Dear GAP Forum, dear Derek,

On Mon, 28 Jul 2003, Derek Holt wrote:

(I sent this message early in July, but I did not see it appear in the
GAP Forum, so apologies if it appears twice!)

We have to apologize! There were severe technical problems with the
server which distributes the GAP forum mails. This is the reason
that we had quite a few mails to the list at once today.

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?

The only way I see is to use (as you say) numerical approximations.
See the page
http://www.math.rwth-aachen.de/~Frank.Luebeck/decimal/init.html
for some programs which can be used for the purpose.

(They are an extension of Jean Michel's deposited GAP3 file
'decimal.g', the functions are enhanced by a simple interval arithmetic
and there are some further utility functions.)

With best regards,

Frank

///  Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64,  ///
\\\                    52062 Aachen, Germany                          \\\
///  E-mail: Frank.Luebeck@Math.RWTH-Aachen.De                        ///
\\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/           \\\