subscripts in CAS?

[Wes Loewer]

What I had in mind was the ability to treat a[k] as you would any other identifier, such as solve([a[1]+a[2]+a[3]=1,a[1]^2+a[3]=2, a[2]-a[3]=3],[a[1],a[2],a[3]])

Perhaps it would be better to just show the application I was working on. The following is a function I wrote for Maxima which calculates the coefficients used for the various polynomial integration rules: Trapezoid Rule (n=1), Simpson's Rule (n=2), Simpson's 3/8 Rule (n=3), etc.

Notice how eqs and coefs are lists of equations and coefficients which are determined at run time. In particular, the linsolve() function uses the coefs list as the list of variables to solve for.

Code:


NewtonCotesWeights(n):=
block ( [a, coefs, eqs, sol, k, i, ret],
    p(x,n):=sum(a[k]*x^k, k, 1, n)+a[0],
    coefs(n):=makelist(a[k],k,0,n),
    eqs(n):=makelist(y[k]=p(k*h,n),k,0,n),
    sol:linsolve(eqs(n),coefs(n)),
    for i: 0 thru n do
      b[i]:=rhs(sol[i+1]),
    ret:factor(integrate(sum(b[k]*x^k, k, 1, n)+b[0],x,0,n*h)),
    for i: 0 thru n do
      kill(b[i]),
    ret
    );

NewtonCotesWeights(3);
(3*(y[3]+3*y[2]+3*y[1]+y[0])*h)/8

I've not been able to figure out how to do this on the Prime. It boils down to being able to treat a subscripted identifier as it would any other identifier.