I suggest to read chapter 12 of the "Weyl" user manual, where a viable 
attempt has been described:

https://github.com/nilqed/weyl/blob/master/reference/Weyl%20Manual.pdf



On Thursday, 13 February 2025 at 11:59:24 UTC+1 Martin Baker wrote:

> The attached file contains my first tentative experiments with what I
> thought of as Finite Topology. Could you take a quick glance at it to
> see if that's what you would describe as Finite Topology, if not could
> you suggest an alternative name?
>
> Anyway its the subject that interests me at the moment and I think it
> should keep me busy for a few years.
>
> Despite what you say about the usefulness of 'geometric realization' I
> would still like to attempt to implement it, just for completeness and
> my own education. I realise that n points will produce 2*n+1 dimensions
> but FriCAS can handle high dimensional matrix algebra, right? That's one
> of the advantages of doing this on a CAS.
>
> My reason for looking at databases for the representation was not
> performance but because the database structure seems to match the
> mathematical structure better. For instance a minimal complex might be a
> graph which is two tables (nodes and edges) and you could use common
> keys or indexes for the source and target relations between the tables.
> But more importantly I am looking for a way to abstract out topological
> constructs such as sheaf and fibration.
>
> It will take me some time to work though the other issues you mention.
>
> As Ralf suggests I will email him off this list about the 'style guide'
> issues in case my questions here are getting annoying.
>
> Martin
>

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