On Sat, Oct 16, 2010 at 5:12 PM, 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 )
Does this help? sage: K = CyclotomicField(12) # 12 = 4*3 sage: K.gens() (zeta12,) sage: z = K.gens()[0] sage: z zeta12 sage: E3 = z^4 sage: E4 = z^3 sage: gens = [ matrix( K, 2, [ E3, 0, 0, E4 ] ), matrix( K, 2, [ -E3, 0, 0, -1 ] ) ] sage: G = MatrixGroup( gens ) sage: G.order() 24 > > 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 > 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
