Hi Jose, thank you for your reply,

I am not sure if I understand everything completely, but it seems to me dangerous that the $\text{simplifyDelta}$ function outputs $m(k,l)$. The reason for this is that $m(k,l)$ could theoretically be non-zero while the values of $k$ and $l$, for example, be greater than $n$ (the upper bound on the sums ( $\sum _{i=1}^n \sum _{j=1}^n m(i,j) \delta _{i,k} \delta _{j,l}$)). In that case, no simplifications should be made because there is not enough information given to the function. ( $\sum _{i=1}^n \sum _{j=1}^n m(i,j) \delta _{i,k} \delta _{j,l} = 0$ if $k>n$ or $l>n$). But I am sure there is a way to construct a nice Mathematica function to deal with this. I will explore the package you suggested me : )

Is this solved now? I have a similar problem where if I define

W = Sum[u[c[x, t + a, a], l[x, t + a, a]], {x, 1, N}]
dWdc = FullSimplify[D[W, c[y, a + t, a]], N >= y && y >= 1 && y \[Element] Integers ]

I still get Delta[x,y] in the output. What am I doing wrong?

It seems the Kronecker delta accepts non-integer values, so I also tried to specify that $k$ had to be an integer, but it does not work either:

mySum = Sum[a[i] b[i], {i, n0, n1}]
myValue = D[mySum, a[k]]
myValue /. {n0 -> 1, n1 -> n}
Simplify[myValue /. {n0 -> 1, n1 -> n}, 
 k >= 1 && k <= n && Element[k, Integers]]

outputs $\sum _{i=1}^n b(i) \delta _{i,k}$

Hi Henrik, thank you for your reply,

I won't necessarily always want to sum over all of the integers. I tried the code you suggested and the only result I get is: $\sum _{i=-\infty }^{\infty } b(i) \delta _{i,k}$. I also added the following line of code:

TeXForm[Simplify[myValue /. {n0 -> -Infinity, n1 -> Infinity}]]

And I still don't get the simplification, that is $\sum _{i=-\infty }^{\infty } b(i) \delta _{i,k}$. It would be helpful if Mathematica were able to do simple simplifications like this. The actual simplification I wanted to make was not this one, but it partly illustrates the point.