What I would like to see is the powerful capabilities in FriCAS/Axiom
for equation solving and so on in "classic mostly commutative algebra"
to be packaged in such a way that they could be adapted for other
axiomatic systems.
Most useful to me would be the ability to write equation solvers in
matrix, quaternion, Clifford algebras where the variables represent, not
real/complex numbers, but elements of these algebras.
Another example is that I am writing code for different types of logic
(Heyting, frames, etc.) and this includes domains for poset, lattice and
so on.
I have documented this here:
http://www.euclideanspace.com/prog/scratchpad/mycode/discrete/logic/
or, if you don't like documentation, you can go straight to the code here:
https://github.com/martinbaker/multivector/blob/master/logic.spad
So could you include this in any changes you are making, in particular:
1) Include poset, frame, lattice, etc. into the category hierarchy.
2) Generalise equation solving capabilities to allow use for other
structures.
3) Include axioms in category definitions.
Martin
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