Subject: double integrals seem to give different answers
From: Richard Fateman
Date: Sat, 21 Nov 2009 16:14:46 -0800
Richard Hennessy wrote:
> This is a bug,
...
If you think that (w^2)^(3/2) should simplify to abs(w^3), then you
inevitably run into problems.
That is what trigsimp, or some component of it, believes.
If you believe, as I do, that there are 2 values, +w^3 and -w^3, and the
computation should proceed
using Both values until
(a) it is determined that It Doesn't Matter Which You Use.
or
(b) the user (or some other computation) decides that Only One Value
Works and uses it.
or
(c) you have to produce an answer Including Both Values.
From this perspective it isn't a bug in integration or trigsimp. And I
suspect the same trick will catch you in
Mathematica or Maple, if they do the same "simplification". There are a
large number of system-independent
mathematical "gotchas".
RJF