Comment #1 on issue 1950 by andy.ter...@gmail.com: Piecewise((x, 0 < x),
(0, Eq(x, 0)), (-x, x < 0))._eval_interval(x, -1, 1) is wrong
http://code.google.com/p/sympy/issues/detail?id=1950
Hmm, I'll take a closer look.
The code is complicated because function is dependent on which intervals
are used, if just the end points are used then the middle intervals may not
be considered.
For example:
p1 = Piecewise((3*x, x < 0), (2*x, x < 1), (x, x >= 1))
p1.eval(x, -2, 2)
should translate to:
(3*x)._eval_interval(x,-2, 0) + (2*x)._eval_interval(x, 0, 1) +
x._eval_interval(x, 1, 2)
9
whereas p1.subs(x, 2) - p1.subs(x, -2) translates to
x.subs(x,2) - (3*x).subs(-2)
8
The bug in the above code is with the handling of the Eq(x, 0) condition,
without it things work as expected:
Piecewise((x, 0 < x), (-x, x < 0))._eval_interval(x, -1, 1)
0
but there are funky cases as always with math, take for example:
Piecewise((x, 0 < x), (oo, Eq(x, 0)), (-x, x < 0))._eval_interval(x, -1, 1)
nan
but should be 1
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