I think I understand the intended structure of the tensor.tensor module a 
bit more now. A lot of the things I have fooled around with are quick hacks 
that don't really fit the use of each class (i.e., just returning a TensMul 
from a covariant derivative function). A quick question - why is it true 
that TensAdd objects are not supposed to support index order? Is this a 
function of the other algorithms like canonicalization that I'm not as 
interested in? 

I'd like to ask more generally what use a tensor is if the indices are 
unordered, but I suppose that just reveals my ignorance as a novice 
physicist - I think of Tensors in a pretty concrete matrix-based way, and 
when I'm not thinking of them as matrices, I'm thinking of them as 
functions, which requires an argument order. 

I will take your advice and look more at sympy.diffgeom for the time being 
- do you know if it's possible to implement mixed tensors there? Perhaps it 
would be easier to build a TensorArray class that provides an interface 
more like sympy.tensor.tensor while using the implementation of 
sympy.diffgeom.

Thank you for taking the time to explain everything about the structure of 
the module.

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