this group at > http://groups.google.com/group/sage-devel > URL: http://www.sagemath.org > -- To post to this group, send an email to sage-devel@googlegroups.com To unsubscribe from this group, send an email to sage-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
