#3237 regression on a simple integral in abs_integrate

[Dima Pasechnik]

In Maxima 5.35.1, this worked:

(%i1) load("abs_integrate")$
(%i2) integrate(1 / (1 + abs(x-5)), x, -5, 6);
(%o2)                          log(11) + log(2)

in 5.38.1, one gets (both with ECL and with SBCL):

(%i1) load("abs_integrate")$
(%i2) integrate(1 / (1 + abs(x-5)), x, -5, 6);
(%o2) limit   %if(- (x - 5) > 0, - log(6 - x), log(abs(x - 4)))
      x -> 6-
                  - limit     %if(- (x - 5) > 0, - log(6 - x), log(abs(x - 4)))
                    x -> - 5+

[Robert Dodier]

The change in behavior appears to be due to commit af38d28 as determined by git bisect.

Not sure what's going on here. git log says:

commit af38d28ca56623451bb94db9afb47eb3c405f82a
Author: Dan Gildea <dgildea>
Date:   Mon Jan 18 14:53:52 2016 -0500

    make orderlessp transitive

    fixes bug [#3072]

    src/simp.lisp:
    o ordfna: use ordhack consistently whenever we see mplus/mtimes

    tests/testsuite.lisp
    o test added for bug [#3072] all pass now

[Robert Dodier]

Dan, can you take a look at this one? I wasn't able to figure out what's going on.

[Dan Gildea]

The change in behavior seems to be caused by a change in the orderlessp order
of the expressions "x" and "signum(x-5)". Before we had

(%i14) x*signum(x-5);
(%o14) x*signum(x-5)
(%i15) ratsimp(1/(signum(x-5)*x - 5*signum(x-5) + 1));
(%o15) 1/((x-5)*signum(x-5)+1)

whereas now we have

(%i11) x*signum(x-5);
(%o11) signum(x-5)*x
(%i12) ratsimp(1/(signum(x-5)*x - 5*signum(x-5) + 1));
(%o12) 1/(signum(x-5)*x-5*signum(x-5)+1)

and abs_integrate does not do well with this more complex expression.
I think that the current behavior is not technically incorrect, although it is ugly.
Any further changes to orderlessp should take into account bug [#3072].

[Barton Willis]

Fixed by [3ca423]. Appended regression test. Closing ticket.