# [Maxima] Definite integrals and asksign

Fri Dec 8 10:21:01 CST 2006

```hi Neilen

my diff_forms package may do this.
Because this problem can be solved by changing integral variable more than
two.
(%i2) batch("cartan_init.bat");

batching #p/home/furuya/sagyo/cartan_init.bat
(%i4)                              infix(@)
(%i5)                              infix(&)
(%i6)                              infix(|)
....
(%o16)                          cartan_init.bat
(%i18) (x2/2+x1/2)*sin((%pi*(-x3/2-(-x3-x2-x1+1)/2+x2/2+x1/2))/2)\$
(%i19) ratsimp(%);
2 %pi x2 + 2 %pi x1 - %pi
(x2 + x1) sin(-------------------------)
4
(%o19)             ----------------------------------------
2

(%i20) f_star([u,v,w],(x:u,y:v-u,z:w-v,(x+y)/2*sin(%pi*(x+y)/2-%pi/4)
*d(x)@d(y)@d(z)));
%pi v   %pi
Du Dv Dw v sin(----- - ---)
2      4
(%o20)                    ---------------------------
2
(%i21) integrate(integrate(integrate(subst([Du=1,Dv=1,Dw=1],%o20),u,0,1-v),
w,1-v,1),v,0,1)\$
(%i22) ratsimp(%);
....
(%i23) display2d:false;
(%i24) %o20;
(%o24) Du*Dv*Dw*v*sin(%pi*v/2-%pi/4)/2
(%i25) %o22;
(%o25) -(sqrt(2)*%pi^2+12*sqrt(2)*%pi-48*sqrt(2))/%pi^4
%o25 is the result.
(%i26) integrate(integrate(integrate(1,u,0,1-v),w,1-v,1),v,0,1);

(%o26) 1/6

I think diff_forms is a glue for cas.

thanks
Gosei Furuya

2006/12/9, Robert Dodier <robert.dodier at gmail.com>:
>
> On 12/8/06, Raymond Toy <raymond.toy at ericsson.com> wrote:
>
> >     Neilen> Would I be correct in guessing that Maxima would have been
> able to figure out
> >     Neilen> what you passed in the assume() above if it had a built in
> multiple integral
> >     Neilen> routine that could consider all the integral limits
> simultaneously?
> >
> > I think that would be a simple matter of programming. :-)  Someone
> > would have to modify the definite integration routines to inform
> > maxima about the range of the variables.  I think it would be fairly
> > difficult for maxima to figure out that 1 - x1 - x2 > 0.
>
> The sum/product code substitutes a gensym for the index of
> summation and then calls assume to assert that the gensym
> is between the limits of summation. This helps Maxima
> simplify some summands. It seems the integration code
> could do likewise.
>
> All the best,
> Robert
> _______________________________________________
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>
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