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