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 <[email protected]> a
écrit :
Dear Forum,
> On Jan 19, 2015, at 1/19/15 2:18, Palcoux Sebastien
> <[email protected]> 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
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