Comment #24 on issue 2128 by [email protected]: Implement more general
piecewise integration algorithm
http://code.google.com/p/sympy/issues/detail?id=2128
Meh after going through the first paper I don't think it helps. It
requires the conversion of a piecewise function to the heaviside functions
based on the break points. My algorithm actually handles the same cases
that it does, see eq 20, where the conditions are simple, i.e. the variable
of differentiation is of the form sym < real number.
Besides we will need to fix heaviside and conditional reasoning first, for
example the following things kill the current implementation:
In [45]: h = Heaviside(2-x)
In [48]: integrate(h, (x, 0, 1))
Out[48]: Integral(Heaviside(2 - x), (x, 0, 1))
For some real fun, playing around with the paper's signum functions:
In [29]: s.subs(y, x)
Out[29]: Piecewise((1, 0 < x), (0, x == 0), (-1, x < 0))
In [34]: integrate(Rational(1,2) *s.subs(y, y - 2) +
Rational(1,2)*s.subs(y, 2 - y), (y, -1,1))
....
Anywho, regardless of this paper we have to sweep over the domain of
integration and find the break points which is what _eval_interval does.
To support fancier things we need better conditional solvers. Then maybe
this algorithm will help us.
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