Hello
Is it possible to do any of the following in Sagemath?

1) Define a sum with arbitrary number of elements, something like :

g= sqrt( sum( a(i)*r(i)^2 , i, 1, n) ),   where a and r are numbers indexed 
by i from 1 to n. Here n is undefined except for being a positive integer. 
I don't want to expand this out in any sense.


2) Process it symbolically, for example

diff( g, r(j))      to get:   a(j)*r(j) / g  


3) Do these things with products as well, for example

define   h = prod( 1+r(i)^2,  i,1,n)

and   diff( h, r(j) )    to produce   h*2*r(j)/(1+r(j)^2) 


I'm trying to work up to taylor approximations of more involved expressions 
for arbitrary n. 

Thanks
Adam

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