> < ^ Date: Mon, 11 Aug 2003 18:32:20 +0200
< ^ From: d.pasechnik@twi.tudelft.nl < >
> < ^ Subject: Re: Testing expression for positivity

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]