Status: Accepted
Owner: asmeurer
Labels: Type-Enhancement Priority-Medium Integration
New issue 2297 by asmeurer: Integral manipulations
http://code.google.com/p/sympy/issues/detail?id=2297
We need methods of Integral to manipulate the Integral. Some things we
could do are:
- Split the Integral as an Add (Integral(f(x) + g(x), x) => Integral(f(x),
x) + Integral(g(x), x))
- Split up the Integral using integration by parts
(Integral(f(x)*g(x).diff(x), (x, a, b)) => f(b)*g(b) - f(a)*g(a) -
Integral(g(x)*f(x).diff(x), (x, a, b))). See also issue 1394.
- Split up the Integral by the limits (Integral(f(x), (x, a, c)) =>
Integral(f(x), (x, a, b)) + Integral(f(x), (x, b, c)))
- Reverse the limits of integration (Integral(f(x), (x, a, b)) =>
-Integral(f(x), (x, b, a)) or Integral(-f(x), (x, b, a)))
- Reorder multidimensional limits (see issue 2292). This must also
consider rewriting the limits in the case where outer integration variables
are in the inner limits.
- Combine any of the above "split" rules.
All of these should work correctly with multidimensional integrals, and
with both definite and indefinite integrals (where applicable).
Can anyone think of any others?
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