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## Main Question or Discussion Point

Hello! I'm doing a code in Mathematica 6.0 in order to calculate a contraction of indices with the Levi-Civita tensor (in six dimensions) and an antiSymmetric tensor A[m,n,p] (it has 3 indices running from 1 to 6). For example in order to turn A into an antisymmetric tensor, I wrote something like this in the code:

Input: A[m, n, p] := 1/6 (A[m, n, p] - A[m, p, n] - A[n, m, p] + A[n, p, m] + A[p, m, n] - A[p, n, m]);

But it seems that mathematica doesnt take it into account because at the end of the final computation, the output shows this kind of things:

2 b (-A[5, 4, 6] B[1, 2, 3] + A[5, 6, 4] B[1, 2, 3] +

A[6, 4, 5] B[1, 2, 3] - A[6, 5, 4] B[1, 2, 3] -

A[3, 5, 6] B[1, 2, 4] + A[3, 6, 5] B[1, 2, 4] +

A[5, 3, 6] B[1, 2, 4] - A[5, 6, 3] B[1, 2, 4] )

(B is another antisymmetric tensor and b is a constant). So , as you see, the first 3 terms should be together because of the antisymmetric property of A, but they arent. The expression is already simplified by mathematica.

Anybody knows how can i fix the code? thank you in advance.

Input: A[m, n, p] := 1/6 (A[m, n, p] - A[m, p, n] - A[n, m, p] + A[n, p, m] + A[p, m, n] - A[p, n, m]);

But it seems that mathematica doesnt take it into account because at the end of the final computation, the output shows this kind of things:

2 b (-A[5, 4, 6] B[1, 2, 3] + A[5, 6, 4] B[1, 2, 3] +

A[6, 4, 5] B[1, 2, 3] - A[6, 5, 4] B[1, 2, 3] -

A[3, 5, 6] B[1, 2, 4] + A[3, 6, 5] B[1, 2, 4] +

A[5, 3, 6] B[1, 2, 4] - A[5, 6, 3] B[1, 2, 4] )

(B is another antisymmetric tensor and b is a constant). So , as you see, the first 3 terms should be together because of the antisymmetric property of A, but they arent. The expression is already simplified by mathematica.

Anybody knows how can i fix the code? thank you in advance.