[GAP Forum] Square root of cyclotomic real number

[Marek Mitros]

Thank you for the answer. It is a pity, that I cannot obtain unitary matrix
from the set of orthogonal columns.
I must think of another method.

Regards,
Marek
13-05-2016 18:08 użytkownik "Alexander Hulpke" <hulpke at fastmail.fm> napisał:

> Dear Forum, Dear Marek Mitros,
>
> Sqrt (as a short hand for the ER cyclotomic) will only work for rational
> numbers. If you wanted a square root of a cyclotomic number you would need
> to factor x^2-a over a suitable cyclotomic field.
>
> Best,
>
>    Alexander Hulpke
>
> > On May 13, 2016, at 8:30 AM, Marek Mitros <marek at mitros.org> wrote:
> >
> > Dear All,
> >
> > I am doing following calculation and I need square root of cyclotomic
> > number being real number. Here is example below. Is there any workaround
> > for this ?
> > What I am doing I obtained vector v of complex number which not unit
> > length. In order to normalize it I perform following and I receive the
> > error. Do I need more knowledge about cyclotomic numbers ?
> >
> > gap> v1:=v/Sqrt(v*ComplexConjugate(v));
> >
> > Error, no method found! For debugging hints type ?Recovery from
> > NoMethodFound
> >
> > Error, no 1st choice method found for `Sqrt' on 1 arguments called from
> >
> > <function "HANDLE_METHOD_NOT_FOUND">( <arguments> )
> >
> > (...)
> >
> > gap> n:=E(20)-E(20)^9;
> >
> > E(20)-E(20)^9
> >
> > gap> RealPart(n);
> >
> > E(20)-E(20)^9
> >
> > gap> Sqrt(n);
> >
> > Error, no method found! For debugging hints type ?Recovery from
> > NoMethodFound
> >
> > Error, no 1st choice method found for `Sqrt' on 1 arguments called from
> >
> >
> > Regards,
> >
> > Marek
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>