I just noticed this 
http://groups.google.com/group/sage-devel/browse_thread/thread/16fc3c4cb4020728
recent thread referencing http://wiki.sagemath.org/days7/coercion,
which addresses alot of the things we had questions about. It's good
to see this restructuring happening, and all the good energy around
this project!

Eric Drechsel

On Feb 14, 5:56 pm, Eric Drechsel <[EMAIL PROTECTED]> wrote:
> Hi, I'm an undergrad at Portland State, where we have been learning
> Sage as part of our Computer Assisted Mathematics Group. We want to
> compute with octonions in Sage, and discussed at our meeting last
> night possibly implementing such an algebra.
>
> As I understand it, multiplication of octonions can be implemented on
> top of the quaternions in a simple way using the Cayley-Dickson
> constructionhttp://en.wikipedia.org/wiki/Octonion#Cayley-Dickson_construction
> .
>
> The difficulty then would seem to be to do it correctly so that it
> works with the rest of sage. I'm willing to do it once badly just for
> fun and then later maybe help with doing it correctly, but I'd like to
> at least get off to a respectable start. Any help would be greatly
> appreciated.
>
> Oh also in searching for existing implementations I saw that boost has
> this:
>    http://www.boost.org/doc/html/boost_math/octonions.html
> but since sage already implements quaternions it seems unnecessary to
> look at boost except perhaps for inspiration.
>
> Regards,
> Eric Drechsel
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