Fix for bug [ 1370433 ] trigsimp(sqrt(%i2)) !=sqrt(trigsimp(%i2))?

On 11/10/06, Raymond Toy <raymond.toy at ericsson.com> wrote:

>     Robert> Here Maxima is making an unstated assumption that symbols
>     Robert> represent real variables unless declared complex.
>     Robert> (declare(y, complex), sqrt(y^2)) => sqrt(y^2)
>     Robert> I don't know if that policy is followed 100%.
>
> This is also controlled by the domain variable.  The default is real,
> so sqrt(x^2) -> abs(x).  If the domain is complex, sqrt(x^2) remains.

domain is probably something we should just cut out.
Although the name suggests some far-reaching effects,
it is documented only to affect sqrt (although of course
there might also be some undocumented effects).
Also, domain interacts badly with declarations --

declare (x, real);
domain : complex;
sqrt (x^2);
  => sqrt(x^2); /* OOPS */

Surely the explicit declaration of x should supersede the
general assumption implied by domain : complex .

On a related note, I am convinced that we need to reconsider
Maxima's declaration system in general, and stuff related to
complex variables in particular.

All the best
Robert