[Axiom-math] FW: computers clifford algebra and differential forms

[Page, Bill]

The following paper describes a system for manipulating and
visualizing differential forms and Clifford multivectors
(geometric algebra) in a symbolic manner on a computer system:

http://citeseer.ist.psu.edu/chard00multivector.html

http://sal-cnc.me.wisc.edu/publications/multivector/multivector-color.pd
f

A multivector data structure for differential forms and equations

Jeffrey A. Chard,  Vadim Shapiro
May 31, 2000

Abstract

We use tools from algebraic topology to show that a class of
structural differential equations may be represented combinatorially
and thus by a computer data structure. In particular, every
differential k-form may be represented by a formal k-cochain over
a cellular structure that we call a starplex, and exterior
differentiation is equivalent to the coboundary operation on the
corresponding k-cochain. Furthermore, there is a one to one
correspondence between this model and the classical finite
cellular model supported by the Generalized Stokes' Theorem, and
translation between the two models can be completely automated.

Our results point the way to a common combinatorial and data
structure well-suited for a physical modeling computer algebra
that unifies finite and infinitesimal, symbolic and numeric,
geometric and physical descriptions of distributed phenomena.
We illustrate the advantages of our approach by a prototype
interactive physics editor that uses the computer algebra to
automatically translate intuitive geometrical/physical
descriptions of balance conditions created by the user into the
corresponding symbolic differential and integral equations.

----------

Axiom already implements both Clifford algebra and differential
forms (see DeRahmComplex) but not in this more modern integrated
approach. I like the way this proposal presents both Clifford
algebras (multivectors) and differential forms in one package
and with one graphical user interface.

I wonder if there is any interest here in a project to implement
something like this in Axiom?

Regards,
Bill Page.