another sqrt simp problem



Am Donnerstag, den 04.11.2010, 12:19 -0700 schrieb Edwin Woollett:
> Hi Dieter,
> 
> Continuing my exploration of Michael Wester's
> examples, is the following:
> ------------------------------
> Maxima 5.22.1 http://maxima.sourceforge.net
> using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (a.k.a. GCL)
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> The function bug_report() provides bug reporting information.
> "2010-11-04"
> 
> (%i1) sqrt (exp(z));
> 
> (%o1) %e^(z/2)
> 
> (%i2) expr : sqrt(exp(z)) - exp(z/2);
> 
> (%o2) 0
> 
> (%i3) [sqrt (exp(%i*2*%pi)),   exp(%i*%pi)];
> 
> (%o3) [1, -1]
> ---------------------------------------------------
> According to Wester,  the simplification Maxima does with
> sqrt ( exp (z) ) is  true if and only if  Im(z) lies in the
> set of intervals ...., (-5 pi, -3 pi),  (- pi, pi),  (3 pi, 5 pi),......
>  Otherwise, the automatic simplification (using principle
> value conventions ) is  - exp(z/2),  as shown in %o3 above.

The simplification of the example (%1) no longer is done by default, if
the argument is a complex value:

(%i1) declare(z,complex)$

(%i2) sqrt(exp(z));
(%o2) sqrt(%e^z)

But for x a real the simplification is done:

(%i3) sqrt(exp(x));
(%o3) %e^(x/2)

Dieter Kaiser