[GAP Forum] Square root of cyclotomic real number

[Alexander Hulpke]

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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