[GAP Forum] Sqrt(1+2i)

[Bill Allombert]

On Wed, Oct 03, 2012 at 02:13:18PM +0200, Marek Mitros wrote:
> Dear Forum Users,
> 
> I need to calculate Sqrt(1+2i) i.e. find the complex number z=a+bi
> such that z^2=(1+2i). Using traditional pen and paper I calculated
> that a=Sqrt((1+Sqrt(5))/2) and b=Sqrt((Sqrt(5)-1)/2). But how to
> express these numbers in GAP ? Is this number cyclotomic or not ?

This number is not cyclotomic (mostly because 5 is not a square in Z).

x:=Indeterminate(Rationals,"x");
t:=GaloisType((x^2-1)^2+4);
IsAbelian(TransitiveGroup(4,t));

false

Cheers,
Bill.