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Question: Can Maple handle dummy indices of tensors?

Question:Can Maple handle dummy indices of tensors?

PoslavskySV 45 Maple
tensor physics
August 12 2013
1

Good day.

Reading the documentation on Physics package in Maple, I did not find information about how Maple handle dummy indices of tensorial expressions. For example, suppose I have the following tensorial expression in Maple: 

    A[mu] * B[~mu] 

with dummy index mu. Then I want to apply the following simple substitution rule:

    A[alpha] = C[alpha]*C[mu]*C[~mu]  

Here, free index alpha should be matched with index mu in x, while dummy index mu should be renamed to avoid a conflict. So, as a result, I would expect something like  

    C[mu]*C[alpha]*C[~alpha]*B[~mu]  

So, my question is can I do such substitutions with tensors in Maple without having to worry about dummy indices?
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