posible bug - clashing variable names in integrals
Subject: posible bug - clashing variable names in integrals
From: Robert Dodier
Date: Sun, 4 Oct 2009 18:51:16 -0600
On 10/4/09, Nathaniel Virgo <nathanielvirgo at gmail.com> wrote:
> All I want to do is to use Maxima to do proofs where factoring expressions
> of the form
>
> integral(integral(f(x),x,a,b)*g(x),x,c,d)
>
> into
>
> integral(f(x),x,a,b)*(integral(g(x),x,a,b)
>
> is an important and frequent step. See for example
> http://en.wikipedia.org/wiki/Conditional_entropy#Chain_rule
Hmm, I don't see where a repeated integration over the same
variable comes into play. In the entropy chain rule, there's an
integration over y and one over x. What's an example which
shows a repeated integration over the same variable?
Entropy is an expected value, right? Usually one has to be
careful --- expectation wrt to which variable? What is an
example of nested expectations in which it is OK to ignore
which variable?
Sorry to be dense about it. I agree that Maxima should be
smarter about nested integrals of the kind you mentioned,
but I don't see how that comes into play in entropy computations.
best
Robert Dodier