[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 V. Kisil     email: kisilv at maths.leeds.ac.uk
--                      www: http://maths.leeds.ac.uk/~kisilv/

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