I think I am making progress with my finite topology code but I would
like to check to see if any of you know if there is any existing code in
the FriCAS library that would help me minimise the code I need to write.
I have been looking at the library code and I thought there is a
possibility that nextLatticePermutation in
SymmetricGroupCombinatoricFunctions might possibly do the sort of thing
I want. Is there tutorial information for this combinator code and do
you think it would help with the following?
I now have two domains that can represent topology. In the first one
each representation is a topology like this:
-- A topology on a finite set.
-- Defined by a list of open sets.
-- Elements are labelled by a NNI number.
Rep := Record(basis:Boolean,topology:List (Set NNI))
In the second one each representation is a topology isomorphism class
like this:
-- A representation of a topology isomorphism class consisting of:
-- unlabeledOpenSets: the cardinality of each set
-- substructure: subset lattice structure represented as a poset
-- Only immediate subsets are listed (like Hasse diagram).
-- Top and bottom are assumed so don't have to be explicitly listed.
Rep := Record(unlabeledOpenSets:List NNI,
substructure:List Record(superset:NNI,subset:NNI))
These two domains have very similar functions but they represent
different things.
I want to be able to convert between these representations. For
instance, given a topology isomorphism class, I want a function that
will list all topologies for that class and also a function to construct
one representative topology. Also I would like a function to go in the
reverse direction.
Do you think the combinator code in the library would help? Also this
subject seems to be related to Galois theory, is there any code in the
library that helps with that?
My code is here:
https://github.com/martinbaker/fricasAlgTop/blob/topology/topology.spad
Although this is still at the stage where I am trying to get the overall
design right and to find out how it relates to existing FriCAS code.
Any ideas appreciated, thanks,
Martin
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