Javier,

[...]
>
> So, it wasn't that hard (for matrices) after all.
Good!
> I don't know whether/
> how this can be applied to the E(9) thing unless there is an
> IsSomething gap method that can be used for them.
Sure, there is
IsCyclotomic
and IsIntegralCyclotomic
for cyclotomics, resp., cyclotomic integers:

gap> IsIntegralCyclotomic(E(9));
true
gap> Field(E(9));
CF(9)


and

IsFFE for finite field elements:

gap> IsFFE(Z(5));
true
gap> Field(Z(5));
GF(5)

for more general fields and for rings it's also doable...

Cheers,
Dima
>
> I'll prepare some doctests and upload a first patch.
>
> Cheers
> J
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