double integrals seem to give different answers




On Sat, 21 Nov 2009, Richard Fateman wrote:

< 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
 
Just to be clear, this is not the root of the error for this integral.
You can verify that by declaring

assume(rho >= 0);

and computing the two integrals.

Leo

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