Roots of unity

[Richard B. Kreckel]

Hi,

On Sun, 20 Jan 2002, Bob McElrath wrote:
> > [...]
> > > What I see as needed in order to write some simplification routines are methods
> > > for the ex class like there are in the numeric class:
> > >     is_real, is_integer, operator<, etc...
> > > And an assume() functionality to create symbols that are reals, integers, etc.
> > 
> > The reason this has not been done is that we have absolutely no idea how
> > to make it consistent.
> 
> Really?  Maybe I haven't thought about it as much as you...
> 
> But it seems you'd need methods:
>     is_real
>     is_negative
>     etc...
> for every function (sqrt, sum, sin, pow, ...), which could then query their
> arguments in the appropriate manner to determine the final result.

The trouble starts already with trivial expressions: If a>0 and b>0, then
(a+b)>0.  But (a-b) would have to return false, as would (b-a).  This
makes it already difficult for sums.  Ternary logic would help a bit,
here.   :-)

[...]
> By nested root you mean something like:
>     sqrt(a+sqrt(b))
> right?

Yes.

Regards
    -richy.
-- 
Richard Kreckel
<Richard.Kreckel at Uni-Mainz.DE>
<http://wwwthep.physik.uni-mainz.de/~kreckel/>