change of variables for integration



Hello list,

I am experimenting with the changevar command.  I'm trying to
find out if i can also make it work for s-dimensional integration.

In one dimension, things are simple.  We can for example do:

depends(f, x)$
'integrate(f(x), x, 0, 2);
changevar(%, y-x/2, y, x);

Which changes

                                   2
                                  /
                                  [
(%i2)                             I  f(x) dx
                                  ]
                                  /
                                   0

into

                                   1
                                  /
                                  [
(%o3)                           2 I  f(2 y) dy
                                  ]
                                  /
                                   0

But can a similar thing be done for s-dimensional integrals too?

Take for example the function:

s: 3;
f(x) := product(x[i], i, 1, s);

Then I have found that I can integrate it using

integrate(integrate(integrate(f(x), x[1], 0, 2), x[2], 0, 2), x[3], 0, 2);

My first question is if the above command can be written shorter and for
more general (maybe even unspecified, sumbolic?) s (suppose you want to play
with the s-value, how would you change the integrate command?).

My second question is then how to apply the variable transformation

y = x/2

for each of the variables and see the transformed expression for the integral?

Thanks for your advice,
Bart

-- 
	"Share what you know.  Learn what you don't."