symbolic integration fails on a very simple test case

[pdehaye]

The following happens

sage: var("x")
x
sage: integrate(abs(x - 1) + abs(x + 1) - 2*abs(x), (x,-Infinity,Infinity))
0
sage: integrate(abs(x - 1) + abs(x + 1) - 2*abs(x),(x,-Infinity,10))
2

The second answer is the correct one, of course...

[kcrisman]

This also happens in Maxima.

Maxima 5.24.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.24
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) integrate(abs(x - 1) + abs(x + 1) - 2*abs(x),x,minf,10);
(%o1)                                  2
(%i2) integrate(abs(x - 1) + abs(x + 1) - 2*abs(x),x,minf,inf);
(%o2)                                  0

I don't know that I would call this "very simple", though, as integrating absolute value things is somewhat tricky when done symbolically.

[pdehaye]

sure, but certainly something i would hope works! also not sure how much of it is due to the infinite interval and how much due to the function itself

[kcrisman]

This is now  reported at this location.

[pdehaye]

fixed over there

[mjo]

Doctest for the correct result.

[mjo]

Fixed now that we've got Maxima 5.26.0. Here's a doctest.

[kcrisman]

I probably would have put it in sage.symbolic.integration.integral.integral somewhere, where there are lots of tests, but I guess this is fine, and otherwise all is well. I'd hate to have you rebase it to that other location, seems a waste... but then again, that's where they are...

Or what do you think? The problem is that we have no canonical location for integral stuff. integrate? is a wasteland, though it points to better sources of doc.

[mjo]

I honestly went through the same thought process. At first, I thought, "I'll put it with the Maxima stuff because it was a Maxima bug." But then I thought, what if we ever drop Maxima completely? This isn't a Maxima test: this tests that our integration works. Whatever we would replace Maxima with should also pass this test!

Then, I had to decide whether to put it in functional.py or under symbolics. I settled on this because it's what gets called first when the user calls integrate(). It's also where you're sent if you look up the code with integrate? or integrate??, so to stay true to the report on the ticket, I put it there.

If the reporter had done,

f = abs(x - 1) + abs(x + 1) - 2*abs(x)
f.integral(...)

I probably would have stuck it in symbolics. It's no big deal to move it, in any case.

[kcrisman]

Well, you'll notice that I did give positive review. You are right about the integration tests not belonging in the Maxima docs, of course.