Operations on sums inside functions in Maxima -

Operations on sums inside functions in Maxima -

i trying compute derivative back-propagation analytically, using maxima. write:

declare(n,[scalar,integer]); declare(i,[scalar,integer]); declare(j,[scalar,integer]); declare(m,[scalar,integer]); declare(n,[scalar,integer]); assume(n>10); assume(i<=n,j<=n,m<=n,n<=n); x1(i):=f(sum(w[i,j]*x0[j],j,1,n));

now trying evaluate:

diff(x1(i),w[i,m])

and returns zero, while supposed return

f(...) * x0[m]

moreover, i've noticed x1(j) returns

sum_j=1^n w[j,j] * x0[j]

while expect alter internal index j other letter, j1 , return

sum_j1=1^n w[j,j1] * x0[j1]

is there way create maxima "smarter" in regards, i.e. create compute derivatives respect indeces , automatically alter letter when there conflict input?

about stuff diff(x1(i),w[i,m]), unfortunately maxima can't handle it. have made progress on differentiating respect indexed variables, works 1 index, not two, have here. if have time work on extending 2 indices, short reply is, i'm afraid, can't done.

function sum backpropagation maxima