Symbolic integration of abs() failure

[Michael Orlitzky]

Originally posted to the mailing list by Pedro Cruz (I hope no one minds me collecting these?):

​http://groups.google.com/group/sage-support/browse_thread/thread/4a24ce95e940820e

Actual result:

sage: integrate(abs(x^2 - 1), x, -2, 2)
integrate(abs(x^2 - 1), x, -2, 2)

Expected result:

sage: integrate(x^2 - 1, x, -2, -1) + integrate(1 - x^2, x, -1, 1) + integrate(x^2 - 1, x, 1, 2)
4

If it's helpful, we can change the limits of integration to avoid the roots. This seems to appease the integrate function:

sage: integrate(x^2, x, -1, 1)
2/3

[Burcin Erocal]

Replying to mjo:

Originally posted to the mailing list by Pedro Cruz (I hope no one minds me collecting these?):

Not at all. I appreciate any effort in this direction. Please make sure that these are not duplicates of already existing tickets though. We started making a list of symbolics tickets on this page. It should make it easier to check the new tickets (also #11591 and #11590) against existing ones.

I am at a conference right now and don't have much time for this.

Note that the patch attached to #8624 loads the abs_integrate package in maxima which might help with some of these issues involving abs(). Unfortunately that patch won't apply any more, since the maxima interface changed quite a bit during the switch to use libECL.

[Karl-Dieter Crisman]

See #11483 for where that issue is currently standing.

I think that the OP meant the following (Maxima) in the last line:

(%i2) integrate(abs(x^2-1),x,-1,1);
                                       4
(%o2)                                  -
                                       3

This would indeed be fixed by the abs_integrate package.

(%i3) load(abs_integrate);
STYLE-WARNING: redefining SIMP-ISREAL-P in DEFUN
(%o3) /Users/.../maxima-5.24.0/share/contrib/integrat\
ion/abs_integrate.mac
(%i4) integrate(abs(x^2-1),x,-2,2);
(%o4)                                  4

[Karl-Dieter Crisman]

This is in fact fixed and documented in #11483, so I guess this ticket can be closed? Since it's actually done, not really invalid per se, I will put an author as well as reviewer, but if the release manager or someone else disagrees with this analysis they can change those fields.

[Michael Orlitzky]

There's a doctest for this in #11638. I was thinking I'd move it to the proper place (in one of the Maxima files) either tomorrow or the next day.

It doesn't matter to me on which ticket I do it, though.

[Karl-Dieter Crisman]

Well, I already gave #11483 nearly positive review... I mean, there are now two different tests for this.

[Michael Orlitzky]

Oh, ok. I forgot there was a test in #11483 (I'm fixing it now). This can safely be closed.