WIP: Cellular Sheaf Macro

[cscaff]

This macro abstracts functions such as:

1. CellularSheaf(vertex_stalks::Vector{Int}, edge_stalks::Vector{Int})
2. set_edge_maps!(s::AbstractCellularSheaf, v1::Int, v2::Int, e::Int, rm1::AbstractMatrix, rm2::AbstractMatrix)

It accepts restriction map matrices as argument parameters and allows a user to declare vertex stalks and linear relations
representing edges in the cellular sheaf. For instance, a user can represent a triangular sheaf using the following julia code:

# Define restriction maps as matrices
A = [1 0 0 0]
B = [1 0 0 0]
C = [1 0 0 0]

# You can pass in the maps as follows: 

triangle = @cellular_sheaf A, B, C begin
    # You can define vertex stalks using the format: name::Stalk{dimension}
    x::Stalk{4}, y::Stalk{4}, z::Stalk{4}

    # Then, you can define your relations as equations:

    # For instance, in "A(x) == B(y)", x and y are incident vertices. A maps x to the shared edge stalk. B maps y to the shared edge stalk.
    A(x) == B(y)
    A(x) == C(z)
    B(y) == C(z)

end

The previous code is the same as writing:

c = CellularSheaf([4, 4, 4], [1, 1, 1])
set_edge_maps!(c, 1, 2, 1, C, C)
set_edge_maps!(c, 1, 3, 2, C, C)
set_edge_maps!(c, 2, 3, 3, C, C)

While the first example may appear like more lines of code, it is far easier to understand the pattern that is occuring, making it easier for developers
to quickly construct cellular sheaves. Likewise, because edge stalk dimensions are inferred, this provides a more disciplined approach to building sheaves,
leaving less room for errors.

[cscaff]

Current Issue: Only multiple parameters are accepted into the macro. I need to fix this, but I'm too sleepy right now to make it work. Will fix when I am awake.

[tylerhanks]

Overall looks great! Just see my comment about the test at the very end. It would also be nice to add a few more tests for other graph topologies, e.g. path graph or star graph.

[jpfairbanks]

@cscaff let's get this merged on Monday, there are significant conflicts that I can't fix in the editor. If tests have to get done in another PR that is OK. I want to start using this code and so we need to this and #37 merged into main

[cscaff]

@cscaff let's get this merged on Monday, there are significant conflicts that I can't fix in the editor. If tests have to get done in another PR that is OK. I want to start using this code and so we need to this and #37 merged into main

I have graduation tomorrow so I'll be pretty busy, but I'm trying to figure out how to fix the conflicts now. Not sure how to view this within VSCode. Looking up tutorials.

[cscaff]

Ok, should be good! @jpfairbanks