Disable abs_integrate

[roed314]

Maxima's abs_integrate contributed package gives us lots of nice new integrals, but also really breaks a lot of stuff, apparently. Add to this list as you see fit:

• Incorrect integral in Maxima #13733 Incorrect integral in Maxima
• Integrating the sgn() function can produce incorrect results #11590 Integrating the sgn() function can produce incorrect results
• cosh integral incorrect because of abs_integrate #14591 cosh integral incorrect because of abs_integrate
• integrate() problem #16643 integrate() infinite loop
• Yet another abs_integrate trig integral problem #17183 Yet another abs_integrate trig integral problem
• Strange integration error/hang with log(abs(sin(x))) #17468 Strange integration error/hang with log(abs(sin(x)))
• Get integral of abs(sin(x)) and abs(cos(x)) right #17511 Get integral of abs(sin(x)) and abs(cos(x)) right
• unsolved piecewise integrals metaticket #17910
• Wrong integration of abs(sin(x)*cos(x)) #23271
• integrate(sqrt(1-4*sin(x)^2),x) is wrong #24117
• This is also blocking update to maxima 5.42, Update maxima to 5.42.2 #26625

---

Old:

Can someone more knowledgeable about using maxima for integration determine what the right warning to show is and when to show it? See #12691 for what a stopgap is.

CC: @nbruin @orlitzky @kcrisman @pjbruin @rwst @paulmasson @mforets

Component: calculus

Keywords: abs_integrate

Author: Ralf Stephan, Frédéric Chapoton

Branch: b5c9cc5

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/12731

[kcrisman]

comment:1

I'm not really sure that this is appropriate for a stopgap. I mean, unless we put in a catch for the specific form like integrate(x * sgn(x^2 - 1/4), x, -1, 0), we would have to put in a stopgap for the entire integration, which is ridiculous.

Unless we checked for the signum function with nonlinear operands in it sometime... but that's more than I have time to parse now.

[kcrisman]

comment:8

Naturally, if it becomes unnecessary to do so, we can just close this as wontfix. This is the best equivalent to a stopgap I can come up with - or possibly we can raise a warning every time abs_integrate is used, though this won't stop the hangs and other weird interactions it causes.

[kcrisman]

comment:10

Unfortunately, a lot of the most popular such integrals are not computed with sympy (yet?). Not even abs(x).

In [1]: from sympy import *

In [2]: x=Symbol('x')

In [3]: integrate( abs(x), x)
Out[3]: Integral(Abs(x), x)

In [4]: integrate( abs(x), (x, 0, 1))
Out[4]: Integral(Abs(x), (x, 0, 1))

[kcrisman]

comment:11

Useful comment from author of abs_integrate:

The assignments extra_definite_integration_methods : [] and extra_integration_methods : [] should render abs_integrate inoperative.
Resorting these lists to their defaults will revive abs_integrate. A kill(all) will remove all traces of abs_integrate--a reload is needed.

So we could conceivably do this in the case that Maxima (or whomever) returns an unevaluated integral, sort of like what we do with solving.

[sagetrac-jakobkroeker]

comment:12

could all developers involved in this ticket eventually meditate on Williams comment:

And why are we using it (abs_integrate) if it is so broken -- it should
require an explicit flag to use at all. Sage is supposed to default
to correct answers unless you otherwise explicitly request otherwise

Does that sound reasonable?

[rwst]

comment:14

Replying to @sagetrac-jakobkroeker:

could all developers involved in this ticket eventually meditate on Williams comment:

And why are we using it (abs_integrate) if it is so broken -- it should
require an explicit flag to use at all. Sage is supposed to default
to correct answers unless you otherwise explicitly request otherwise

Does that sound reasonable?

Yes, and it's the only option because that package causes so much collateral damage, not only in integrate. Turning it off only triggers a few minor doctest failures, most of them (9) in interfaces/maxima_lib.py.

[fchapoton]

Changed branch from u/rws/disable_abs_integrate to u/chapoton/12731

[kcrisman]

comment:44

Thanks - I wish there was a better fix than disabling. Can you briefly comment on

• The removal of the radexpand example
• the known bug ones
  I'm sure they are quite logical but a quick glance fails to reveal it, as opposed to where you put the unevaluated integral in to replace the abs_integrate behavior.

Or maybe this was already present behavior and you really did just refresh this, in which case no worries. It seems like comment:33 was the last substantive part of the discussion and memory fails.

[fchapoton]

comment:45

Tagging by known bug allows to remember that one could hope for the answer displayed. I think Jeroen suggested to keep the doctest in this way, rather than remove them.

And the radexpand example no longer works without abs_integrate, just returning unevaluated.

[fchapoton]

comment:46

bot is morally green, please review

[dimpase]

Reviewer: Dima Pasechnik

[dimpase]

comment:47

looks good to me. Please add yourself as authors/reviewers...

[fchapoton]

Changed author from Ralf Stephan to Ralf Stephan, Frédéric Chapoton

[vbraun]

Changed branch from u/chapoton/12731 to b5c9cc5

[kcrisman]

Changed commit from b5c9cc5 to none

[kcrisman]

comment:50

At least according to github, the following stuff in sage/maxima_lib.py was not removed (probably because it still passes doctests as Maxima proper improved in the meantime):

        Make sure the abs_integrate package is being used,
        :trac:`11483`. The following are examples from the Maxima
        abs_integrate documentation::
            sage: integrate(abs(x), x)
            1/2*x*abs(x)

[embray]

comment:51

Not in Sage 8.8. Let's please to try keep tickets' milestones related to the release in which we actually intend to include them, and in particular the release in which they were actually included, especially when closing tickets.