> In addition to what David Roe said, if I remember correctly MatrixGroups in
> Sage are implemented for matrices over finite fields. At some point I think it
> calls GAP for the computations.
>
> If your field is not finite, it might be better to use GAP directly
> since Sage only
> has infinite modular (matrix) groups implemented.
>
> If your field is not an abelian extension of QQ then even GAP lacks
> the functionality.
> If you need to do some *serious* computations
> in a finite matrix group defined over a non-abelian extension of QQ
> then you might try emailing the GAP support list, but of course no promises.

I just see your answer as well...

The field is the universal cyclotomic field (the smallest field
containing QQ and all complex roots of unities), and what I wanted to
do is to define a matrix group with generators being matrices in
cyclotomics. I thought that it would be a good idea to have the
possibility in sage to construct matrices in the UCF, play with them
and also have matrix groups with those. Are you saying it is difficult/
impossible to use the current implementation of MatrixGroup to make
this work?

Thanks, Christian

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