Comment #15 on issue 1772 by smichr: Integral(1,x).is_number fails
http://code.google.com/p/sympy/issues/detail?id=1772
Aaron wrote -- but it doesn't show up here:
I think it should call is_zero on the integrand. If that can't handle
trivial cases, then is_zero needs to be improved.
One way that that could be done is to note that Poly(expr).is_zero is
smarter than expr.is_zero.
[cut]
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Poly is better because it does some things like cancel before creating the
Poly instance. Are those the sorts of things you are referring to? But
let's say is_zero returns a false False (e.g.
Poly(cos(x)**2+sin(x)**2-1).is_zero -> False) then under what
circumestances can we know that the False is false?
Ohh...this brings back the is_zero dilemma and unprovability. Is there a
set of symbols/operators for which we *know* a zero can't be hidden when
you do Poly instantiation? Richardson tells us that expressions made from
Rationals + pi + log(2) + x + (=-*/) + sin + exp + abs + composition might
be a recursively unprovable zero. But does someone else have a theorem
where you know, for a given expression, whether it for sure isn't zero?
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