[GiNaC-list] Exterior algebra tools?
Vladimir Kisil
kisilv at maths.leeds.ac.uk
Thu May 24 00:11:23 CEST 2007
Dear Abe,
>>>>> "AS" == Abraham D Smith <adsmith at ams.org> writes:
AS> I've read through the documentation fairly carefully, but I
AS> haven't seen any routines for working with exterior differential
AS> forms so far.
GiNaC has a basic support for general Clifford algebras and you can
use it for differential forms in two ways.
1. Create a Clifford unit with zero as its metric---these will be
differentials dx_j, since they obey
dx_j dx_i = - dx_i dx_j, dx_i dx_i = 0
2. You may translate all questions on differential forms to standard Clifford
algebras, see:
http://en.wikipedia.org/wiki/Clifford_algebra (notably sections 5.1 and 10.1):
AS> Has anyone written a library to deal with alternating forms,
AS> including things like wedge-products,
The product of Clifford units is exactly the wedge-product (do not
forget use canonicalise_clifford() to simplify term).
AS> exterior differentiation,
AS> Lie derivatives (via Cartan's formula), and left-hook (inner
AS> product with vectors)?
This is not implemented in the GiNaC core so far...
Best wishes,
Vladimir
--
Vladimir V. Kisil email: kisilv at maths.leeds.ac.uk
-- www: http://maths.leeds.ac.uk/~kisilv/
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