[Axiom-developer] exterior algebra

[root]

Bertfried,

A while ago we had talked about developing Axiom's clifford algebra
package to do more things, similar to the package you wrote. 

I spent some time this summer reading up on clifford/exterior algebras.

I've been thinking about this in the background. Potentially a useful
way to approach the development of such a package is in a mentor/student
style. You, of course, have the mentor role.

  (An aside: I've been pondering ways to develop algebra in Axiom
   and the mentor/student model is one I'd like to explore. Since
   you've already done a similar package elsewhere this should not
   involve a lot of "advisor" time. But, like any teaching exercise,
   it still requires a fair bit of careful thought)

It would be useful if you could provide an input file that showed
a graded set of exercises, starting with the most trivial and working
toward more complex, in an input file. The idea is to show what Axiom
can currently do up until it reaches the limits of the current 
implementation. 

Following that would be a few examples of what you would expect it to
do but which is not yet implemented. Each of these would have either
a book/paper reference (so I can look it up), and the expected result.
I can attempt an implementation and you can give feedback about
correctness and completeness.

The end result is a documented set of "class notes" which illustrate
Axiom's capabilities and new features.

So I'm asking you to construct an input file that gently approaches
and steps over the edge of what Axiom can currently do, with a
suitable set of references and I'll take it from there.

Tim