Dear GAP Forum,

On Mon, Aug 11, 2003 at 02:15:40PM +0200, Bill Allombert wrote:
> > 
> > I have an expression, z,  say, involving the n-th roots of unity E(n), which
> > evaluates to a real number (i.e. ComplexCojugate(z) = z.) For example
> > z := E(5) + E(5)^-1 + E(3) + E(3)^-1;
> > 
> > Is there any way to test within GAP whether z is greater than 0, numerically?
> 
>   I believe there is two answers:
> 
> 1) You can't, because z is defined up to conjugacy and some conjugates
> can be positive and other negative. For example z:=E(8)+E(-8) can be both
> sqrt(2) and -sqrt(2).

in GAP E(n) has a canonical meaning; it is a well-defined
complex number:

Operations for Cyclotomics ____________________________ Cyclotomic
Numbers

E( <n> )

`E'  returns  the  primitive  <n>-th  root  of  unity $e_n = e^{2pi
i/n}$.

HTH,
Dmitrii
http://www.thi.informatik.uni-frankfurt.de/~dima/