Back in 2008, I said I was interested in adding support for Clifford algebras / Geometric Algebra to Sage. Since then I have found out that there is some support available in Axiom. Now that there is renewed interest in Exterior algebras, I would like to better understand how to incorporate both the Exterior algebras and the Clifford algebras into Sage in a way that makes sense both in terms of coercion and in terms of Categories, Is there an existing structure we could bolt our implementations into, or do we need to define these ourselves? I would much prefer elegance and logical consistency over convention. I do know that there are lots of conventions hanging around Clifford algebras and spinors, but I don't want these to get in the way.
As a prototype, I added a Python interface to GluCat <http://glucat.sf.net>, implemented via Cython code. (GluCat implements both the Clifford and the exterior product, as well as inner products and the left contraction.) I began the Python interface at Sage Days 10 in Nancy, and am still refining this interface in anticipation of Cython v0.16. I did not try to add this to Sage (1) because it only implements a special case (up to 64 generators, Real field via float, double, dd_real or qd_real), (2) because it employs its own convention for generators and basis elements (signed index sets), (3) because I did not understand coercion or Categories in Sage, (4) because my ARC grant applications which included this work were unsuccessful, but mostly (5) because I did not make the time to do this. -- To post to this group, send an email to [email protected] To unsubscribe from this group, send an email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-devel URL: http://www.sagemath.org
