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I have this simple question, given the following sum: Sum[A[i][j][k],{j,0,10},{k,0,10},{i,0,5}]

I would like to apply the condition

$ A[i][j][k]=A[i][k][j] $

How can i do that ?

Thanks

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    $\begingroup$ Maybe something like Sum[If[j == k, A[i][j][k], 2 A[i][j][k]], {j, 0, 10}, {k, j, 10}, {i, 0, 5}]. $\endgroup$
    – JimB
    Commented Sep 8, 2022 at 17:52

1 Answer 1

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Using a conditional pattern:

Sum[A[i][j][k], {j, 0, 10}, {k, 0, 10}, {i, 0, 5}] /.
  A[i_][j_][k_] /; j > k -> A[i][k][j]

(*    A[0][0][0] + 2 A[0][0][1] + 2 A[0][0][2] + ...
      ... + A[5][9][9] + 2 A[5][9][10] + A[5][10][10]    *)

Using explicit construction:

Sum[A[i][Min[j, k]][Max[j, k]], {j, 0, 10}, {k, 0, 10}, {i, 0, 5}]

(*    same as above    *)
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