Las Vegas algorithm for exterior algebraic shifting #5587
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| @doc raw""" | ||
| complex_faces(K::SimplicialComplex) | ||
| Returns a Set{Set{Int}} containing all simplices of K. | ||
| complex_faces(K::SimplicialComplex, dim::Int) | ||
| Returns a Set{Set{Int}} containing all d-simplices of K. | ||
| """ | ||
| complex_faces(K :: SimplicialComplex) = union(complex_faces_by_dimension(K)...) :: Set{Set{Int}} | ||
| complex_faces(K :: SimplicialComplex, dim::Int) = complex_faces_by_dimension(K, mindim=dim)[dim+1] :: Set{Set{Int}} |
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The docstrings in this file are not properly formatted.
This function should probably be renamed to just faces (we have the same for polyhedra, without the variant without a dimension).
I think complex_faces_by_dimension should be removed, faces(K,dim) can be implemented directly without first allocating a vector for all dimensions. And faces(K) could use elements(p::PartiallyOrderedSet) instead of splatting+union.
| return uniform_hypergraph(faces, n, only(Set(length.(faces)))) | ||
| end | ||
| const CollectionTypes = Union{Set{Set{Int}}, Vector{Vector{Int}}, Vector{Combination{Int}}} | ||
| uniform_hypergraph(faces::CollectionTypes, n::Int, k::Int) = UniformHypergraph(n, k, sort(collect(Set(sort.(collect.(Set.(faces))))))) |
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Even though this was not really changed in this PR that sort(... looks weird and inefficient (converting to a (unordered) set first and then sorting it).
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see latest commits
| end | ||
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| function load_object(s::DeserializerState, K::Type{UniformHypergraph}) | ||
| return uniform_hypergraph(load_object(s, Vector{Vector{Int}})) |
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We could assume that the data is properly sorted and avoid the re-sort on load?
(But if we change the construction to avoid at least some of the sorting this could be ok?)
| end | ||
| for k=i+1:nrows(M) | ||
| M[k, :] = M[i, j]*M[k, :] - M[k, j] * M[i, :] | ||
| M[k, :] = M[i, j]*M[k:k, :] - M[k, j] * M[i:i, :] |
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Why is this changed here? If it was wrong then a test would be good.
| Returns a Vector{Set{Set{Int}}} fs such that fs[d+1] contains all d-simplices of K. | ||
| """ | ||
| function complex_faces_by_dimension(K :: SimplicialComplex; mindim::Int=0) |
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This doesn't use the mindim argument (but I suggested to remove this function anyway).
And it currently starts from rank 1 so it would omit the bottom element (i.e. the empty face of dimension -1).
Co-authored-by: Benjamin Lorenz <[email protected]>
…g-shifting-post-issac
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las vegas algorithm for computing the exterior algebraic shifting.
Includes improvements that takes advantage of the lower dimensional faces and eliminates higher co faces when the result is a shifted complex.