Re: [boost] [PQS] rank of a physical quantity?

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:
> http://en.wikipedia.org/wiki/Tensor
> 
> (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.
> _______________________________________________
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> 

   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