Comment #6 on issue 3793 by asmeu...@gmail.com: Integrate hangs
http://code.google.com/p/sympy/issues/detail?id=3793
It's because when you expand, there are fewer terms in each trig function
(because for example, something like sin(pi*(x - 1)) goes to sin(pi*x -
pi), which is transformed to -sin(pi*x)).
heurisch seems very poorly optimized for things like sin(pi*(x - 1)). I
think it's because at line 244 of heurisch.py, cancel() is called on the
derivative, meaning that the derivative of sin(pi*(x - 1)) is in terms of
cos(pi*x) instead of cos(pi*(x - 1)), and it later has a hard time
recognizing the two as being derivatives on one another.
I guess what really should happen is that cancel() should also be called on
the original f (line 187 or thereabouts). Or something like terms =
set([cancel(i) for i in terms]) before line 243. I'm not sure if this will
be a performance hit, in the general case, though. It's worth playing
around with it and benchmarking it, though. I can confirm that changing
line 187 to terms = components(cancel(f), x) causes all of the integrals
from this issue to return instantly (the OP integral remains unevaluated,
though).
I don't currently have the time to test this to make sure it isn't really a
performance regression, but if someone else wants to, and you find that it
isn't, please make a pull request.
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