On Thu, 11 May 2006 11:13:34 -0400 (EDT) "Robert G. Brown" <[EMAIL PROTECTED]> 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
