Mark,
Thanks for the bug report and (especially) your clear and detailed analysis. I have fixes for each of these bugs.
The fix for abs_defint(unit_step(x),x,99,100) is what you suggested.
To fix abs_defint(unit_step(unit_step(x)),x,-1,0), I changed the signum representation for unit_step to
unit_step(x) = (signum(x)*(signum(x)+1))/2
Additionally, some abs_integrate functions convert terms such as signum(nonconstant polynomial)^2 to 1. In the
context of an integrand signum(nonconstant polynomial)^2 = 1 is an OK identity, I think.
It will take me some time to re-think and improve these fixes. Maybe you could file a bug report--I like
having a record of bugs.
Again, thanks for your bug report.
--Barton
(author of abs_integrate)
-----maxima-bounces at math.utexas.edu wrote: -----
>I?have?found?some?bugs?in?abs_integrate.mac:
>(%i3)?abs_defint(unit_step(x),x,99,100);
>(%o3)?100
>(%i4)?abs_defint(unit_step(unit_step(x)),x,-1,0);
>(%o4)?1/2