Does anyone have a good idea on how to do this?
I have two polynomials
alpha := x -> sum('a[k]*x^k','k'=0..N);
beta := x -> sum('b[k]*x^k','k'=0..N);.
where N is some constant. I then create a third polynomial
g := x -> beta(alpha(x))^2;
Then I integrate g(x) from some point to an other point, say -1 to 2:
d_tot := int(g(x), x=-1..2);
The result is now a 'polynomial' of the indexes a[i] and b[i] from alpha and beta. So far so good but here I'm stuck.
Next I would like to choose the indexes a[i] and b[i] for all i=0..N in order to minimize d_tot. Therefore I want Maple to see the a[i]'s and b[i]'s as variables and not coefficients so I can do some manipulations (for instance try minimize(d_tot)).
I am however unable to do this and as I understand it the problem is that Maple thinks of the indexes as constants rather then variables.
So, how should I program this?