integration asks to many questions



By the way:

if I use a self defined function
dint(f,v,a,b):=subst(b,v,integrate(f,v))-subst(a,v,integrate(f,v));

instead of integrate for the integral with bounds, no questions are ask,
and the result seems to be OK.

Is there a reason, build in integral is working differently?

Detlef

Am Freitag, den 13.04.2007, 19:45 +0200 schrieb Detlef Schmicker:
> Hi,
> 
> I wonder if somebody is working on integration. The integral I needed is
> somewhat complex, but it is solved e.g. by mathematica without any
> questions.
> 
> One problem of cause is, missing two dimensional integration, therefore
> I am not able to answer the question to the sign of cos(kp x2).
> 
> But other questions are not necessary too. Maybe maxima should try all
> options, and check if the result really differs. In my case it does not,
> independend of a number of answers.
> 
> I would help fixing, but I would not love to be the only one working on
> the integration. I read in the archive, somebody already had the wish to
> have multidimensional integration. Here is a reason, it is necessary.
> Otherwize I have to split the integral by hand to have correct answers
> to cos(kp x2).
> 
> Detlef
> 
> (sorry, the output is not always readable in here, don't know a better
> way) 
> 
> detlef at sarge:~$ maxima
> 
> Maxima 5.10.0 http://maxima.sourceforge.net
> Using Lisp GNU Common Lisp (GCL) GCL 2.6.7 (aka GCL)
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> This is a development version of Maxima. The function bug_report()
> provides bug reporting information.
> (%i1) p:(1+
> a*cos(kp*x1)+a*cos(kp*x2)+a*a*cos(kp*x1)*cos(kp*x2))*sin(kp*(x1-x2)/4);
>           kp (x1 - x2)    2
> (%o1) sin(------------) (a  cos(kp x1) cos(kp x2) + a cos(kp x2) + a
> cos(kp x1)
>                4
> 
> + 1)
> (%i2) p2:p*(1+c*cos(kp*(x1+x2)/2));
>           kp (x1 - x2)    2
> (%o2) sin(------------) (a  cos(kp x1) cos(kp x2) + a cos(kp x2) + a
> cos(kp x1)
>                4
>                                                              kp (x2 +
> x1)
>                                                  + 1) (c
> cos(------------) + 1)
>                                                                   2
> (%i3) integrate(integrate(p2^2,x1,-4*%pi/kp,4*%pi/kp),x2,5*%pi/kp/2,7*%
> pi/kp/2);
> 
> Is  kp  positive or negative?
> 
> p;
> Is  a  zero or nonzero?
> 
> n;
> Is  a c  positive, negative, or zero?
> 
> n;
> Is  c  zero or nonzero?
> 
> n;
> Is  a  positive or negative?
> 
> n;
> Is  c  positive or negative?
> 
> p;
> Is  cos(kp x2)  positive, negative, or zero?
> 
> p;
> Is  kp  positive or negative?
> 
> p;
>              2  4           3         2  2                    2   2
> (%o3) ((3 %pi  a  - 40 %pi a  + 24 %pi  a  - 72 %pi a + 12 %pi ) c
>             4         2  3            2         2                      2
> 4
>  + (16 %pi a  - 24 %pi  a  + 152 %pi a  - 48 %pi  a + 48 %pi) c + 6 %pi
> a
>            3         2  2                    2       2
>  - 48 %pi a  + 24 %pi  a  - 96 %pi a + 24 %pi )/(6 kp )
> (%i4)
> 
> 
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