Question: Tensor summation

Hi, I have a problem with tensor calculus. Please guide me.

I have two Tensors B[mu, nu] and A[~mu, ~nu].

Furthermore, I have two mixed tensors as U[~1, mu, nu] and U[~2,mu,nu]

rho, mu, and nu can run from 1 to 2. Hence, A, B, and both Us are 2*2 matrices.

Note that there was only one U, but since it is a mixed tensor, hence I have separated it into two tensors for making it easy.

Now I want to compute the following summation:

U[~rho,mu,nu] U[~alpha,beta,gamma] B[rho,alpha] A[~mu,~beta] A[~nu,~gamma].

Maple must give a number for rho, mu, nu, alpha, beta, and gamma (which can take 1 and 2) and compute "all" possible summations. Since the result will be just "a number", hence I could not use TensorArray.

How can I do it and get a result?

The forms of all tensors are in the attached maple file:


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