> 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

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