On Dec 11, 2007 5:49 AM, Mike Hansen <mhansen at gmail.com> wrote:
> I am now getting an issue with radcan under the complex domain.
>
> (%i13) domain: complex$
> (%i14) radcan( sqrt(x^2) - x );
> (%o14) 0
> (%i15) domain: real$
> (%i16) radcan( sqrt(x^2) - x );
> (%o16) abs(x) - x
>
This is not all about radcan.
sqrt(x^2), domain:complex => sqrt(x^2)
sqrt(x^2), domain: real => abs(x)
Radcan does nothing with abs(x).
On the other hand, radcan simplifies (x^a)^b => x^(a*b) for all a, b. This
is by design.
It is not at all clear what the "correct" thing to do with (z^2)^(1/2) in
general; should z^(2/2) also be different from z? We could have a long
discussion about principal values, cuts, continuity, etc., but....
-s