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c29000d912
...
463a3b21e1
engine-proto
@ -12,68 +12,46 @@ using Groebner
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abstract type Element{T} end
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abstract type Element{T} end
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mutable struct Point{T} <: Element{T}
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mutable struct Point{T} <: Element{T}
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coords::Vector{MPolyRingElem{T}}
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coords::Union{Vector{MPolyRingElem{T}}, Nothing}
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vec::Union{Vector{MPolyRingElem{T}}, Nothing}
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vec::Union{Vector{MPolyRingElem{T}}, Nothing}
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rel::Nothing
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rel::Nothing
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## [to do] constructor argument never needed?
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## [to do] constructor argument never needed?
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Point{T}(
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Point{T}(
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coords::Vector{MPolyRingElem{T}} = MPolyRingElem{T}[],
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coords::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing,
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vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing
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vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing
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) where T = new(coords, vec, nothing)
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) where T = new(coords, vec, nothing)
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end
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end
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##coordnames(_::Point) = [:xₚ, :yₚ, :zₚ]
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coordnames(_::Point) = [:xₚ, :yₚ, :zₚ]
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function buildvec!(pt::Point)
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function buildvec(pt::Point, coordqueue)
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coordring = parent(pt.coords[1])
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coordring = parent(coordqueue[1])
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pt.coords = splice!(coordqueue, 1:3)
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pt.vec = [one(coordring), dot(pt.coords, pt.coords), pt.coords...]
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pt.vec = [one(coordring), dot(pt.coords, pt.coords), pt.coords...]
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end
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end
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mutable struct Sphere{T} <: Element{T}
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mutable struct Sphere{T} <: Element{T}
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coords::Vector{MPolyRingElem{T}}
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coords::Union{Vector{MPolyRingElem{T}}, Nothing}
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vec::Union{Vector{MPolyRingElem{T}}, Nothing}
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vec::Union{Vector{MPolyRingElem{T}}, Nothing}
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rel::Union{MPolyRingElem{T}, Nothing}
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rel::Union{MPolyRingElem{T}, Nothing}
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## [to do] constructor argument never needed?
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Sphere{T}(
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Sphere{T}(
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coords::Vector{MPolyRingElem{T}} = MPolyRingElem{T}[],
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coords::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing,
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vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing,
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vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing,
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rel::Union{MPolyRingElem{T}, Nothing} = nothing
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rel::Union{MPolyRingElem{T}, Nothing} = nothing
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) where T = new(coords, vec, rel)
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) where T = new(coords, vec, rel)
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end
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end
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##coordnames(_::Sphere) = [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
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coordnames(_::Sphere) = [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
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function buildvec!(sph::Sphere)
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function buildvec(sph::Sphere, coordqueue)
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coordring = parent(sph.coords[1])
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coordring = parent(coordqueue[1])
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sph.coords = splice!(coordqueue, 1:5)
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sph.vec = sph.coords
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sph.vec = sph.coords
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sph.rel = mprod(sph.coords, sph.coords) + one(coordring)
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sph.rel = mprod(sph.coords, sph.coords) + one(coordring)
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end
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end
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const coordnames = IdDict{Symbol, Vector{Union{Symbol, Nothing}}}(
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nameof(Point) => [nothing, nothing, :xₚ, :yₚ, :zₚ],
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nameof(Sphere) => [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
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)
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coordname(elem::Element, index) = coordnames[nameof(typeof(elem))][index]
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function pushcoordname!(coordnamelist, indexed_elem::Tuple{Any, Element}, coordindex)
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elemindex, elem = indexed_elem
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name = coordname(elem, coordindex)
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if !isnothing(name)
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subscript = Subscripts.sub(string(elemindex))
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push!(coordnamelist, Symbol(name, subscript))
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end
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end
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function takecoord!(coordlist, indexed_elem::Tuple{Any, Element}, coordindex)
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elem = indexed_elem[2]
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if !isnothing(coordname(elem, coordindex))
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push!(elem.coords, popfirst!(coordlist))
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end
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end
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# --- primitive relations ---
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# --- primitive relations ---
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abstract type Relation{T} end
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abstract type Relation{T} end
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@ -121,38 +99,22 @@ function Base.push!(ctx::Construction{T}, rel::Relation{T}) where T
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end
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end
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function realize(ctx::Construction{T}) where T
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function realize(ctx::Construction{T}) where T
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# collect coordinate names
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# collect variable names
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coordnamelist = Symbol[]
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coordnamelist = Symbol[]
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elemenum = enumerate(ctx.elements)
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elemenum = enumerate(ctx.elements)
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for coordindex in 1:5
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for (index, elem) in elemenum
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for indexed_elem in elemenum
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subscript = Subscripts.sub(string(index))
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pushcoordname!(coordnamelist, indexed_elem, coordindex)
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append!(coordnamelist,
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end
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[Symbol(name, subscript) for name in coordnames(elem)]
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)
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end
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end
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display(collect(elemenum))
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display(coordnamelist)
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println()
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# construct coordinate ring
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# construct coordinate ring
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coordring, coordqueue = polynomial_ring(parent_type(T)(), coordnamelist, ordering = :degrevlex)
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coordring, coordqueue = polynomial_ring(parent_type(T)(), coordnamelist, ordering = :degrevlex)
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# retrieve coordinates
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for (_, elem) in elemenum
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empty!(elem.coords)
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end
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for coordindex in 1:5
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for indexed_elem in elemenum
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takecoord!(coordqueue, indexed_elem, coordindex)
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end
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end
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# construct coordinate vectors
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# construct coordinate vectors
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for (_, elem) in elemenum
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for (_, elem) in elemenum
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buildvec!(elem)
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buildvec(elem, coordqueue)
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display(elem.coords)
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display(elem.vec)
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println()
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end
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end
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# turn relations into equations
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# turn relations into equations
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@ -1,110 +0,0 @@
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module HittingSet
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HittingSetProblem{T} = Pair{Set{T}, Vector{Pair{T, Set{Set{T}}}}}
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# `subsets` should be a collection of Set objects
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function HittingSetProblem(subsets, chosen = Set())
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wholeset = union(subsets...)
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T = eltype(wholeset)
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unsorted_moves = [
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elt => Set(filter(s -> elt ∉ s, subsets))
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for elt in wholeset
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]
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moves = sort(unsorted_moves, by = pair -> length(pair.second))
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Set{T}(chosen) => moves
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end
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function Base.display(problem::HittingSetProblem{T}) where T
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println("HittingSetProblem{$T}")
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chosen = problem.first
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println(" {", join(string.(chosen), ", "), "}")
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moves = problem.second
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for (choice, missed) in moves
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println(" | ", choice)
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for s in missed
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println(" | | {", join(string.(s), ", "), "}")
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end
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end
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println()
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end
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function solve(pblm::HittingSetProblem{T}, maxdepth = Inf) where T
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problems = Dict(pblm)
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println(typeof(problems))
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while length(first(problems).first) < maxdepth
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subproblems = typeof(problems)()
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for (chosen, moves) in problems
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if isempty(moves)
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return chosen
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else
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for (choice, missed) in moves
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to_be_chosen = union(chosen, Set([choice]))
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if isempty(missed)
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return to_be_chosen
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elseif !haskey(subproblems, to_be_chosen)
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push!(subproblems, HittingSetProblem(missed, to_be_chosen))
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end
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end
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end
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end
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problems = subproblems
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end
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problems
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end
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function test(n = 1)
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T = [Int64, Int64, Symbol, Symbol][n]
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subsets = Set{T}.([
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[
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[1, 3, 5],
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[2, 3, 4],
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[1, 4],
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[2, 3, 4, 5],
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[4, 5]
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],
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# example from Amit Chakrabarti's graduate-level algorithms class (CS 105)
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# notes by Valika K. Wan and Khanh Do Ba, Winter 2005
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# https://www.cs.dartmouth.edu/~ac/Teach/CS105-Winter05/
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[
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[1, 3], [1, 4], [1, 5],
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[1, 3], [1, 2, 4], [1, 2, 5],
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[4, 3], [ 2, 4], [ 2, 5],
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[6, 3], [6, 4], [ 5]
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],
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[
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[:w, :x, :y],
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[:x, :y, :z],
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[:w, :z],
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[:x, :y]
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],
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# Wikipedia showcases this as an example of a problem where the greedy
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# algorithm performs especially poorly
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[
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[:a, :x, :t1],
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[:a, :y, :t2],
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[:a, :y, :t3],
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[:a, :z, :t4],
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[:a, :z, :t5],
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[:a, :z, :t6],
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[:a, :z, :t7],
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[:b, :x, :t8],
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[:b, :y, :t9],
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[:b, :y, :t10],
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[:b, :z, :t11],
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[:b, :z, :t12],
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[:b, :z, :t13],
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[:b, :z, :t14]
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]
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][n])
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problem = HittingSetProblem(subsets)
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if isa(problem, HittingSetProblem{T})
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println("Correct type")
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else
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println("Wrong type: ", typeof(problem))
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end
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problem
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end
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end
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