Difference in interactivity with two sums

Hi!

At http://trac.sagemath.org/sage_trac/ticket/11990, the question is
raised about the discrepancy in behavior below.


Maxima 5.28.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.55.0-abb03f9
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.
(%i1) load(simplify_sum);
(%o1) /Applications/MathApps/Maxima.app/Contents/Resources/maxima/share/maxima\
/5.28.0/share/solve_rec/simplify_sum.mac
(%i2) simplify_sum(sum(2^m,m,0,inf));

sum: sum is divergent.
#0: simplify_sum(expr='sum(2^m,m,0,inf))
 -- an error. To debug this try: debugmode(true);
(%i3) simplify_sum(sum(m,m,0,inf));
Is  m  positive, negative, or zero?


But in both cases m isn't a variable that can be +, -, 0, but rather a
dummy variable that goes from 0 to infinity.  Naturally the sum of 0
is 0 and any other sum diverges in the second case, and in the first
case it always diverges if one fixes m, but in both cases this sort of
misses the point of m being the index which changes, and isn't fixed!

Thanks for any explanation - perhaps this is something specific to
solving recurrences, where simplify_sum lives anyway.  But in other
cases

(%i4) integrate(m,m,0,inf);

defint: integral is divergent.
 -- an error. To debug this try: debugmode(true);

it doesn't ask for whether m is positive, negative, or zero!