After finding Maple inflexible and temperamental, I am interested in using GiNaC for some computations in exterior differential systems. I've read through the documentation fairly carefully, but I haven't seen any routines for working with exterior differential forms so far. Has anyone written a library to deal with alternating forms, including things like wedge-products, exterior differentiation, Lie derivatives (via Cartan's formula), and left-hook (inner product with vectors)? Thanks, Abe Smith (Duke University)
Dear Abe,
"AS" == Abraham D Smith <adsmith@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@maths.leeds.ac.uk -- www: http://maths.leeds.ac.uk/~kisilv/
We are working on a Python module built on top of GiNaC that implements alternating forms etc. The project is in its early stages, but you can download the development repository with hg clone http://www.fenics.org/dev/exterior if you have mercurial (hg) installed. Regards, Kent-Andre Mardal Simula Research Laboratory
After finding Maple inflexible and temperamental, I am interested in using GiNaC for some computations in exterior differential systems.
I've read through the documentation fairly carefully, but I haven't seen any routines for working with exterior differential forms so far.
Has anyone written a library to deal with alternating forms, including things like wedge-products, exterior differentiation, Lie derivatives (via Cartan's formula), and left-hook (inner product with vectors)?
Thanks, Abe Smith (Duke University)
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participants (3)
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Abraham D. Smith
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kent-and＠simula.no
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Vladimir Kisil