Martin Baker wrote:
The GrassmannAlgebra domain has been added to Axiom. --Tim
Tim,
Thanks, do you have any views about how it should evolve from here? I think
the first stage is to fix the known issues and get the inverse function
working well enough to be able to implement transforms for any metric. At
that stage I think the code should be useful for experimenting with
geometry/physics applications.
Then at some stage I think it would be good if there were to be some sort of
discussion about the code and naming structure. For instance: how the
categories and so on should be designed to relate to other algebra families in
Axiom such as Cayley-Dickson, Spinor, Hopf and Tensor Algebras.
Martin
Well Axiom is all about organizing the algebra into hierarchical
categories where
each category build on prior ones.
Is there a natural hierarchy of these algebras? If so, I think it is
important to
extract that hierarchy, define the operations at the category level even
if they
do not have an implementation there, and layer the categories naturally.
I would start by just writing the Cayley-Dickson, Spinor, Hopf, and Tensor
domain definitions (without implementations), find the common operations,
collect them into a category, and inherit from that category.
I know a little bit about Clifford algebra and I'm reading the Grassman
algebra book now but I do not know enough to say anything about what
would be common among the various algebras.
Tim
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