gsl_quaternion proposition

picca@synchrotron-soleil.fr picca@synchrotron-soleil.fr
Thu May 11 16:31:00 GMT 2006


On Thu, 11 May 2006 11:13:34 -0400 (EDT)
"Robert G. Brown" <rgb@phy.duke.edu> wrote:

> But this is getting a bit OT, sorry.  This does answer Linas's question,
> at least to some extent.  Although one certainly can do any actual
> computations associated with quaternions by means of the various already
> supported operations in the Grassman product (and by making up one's own
> quaternion struct as needed) or via complex matrices or with 4x
> matrices, all within the GSL, the process might be easier and more
> portable if they were consistently supported within the library as named
> entities.

so creating a gsl_quaternion might be the begining of lie algebras in
the GSL ? after this we can add octonion etc...

>  Second, it is possible that 3-vector rotations are more
> efficient when done by multiplying quaternions, although I'd want to see
> it proven by actual code; other S3/SO(3R)/SU(2) operations can fairly
> naturally be done in quaternionic form (and sometimes encapsulate
> physics algebraically expressed in that form.

I think that composition of rotation are more accurate with quaternions
than with matrix product. I do not catch the S3/SO(3R)/SU(2) (you know
material science ;).

> A lot of this is also true indeed if support for lie algebras and groups
> were added to the GSL (although exactly how to add it -- once again it
> is "there" insofar as one can select matrix representations already, so
> this is largely a matter of specifying the data objects and methods e.g.
> group members, the associated group product rules, the generators.  The
> rotation group is obviously useful.  The Lorentz group is also, although
> one starts to hit on the problem talked about a year or two ago about
> the difficulty of specifying tensors higher than second rank in the GSL.
> Getting up to the higher U(n) or SU(n) or SO() (etc) groups, though --
> you hit an ever smaller list of possible numerical applications, do you
> not?  So that once again having it is partly to encourage new work in it
> and understanding of it.

If I understand we could add something more generic by defining a lie
object which different generator for complex numbers, quaternions and
octonion. Just by providing the multiplication table of the object ?

> Maybe it
> could be a joint maxima/GSL effort?

Yes it seems to be a long term program :), do you have some knowledge of maxima ?

Fred



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