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Labels: Type-Enhancement Priority-Medium Integration Sets
New issue 3716 by mrock...@gmail.com: Integrals over non-interval sets
http://code.google.com/p/sympy/issues/detail?id=3716
integrate supports the following syntax
integrate(integrand, (symbol, set))
e.g.
integr
Issue 3716: Integrals over non-interval sets
http://code.google.com/p/sympy/issues/detail?id=3716
This issue is now blocking issue sympy:3711.
See http://code.google.com/p/sympy/issues/detail?id=3711
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Comment #2 on issue 3716 by asmeu...@gmail.com: Integrals over non-interval
sets
http://code.google.com/p/sympy/issues/detail?id=3716
Wow, I didn't know we could do that.
For integral over a finite set, wouldn't that always be 0? Regardless, we
should allow it.
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Comment #3 on issue 3716 by mrock...@gmail.com: Integrals over non-interval
sets
http://code.google.com/p/sympy/issues/detail?id=3716
This comes up in stats. Queries like P(X**2 > 1) produce an integrand (the
probability density function) and the domain (in this case the union x < -1
U x
Comment #4 on issue 3716 by asmeu...@gmail.com: Integrals over non-interval
sets
http://code.google.com/p/sympy/issues/detail?id=3716
Are sets able to rewrite themselves as a union of intervals?
Also, care is needed. Integral(f(x), (x, Union(Interval(a, b), Interval(c,
d))) is not the same
Comment #5 on issue 3716 by asmeu...@gmail.com: Integrals over non-interval
sets
http://code.google.com/p/sympy/issues/detail?id=3716
Also, I'm not sure what the mathematically correct thing do to with a delta
function over a finite set is. From the definition I've seen, all integrals
are
Comment #6 on issue 3716 by mrock...@gmail.com: Integrals over non-interval
sets
http://code.google.com/p/sympy/issues/detail?id=3716
Are sets able to rewrite themselves as a union of intervals?
I don't believe so, no. I think Interval(a, a) is actually transformed
into FiniteSet(a).
Comment #7 on issue 3716 by asmeu...@gmail.com: Integrals over non-interval
sets
http://code.google.com/p/sympy/issues/detail?id=3716
The real issue is that Interval(b, a) represents the empty set when b > a
but Integral(f(x), (x, b, a)) = -Integral(f(x), (x, a, b)). The best I can
think
Comment #8 on issue 3716 by mrock...@gmail.com: Integrals over non-interval
sets
http://code.google.com/p/sympy/issues/detail?id=3716
I think when using integrate(integrand, (symbol, interval)) you're assuming
the positive case. This case can be clearly selected by using (symbol,
interva
Comment #9 on issue 3716 by asmeu...@gmail.com: Integrals over non-interval
sets
http://code.google.com/p/sympy/issues/detail?id=3716
I mean with a, b, c, and d symbolic. I guess NotImplementedError is ok for
those. It will still solve issue 3711 for explicit inputs.
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