Re: gsl_quaternion proposition

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

I demand that picca@synchrotron-soleil.fr are belonging when Thu, May 11, 2006 at 02:27:29PM +0200:
> On Wed, 10 May 2006 12:03:20 -0500
> linas@austin.ibm.com (Linas Vepstas) wrote:
> 
> > What is the intent of this? Are you thinking of creating some 
> > gsl_sf_* routines to accept this type? What's the grand vision?
> 
> For me the intend is to use quaternions to compute rotations in the 3D
> space. 

OK.

> It is more accurate than matrix multiplication. 

!! I'm a little surprised by this statement. The round-off errors
from working with a 2x2 matrix directly, versus decomposing it 
via the 2x23 Paul matrices (quaternions) would seem to be nearly 
the same.

> > The other possible way to generalize is to su(n) and other Lie algebrs,
> > but I don't see the point.
> 
> Maybe but I do not have the competences to do the generalization.
> With your help why not ?

Many reasons not to do it:
-- presumably, there are already algebra packages that do this.
-- this is breaking new ground for GSL; there's no precedent.
-- I personally have no grand vision for what to do with this.
   I can imagine useful tools: maybe something that automatcally
   gave you the different representations. Something that 
   automatically allowed you to work in homogenous spaces 
   (aka the Wigner-Seitz cells for general Lie groups). Something
   that atomatically computed Anosov flows/horocycle flows. 
   Generalizations of hypergeometric functions. Generalizations of 3-j
   and 6-j symbols. I dunno. This is all obscure, narrow-interest 
   stuff.  I don't know what others would find useful.

--linas