Re: gsl_quaternion proposition

[linas at austin dot ibm dot com (Linas Vepstas)]

I demand that Robert G. Brown are belonging when Thu, May 11, 2006 at 10:00:10PM -0400:
> 
> That's why I am hesitant about seeing quaternions done out of context,
> as it were.  If anybody ever does decide to do a real Clifford/Geometric
> algebra package with the grade (dimension) of the algebra basically a
> free input parameter, it would both include quaternions as a particular
> grade and would probably represent them slightly differently.  Of course
> the same could be said about complex.

There is one other narrow area where quaternions and octonians
(together with real and complex) enjoy a "special" place in the 
grand scheme of things, and that is in the Berger classification
of Riemann symetric spaces (see wikipedia entries on "holonomy"
and "Calabi-Yau manifold"). Basically, if a space is symmetric,
its going to be a product of real or complex or quaternion 
or octonian thise SO(n) or SU(n) or Sp(n) or the special cases 
of G_2 or Spin(7)). But again, this is "obscure" and would not
be an argument for inclusion in GSL.

The point is only that quaternions are in a certain way "special"
and in a certain way a "natural" extension of the complex numbers 
in a way that general clifford algebras are not.

--linas