< ^ From:

> < ^ Subject:

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/

> < [top]