Stavros Macrakis wrote:
> Don't the expressions sqrt(1/x) and 1/sqrt(x) denote the same analytic
> function over C-{0}?
>
> It is only when we try to restrict to a particular sheet that we run into
> problems, right?
>
> So shouldn't the default be radexpand:all?
I agree completely to that. They agree on x>0 and thus by analytic
continuation they agree on a common sector of definition. It is
when trying to define a particular determination on the sector
C - {x<0} that one encounters problems, which are of conventional origin.
When using a CAS one expects the computer to find "simplifications" one is
not aware of, and these conventions get in the way of such simplifications,
which is a pity. In particular maple has the simplify(***,symbolic) to
simplify expressions without any regards to branches of multivalued
functions and it is very useful.
--
Michel Talon