Quaternions in Python

[Carl Banks]

Paul Rubin <phr-n2001 at nightsong.com> wrote:
> Erik Max Francis <max at alcyone.com> writes:
>> > I think there's a simple way to represent quaternions as 3x3 matrices.
>> > So you could probably just store them that way and use NumPy for the
>> > arithmetic.
>> 
>> ... which rather defeats the purpose for using quaternions in the first
>> place.
> 
> Nah.  I mean, if efficiency was a big issue, you wouldn't be using an
> interpreted language in the first place.  What's left, if you have a
> good matrix package, is something like if your language had complex
> numbers but didn't have reals.  You can still represent the reals as
> complexes.  For that matter, lots of languages have had reals but no
> integers.  It hasn't been that bad a problem.

You severely underestimate the difficulty of doing this.  While any
quarternion can be represented as a 3x3 matrix, not every 3x3 matrix
is a quarternion.  And keeping your matrix in "quarternion form" when
you do arithmetic is not trivial.

To wit, a quarternion has 4 components.  A 3x3 matrix has 9
components.  Therefore, when doing quarternion arithmetic using a 3x3
matrix, you must be sure the resulting matrix satisfies 5 constraints.
And, IIRC, the constraints are not simple.

(Contrast this to using a complex as a real.  Here, only one very
simple constraint, namely Im(z)==0, must be maintained.)


-- 
CARL BANKS