[GAP Forum] nested irrationals

[Bill Allombert]

On Mon, Apr 06, 2015 at 08:44:39PM +0100, Jim Talbert wrote:
> Hi all,
> 
> I have ay simple question.  I am utilizing GAP in a way that necessitates
> the construction of explicit matrix representations of group generators.
> These matrices can in my case depend on things like x^(1/4), e.g.
> ER(ER(x)).  However, the ER command can only deal with rational arguments,
> so ER(ER(16))=2 works fine, but ER(ER(8)) is problematic.  I have looked
> through the documentation and don't see an obvious way to get around the
> problem.  Can anyone help?

ER(ER(8)) is not a cyclotomic number, so it cannot be represented this way.

What you can do is to use the monomorphism:
GL_n(K(ER(x))) -> GL_(2*n)(K).
which replace the coefficient a+b*ER(x) by the matrix [[a,b*x],[b,a]]

You will get larger matrices with simpler coefficients.

Cheers,
Bill.