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. _______________________________________________ Axiom-math mailing list [email protected] http://lists.nongnu.org/mailman/listinfo/axiom-math
