Re: [Axiom-developer] GrassmannAlgebra domain

[Tim Daly]

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