defint1 abs trouble

This is a bug in integrate:

(%i1) expr:exp(-abs(x))$ integrate(expr,'x,minf,0);
(%o2)                                  1
(%i3) assume(x<0)$ integrate(expr,'x,minf,0);
defint: integral is divergent.
 -- an error. To debug this try: debugmode(true);

The user should absolutely not have to fiddle with internal variables like
?dosimp to get this right.

I have filed this as bug
3507277<https://sourceforge.net/tracker/?func=detail&aid=3507277&group_id=4933&atid=104933>;
.
         -s



On Sat, Mar 17, 2012 at 17:10, Edwin Woollett <woollett at charter.net> wrote:

> I have found a definite integral  which integrate
> can do but mydefint1 (revised to see what
> is going on)  cannot do, leading to a defint complaint. The example
> involves
> the abs function.
> ------------------------------**---------------------
>
> (%i1) integrate (exp (-abs (x)), x, minf, 0);
> (%o1)                                  1
>
> (%i2) assume(x < 0);
> (%o2)                               [x < 0]
>
> (%i3) integrate (exp (-abs (x)), x, minf, 0);
> (%o3)                                  1
>
> (%i4) forget(x<0);
> (%o4)                               [x < 0]
> (%i5) facts();
> (%o5)                                 []
>
> (%i6) mydefint1 (e78, x78, a78, b78) :=
> block  ( [domain : complex, xmin, xmax,
>                            assumeL : [],  res1,  _ans],        xmin : min
> (a78, b78),
>   xmax : max (a78, b78),
>   if xmin  #  minf then assumeL : cons ( x78 > xmin, assumeL),
>   if xmax # inf then assumeL : cons (x78 < xmax, assumeL),
>   if debug then display (xmin, xmax, assumeL),
>   _ans : apply ( 'assume,  assumeL ),
>   res1 : ratsimp (integrate (e78, x78, a78, b78 ) ),
>   apply ( 'forget,  _ans),
>   res1)$
>
> (%i7) debug:true$
>
> (%i8) mydefint1 ( exp (-abs (x)), x, minf, 0);
>
>                                 xmin = minf
>
>                                  xmax = 0
>
>                              assumeL = [x < 0]
>
> defint: integral is divergent.
>
> #0: mydefint1(e78=%e^-abs(x),x78=**x,a78=minf,b78=0)
> -- an error. To debug this try: debugmode(true);
>
> (%i9) facts();
> (%o9)                               [0 > x]
>
> ------------------------------**----------------------------
> I don't see what difference there is in terms of
> assumptions between calling integrate directly
> and using mydefint1 in the above example.
>
> If I remove the abs(x) part, both methods work:
> ------------------------------**-------------------------
> (%i10) forget(x<0);
> (%o10)                              [x < 0]
> (%i11) facts();
> (%o11)                                []
>
> (%i13) integrate(exp(x),x,minf,0);
> (%o13)                                 1
>
> (%i14) mydefint1(exp(x),x,minf,0);
>                                 xmin = minf
>
>                                  xmax = 0
>
>                              assumeL = [x < 0]
>
> (%o14)                                 1
>
> (%i15) facts();
> (%o15)                                []
> ------------------------------**------------------------------**-
> So something about the presence of abs in the
> integrand prevents mydefint1 from working
> as expected.
>
> Ted
>
>
>