Question on eliminating certain specific patterns of variables

Questions
1

Hi, I am using the following function::

Refine[D[(Sum[((u[k, t] - u[k, t - 1])^2)/T, {k, 1, 10}, {t, 1, 5}] +
     2*(Sum[Sum[(u[i, t] - u[i, t - 1])*(u[j, t] - u[j, t - 1]), {i,
           1, 9}, {t, 1, 5}], {j, 2, 10}]/T)*F)^(1/2), u[1, 1]]]

Here, I am trying to eliminate the overlapping square terms in order to get the pure covariance variable from

2*(Sum[Sum[(u[i, t] - u[i, t - 1])*(u[j, t] - u[j, t - 1]), {i, 1, 9}, {t, 1, 5}], {j, 2, 10}]/T

I am trying to eliminate the resulting variables having same squared expressions of [(u[i,t]-u[i,t-1])(u[i,t]-u[i,t-1])] which contains the same element "i’. For example, I would like to eliminate something like (u[1,2]-u[1,1])*(u[1,2]-u[1,1]). I tried the functions “except” and “eliminate” but did not get the desired outcome at all. Could you please help me out with this critical problem..? Thank you so much in advance. :slight_smile:

2

If you can look at the output from your Refine and post a few example products which you see in that and which you want eliminated then someone should be able to write an example replacement pattern to eliminate those and perhaps eliminate other similar products.