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Re: [Axiom-developer] GrassmannAlgebra domain

From: Tim Daly
Subject: Re: [Axiom-developer] GrassmannAlgebra domain
Date: Thu, 10 Dec 2009 15:03:34 -0500
User-agent: Thunderbird (Windows/20090302)

Martin Baker wrote:
The GrassmannAlgebra domain has been added to Axiom. --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.


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.


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