[GAP Forum] Sqrt for the cyclotomic numbers

[Palcoux Sebastien]

Dear Alexander and Forum,
If the cyclotomic number is the square of a cyclotomic number, is there an easy way to find it?
The number I need are the eigenvalues of the matrix of the unitarized inner product of an irreducible representation of a finite group (see the comment of Paul Garett here: http://math.stackexchange.com/q/1107941/84284). This matrix is positive, I guess its eigenvalues are always cyclotomic (true for the examples I've looked, but I don't know in general), and I hope they are square of cyclotomic. Thanks to these square roots I can compute the unitary matrices for the irreducible representation.
Remark: a function on GAP computing the unitary irreducible representations seems very natural, so if there is not such a function, this should means that there are problems for computing them in general with GAP, isn't it?
Best regards,Sebastien Palcoux        

     Le Mardi 20 janvier 2015 3h13, Alexander Hulpke <hulpke at fastmail.fm> a écrit :
   

 Dear Forum,

> On Jan 19, 2015, at 1/19/15 2:18, Palcoux Sebastien <sebastienpalcoux at yahoo.fr> wrote:
> 
> Hi,
> Is it possible to extend the function Sqrt on the cyclotomic numbers?

How would you represent this root? In general the square root of a cylotomic is not cyclotomic again. (You could form a formal AlgebraicExtension, but then you lose the irrational cyclotomics for operations.)

Regards,

  Alexander Hulpke