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
construction http://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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