More questions about Maxima's tensor functions

> most texts eg YC Fung, "Foundations of Solid Mechanics", 
> write the formulae using only covariant indices.

I understand why they do that, but I personally always felt that it's one of
those "simplifications" that actually make things more complicated in the
end. (I certainly found that it made it much harder for me to learn some
fundamental concepts.)

The bottom line is that just because switching between vectors and covectors
is trivial in flat space when using a rectilinear coordinate system, it's
not an excuse for confusing the two. They're not the same, not even as
geometric objects.

In any case, since itensor is designed to work in the context of general
relativity utilizing the full machinery of Riemannian geometry, the
distinction between covariant and contravariant indices is strictly
enforced.

> I think that I need to contract the E tensor with one of the metric
tensors

Yes, probably. Otherwise, you may arrive at a result that is valid only
under specific circumstances, or not at all.

> Can I suggest that the documentation might be updated to be make
> it clearer what the intended use of the ctensor package is?

I'm still trying to figure that one out 

Seriously, I began as a tensor package user myself; it's just that they were
orphaned, nearly non-functional, and nobody was working on them, so I
volunteered. Though I've done a lot of work on them already, I'm still
learning myself as to what they can and cannot be used for, and how they
might be improved.

> This is usually showing how to express and manipulate vector
> equations in tensorial notation eg dot and cross products.

I think that the fact is, that's not what the tensor packages are for. That
kind of manipulation can be done using the built-in matrix/vector/list/etc.
capabilities of Maxima. The tensor packages are primarily meant to address
the specialized needs of relativity/gravitational theory. At least that's
how they got started, though I certainly hope to make them as generic as
possible!

So what we really need is a tutorial that tells users how to solve tensor
problems, which tools are appropriate for which task, and in particular,
when would the tensor algebra packages be of use.

> I think a good start might be to take the text and examples from the 
> introduction of your paper "Tensor Manipulation in GPL Maxima" and turn 
> that into a demo.

Hmmm. I'll take a closer look at that. The "basic" demos you see are really
just a reorganized version of the content that was in the old demo files for
ctensor/itensor, and perhaps something simpler would indeed be appropriate.


Viktor