Subject: double integrals seem to give different answers
From: Richard Hennessy
Date: Sun, 22 Nov 2009 01:38:50 -0500
Many books define for rational expressions x^(n/m) as (x^n)^(1/m) (which is
a problem for irrational or transcendental numbers, others use x^y equals
(%e^(log(x)))^y for any x and y. Since no one can dictate which definition
to use for Maxima there is never going to be agreement on the "right"
answer.
Rich
--------------------------------------------------
From: "Richard Fateman" <fateman at cs.berkeley.edu>
Sent: Saturday, November 21, 2009 7:14 PM
To: "Maxima List" <maxima at math.utexas.edu>
Cc: "G. Jay Kerns" <gkerns at ysu.edu>
Subject: Re: [Maxima] double integrals seem to give different answers
> 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
>
>
>
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