Updates:
Labels: EasyToFix
Comment #7 on issue 1696 by [email protected]: integral of heaviside
http://code.google.com/p/sympy/issues/detail?id=1696
But an algorithm to convert general piecewise expressions to use Heaviside
would be very useful. Because usually, integrate() has a better chance of
integrating Heaviside than Piecewise (especially if the limits are
infinite, or if the integral is indefinite).
Actually, a better thing to do would be to add something that should have
been added a long time ago, a special derivative for heurisch. This way,
we could define Heaviside(x).heurisch_diff(x) to be 0 for heurisch, but
keep Heaviside(x).diff(x) as DiracDelta(x). As I noted above, heurisch
just needs to know what the derivative is in terms of the function itself
to work. This would also let us do things like change tan(x).diff(x) to
the more common sec(x)**2, but still make integrals in terms of tan(x) work.
This would be easy to implement. Just add a new method heurisch_diff() to
these functions, and check if it is defined and use it in heurisch instead
of diff. Probably we should use a better name than that, since it could be
useful outside of heurisch too (in particular, in other integration
algorithms).
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