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From: John Phillips (phillips_at_[hidden])
Date: 2006-06-20 12:51:47

Oleg Abrosimov wrote:
> There is a very good article in wikipedia about tensors in which tensor
> rank is also described:
> (snip...)
> I'm envision something like boost::operators that can be used to define
> quantities like length or torque (it can be used to define new system of
> units/dimensions). something like:
> struct length : boost::pqs::quantity<1/*rank*/> {...};

   I think you have some nice ideas for the foundations of a Tensor
library, but not for a part of the units and dimensions library. All of
the problems you bring up are problems based in the representations and
algebra of tensors. Things like the difference between vectors and
pseudo-vectors, and rank issues. You never used the terms covariant and
contravariant, but that seems to be where you are working from.
   Unfortunately, if you start down this road, it quickly presents its
own problems. From Tensor theory, we know that there are indexed arrays
of quantities that can interact with tensors, but are not tensors
themselves (the Christoffel symbols, for example). Should this also
become part of the units library? What about the fact that the algebra
of two index tensors is not the same as the algebra of matrices? Do we
need to add something else to account for that? What about magnitudes of
vector and pseudovector quantities? The magnitude of a torque makes
complete physical sense, it is a scalar, and it is still a bad idea to
add one to an energy.

No, on the whole I think te units and dimensions library should try to
retain focus on units and dimensions. That is already a huge issue, and
it has more than sufficient complexity on its own. Tensors are good and
very interesting objects, but the only concern the units library should
have for them is in picking a design that doesn't automatically break them.

> Hope this post would be helpful for units/dimensions subcommunity in
> this list ;-)
> Best regards,
> Oleg Abrosimov.
> _______________________________________________
> Unsubscribe & other changes:

   I think all of this discussion has been quite helpful and valuable
for the interested subcommunity. I doubt there is anyone paying
attention to it who hasn't learned a few things in the process.

                        John Phillips

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