#2859 Maxima should integrate abs(sin(x)) correctly

[kcrisman]

And abs(cos(x)) - at least it should work correctly with load(abs_integrate). But see among others, https://sourceforge.net/p/maxima/bugs/2520/ and the very long discussion at http://trac.sagemath.org/ticket/13364 Apparently the integral gotten isn't useful for definite integrals, either. And

(%i5) integrate(abs(sin(x)),x,0,%pi);

(%o5) 'integrate(abs(sin(x)),x,0,%pi)

even though this function is nonnegative on that entire interval! And

(%i2) integrate(abs(cos(x)),x,0,%pi);

log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
log: encountered log(0).
(%o2)                                 - 1

Presumably https://sourceforge.net/p/maxima/bugs/2853/ might help some with this, but the answer is still wrong for the usual meaning of abs!

[Robert Dodier]

With Maxima 5.35.1, I find that abs_integrate + integrate(abs(sin(x)),x,0,%pi) causes a stack overflow. Looks like sooner or later taylor is called and it gets stuck there. I've reported the apparent problem with taylor as bug #2860.

[Robert Dodier]

Minor update. Today I observed the following. I'm still getting a stack overflow for abs_integrate + integrate(abs(sin(x)),x,0,%pi).

For the other one, I get:

(%i1) load(abs_integrate);
WARNING: redefining MAXIMA::OPAPPLY in DEFMACRO
WARNING: redefining MAXIMA::OPCONS in DEFMACRO
ARRSTORE: use_fast_arrays=false; allocate a new property hash table for $INTABLE2
(%o1) 
    /home/robert/maxima/maxima-code/share/contrib/integration/abs_integrate.mac
(%i2)  integrate(abs(cos(x)),x,0,%pi);
(%o2)                                 - 1

i.e. I get -1 but without all the "log(0)" messages. Not sure how meaningful or relevant that is.

(%i3) build_info();
(%o3) 
Maxima version: "branch_5_40_base_195_gfde5b07_dirty"
Maxima build date: "2017-08-16 21:53:41"
Host type: "i686-pc-linux-gnu"
Lisp implementation type: "SBCL"
Lisp implementation version: "1.3.13"

[Barton Willis]

Fixed by Commit [3ca423] . Closing ticket.