On Wed, Mar 20, 2019 at 1:37 PM Dima Pasechnik <dimp...@gmail.com> wrote:
>
> On Wed, Mar 20, 2019 at 1:27 PM mmarco <mma...@unizar.es> wrote:
> >
> > So the bug is really in the abs_integrate package for maxima? In that case: 
> > is it really worth it to import it by default?
>
> removing it makes 7 tests fail in src/sage/interfaces/maxima_lib.py
>
> perhaps it should be applied more intelligently, but this seems to
> require parsing for abs() and sgn()...

I would not mind to see not loading abs_integrate by default, and
modifications to examples and tests
to explicitly load abs_integrate before running affected examples...

>
> >
> >
> > El miércoles, 20 de marzo de 2019, 13:58:46 (UTC+1), Dima Pasechnik 
> > escribió:
> >>
> >> On Wed, Mar 20, 2019 at 05:36:59AM -0700, mmarco wrote:
> >> > I am trying to pinpoint the following bug:
> >> >
> >> > sage: integral(sqrt(1+cos(x)^2),x)
> >> > -1/24*sin(3*x) + 1/8*sin(x)
> >> >
> >> >
> >> > which is incorrect. One would think that maxima is returning a wrong
> >> > answer, but if we ask directly to maxima, it leaves the integral as it 
> >> > is:
> >> indeed, it is an elliptic integral, cannot be done in elementary
> >> functions.
> >>
> >> The problem comes from src/sage/interfaces/maxima_lib.py
> >> loading abs_integrate:
> >>
> >> sage --maxima
> >> ;;; Loading #P"/mnt/opt/Sage/sage-dev/local/lib/ecl/sb-bsd-sockets.fas"
> >> ;;; Loading #P"/mnt/opt/Sage/sage-dev/local/lib/ecl/sockets.fas"
> >> ;;; Loading #P"/mnt/opt/Sage/sage-dev/local/lib/ecl/defsystem.fas"
> >> ;;; Loading #P"/mnt/opt/Sage/sage-dev/local/lib/ecl/cmp.fas"
> >> Maxima 5.41.0 http://maxima.sourceforge.net
> >> using Lisp ECL 16.1.2
> >> Distributed under the GNU Public License. See the file COPYING.
> >> Dedicated to the memory of William Schelter.
> >> The function bug_report() provides bug reporting information.
> >> (%i1) load(abs_integrate);
> >> ARRSTORE: use_fast_arrays=false; allocate a new property hash table for 
> >> $INTABLE2
> >> (%o1) 
> >> /mnt/opt/Sage/sage-dev/local/share/maxima/5.41.0/share/contrib/integrati\
> >> on/abs_integrate.mac
> >> (%i3) display2d : false;
> >> (%o3) false
> >> (%i4) integrate(sqrt(1+cos(x)^2),x);
> >>
> >> (%o4) ((2*sin(3*x)+6*sin(x))*false-sin(3*x)+3*sin(x))/24
> >>
> >> Which does not make much sense, and apparently Sage gets the bit of it
> >> after "false"...
> >>
> >> Dima
> >> >
> >> > sage: f = sqrt(1+cos(x)^2)
> >> > sage: maxima.integrate(f._maxima_(),x)
> >> > 'integrate(sqrt(cos(_SAGE_VAR_x)^2+1),_SAGE_VAR_x)
> >> >
> >> > which is the same result we get with sympy and fricas, and even by maxima
> >> > itself:
> >> >
> >> > Maxima 5.41.0 http://maxima.sourceforge.net
> >> > using Lisp ECL 16.1.2
> >> > Distributed under the GNU Public License. See the file COPYING.
> >> > Dedicated to the memory of William Schelter.
> >> > The function bug_report() provides bug reporting information.
> >> > (%i1) integrate(sqrt(1+cos(x)^2),x);
> >> >                             /
> >> >                             [         2
> >> > (%o1)                       I sqrt(cos (x) + 1) dx
> >> >                             ]
> >> >                             /
> >> >
> >> >  So something strange is going on when we call maxima internally to 
> >> > compute
> >> > that integral. I have tried to trace it, but I got lost in the
> >> > intrincancies of the maxima interface.
> >> >
> >> > Does somebody know what exactly is causing this discrepancy?
> >> >
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