Status: New
Owner: ----
Labels: Type-Defect Priority-Medium
New issue 3801 by [email protected]: Piecewise integration failure
http://code.google.com/p/sympy/issues/detail?id=3801
I'm trying to obtain symbolic integrals for what I thought to be some
rather straightforward piecewise functions.
A very simple case is:
⎧0 for t < t₀
⎪
f(t) = ⎨x for t₀ ≤ t
⎪
⎩0 for t ≥ t₁
Using current git master (1cb25e57), I can obtain an indefinite integral:
In [2]: f = Piecewise((0, t < t0), (x, t0 <= t < t1), (0, t >= t1))
In [3]: integrate(f, t)
Out[3]:
⎧ 0 for t < t₀
⎪
⎨t⋅x for t₀ ≤ t
⎪
⎩ 0 for t ≥ t₁
However, if I then try to obtain the definite integral over the interval
(t0, T), I get an unevaluated integral (and .doit() doesn't help):
In [4]: integrate(f, (t, t0, T))
Out[4]:
T
⌠
⎮ ⎧0 for t < t₀ dt
⎮ ⎪
⎮ ⎨x for t₀ ≤ t
⎮ ⎪
⎮ ⎩0 for t ≥ t₁
⌡
t₀
Now, I accept this is not as trivial as it looks because sympy doesn't know
if t1 > t0 etc. But it seems like there is some understanding of how to
deal with that, because if I try the interval (0,1) I get:
ValueError: Called interval evaluation over piecewise function on undefined
intervals (0, Min(0, t0)), (Min(1, t0), Min(1, Max(0, t0))), (1, Min(1,
Max(0, t1)))
I also tried giving some assumptions:
with assuming(Q.is_true(T > t0), Q.is_true(t1 > t0)):
pprint(integrate(f, (t, t0, T)))
...but again I get the same result.
Is this a duplicate? I have seen issue 2937, but that is marked as fixed.
It refers to issue 2128, but the latest comment there suggests the examples
there were fixed in https://github.com/sympy/sympy/pull/1376, except for
some evalf problems.
Is there something that makes this example more difficult? Am I missing
some way to get the results I want?
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