Engine prototype #13
@ -1,3 +1,5 @@
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include("hitting-set.jl")
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module Engine
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module Engine
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export Construction, mprod
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export Construction, mprod
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@ -6,27 +8,25 @@ import Subscripts
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using LinearAlgebra
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using LinearAlgebra
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using AbstractAlgebra
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using AbstractAlgebra
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using Groebner
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using Groebner
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using ..HittingSet
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# --- commutative algebra ---
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# --- commutative algebra ---
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# as of version 0.36.6, AbstractAlgebra only supports ideals in multivariate
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# polynomial rings when coefficients are integers. in `reduce_gens`, the
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# `lmnode` constructor requires < to be defined on the coefficients, and the
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# `reducer_size` heuristic requires `ndigits` to be defined on the coefficients.
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# this patch for `reducer_size` removes the `ndigits` dependency
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##function Generic.reducer_size(f::T) where {U <: MPolyRingElem{<:FieldElement}, V, N, T <: Generic.lmnode{U, V, N}}
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## if f.size != 0.0
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## return f.size
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## end
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## return 0.0 + sum(j^2 for j in 1:length(f.poly))
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##end
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# as of version 0.36.6, AbstractAlgebra only supports ideals in multivariate
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# as of version 0.36.6, AbstractAlgebra only supports ideals in multivariate
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# polynomial rings when the coefficients are integers. we use Groebner to extend
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# polynomial rings when the coefficients are integers. we use Groebner to extend
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# support to rationals and to finite fields of prime order
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# support to rationals and to finite fields of prime order
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Generic.reduce_gens(I::Generic.Ideal{U}) where {T <: FieldElement, U <: MPolyRingElem{T}} =
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Generic.reduce_gens(I::Generic.Ideal{U}) where {T <: FieldElement, U <: MPolyRingElem{T}} =
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Generic.Ideal{U}(base_ring(I), groebner(gens(I)))
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Generic.Ideal{U}(base_ring(I), groebner(gens(I)))
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function codimension(I::Generic.Ideal{U}, maxdepth = Inf) where {T <: RingElement, U <: MPolyRingElem{T}}
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leading = [exponent_vector(f, 1) for f in gens(I)]
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targets = [Set(findall(.!iszero.(exp_vec))) for exp_vec in leading]
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length(HittingSet.solve(HittingSetProblem(targets), maxdepth))
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end
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dimension(I::Generic.Ideal{U}, maxdepth = Inf) where {T <: RingElement, U <: MPolyRingElem{T}} =
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length(gens(base_ring(I))) - codimension(I, maxdepth)
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# --- primitve elements ---
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# --- primitve elements ---
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abstract type Element{T} end
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abstract type Element{T} end
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@ -183,6 +183,7 @@ s = Engine.Sphere{CoeffType}()
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a_on_s = Engine.LiesOn{CoeffType}(a, s)
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a_on_s = Engine.LiesOn{CoeffType}(a, s)
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ctx = Engine.Construction{CoeffType}(elements = Set([a]), relations= Set([a_on_s]))
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ctx = Engine.Construction{CoeffType}(elements = Set([a]), relations= Set([a_on_s]))
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ideal_a_s = Engine.realize(ctx)
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ideal_a_s = Engine.realize(ctx)
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println("A point on a sphere: ", Engine.dimension(ideal_a_s), " degrees of freeom")
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b = Engine.Point{CoeffType}()
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b = Engine.Point{CoeffType}()
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b_on_s = Engine.LiesOn{CoeffType}(b, s)
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b_on_s = Engine.LiesOn{CoeffType}(b, s)
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@ -190,6 +191,7 @@ Engine.push!(ctx, b)
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Engine.push!(ctx, s)
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Engine.push!(ctx, s)
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Engine.push!(ctx, b_on_s)
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Engine.push!(ctx, b_on_s)
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ideal_ab_s = Engine.realize(ctx)
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ideal_ab_s = Engine.realize(ctx)
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println("Two points on a sphere: ", Engine.dimension(ideal_ab_s), " degrees of freeom")
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spheres = [Engine.Sphere{CoeffType}() for _ in 1:3]
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spheres = [Engine.Sphere{CoeffType}() for _ in 1:3]
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tangencies = [
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tangencies = [
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@ -200,5 +202,6 @@ tangencies = [
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)
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)
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for n in 1:3
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for n in 1:3
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]
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]
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ctx_chain = Engine.Construction{CoeffType}(elements = Set(spheres), relations = Set(tangencies))
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ctx_tan_sph = Engine.Construction{CoeffType}(elements = Set(spheres), relations = Set(tangencies))
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ideal_chain = Engine.realize(ctx_chain)
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ideal_tan_sph = Engine.realize(ctx_tan_sph)
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println("Three mutually tangent spheres: ", Engine.dimension(ideal_tan_sph), " degrees of freeom")
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@ -1,13 +1,15 @@
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module HittingSet
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module HittingSet
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export HittingSetProblem, solve
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HittingSetProblem{T} = Pair{Set{T}, Vector{Pair{T, Set{Set{T}}}}}
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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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# `targets` should be a collection of Set objects
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function HittingSetProblem(subsets, chosen = Set())
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function HittingSetProblem(targets, chosen = Set())
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wholeset = union(subsets...)
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wholeset = union(targets...)
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T = eltype(wholeset)
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T = eltype(wholeset)
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unsorted_moves = [
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unsorted_moves = [
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elt => Set(filter(s -> elt ∉ s, subsets))
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elt => Set(filter(s -> elt ∉ s, targets))
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for elt in wholeset
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for elt in wholeset
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]
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]
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moves = sort(unsorted_moves, by = pair -> length(pair.second))
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moves = sort(unsorted_moves, by = pair -> length(pair.second))
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@ -32,7 +34,6 @@ end
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function solve(pblm::HittingSetProblem{T}, maxdepth = Inf) where T
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function solve(pblm::HittingSetProblem{T}, maxdepth = Inf) where T
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problems = Dict(pblm)
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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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while length(first(problems).first) < maxdepth
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subproblems = typeof(problems)()
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subproblems = typeof(problems)()
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for (chosen, moves) in problems
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for (chosen, moves) in problems
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@ -56,7 +57,7 @@ end
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function test(n = 1)
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function test(n = 1)
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T = [Int64, Int64, Symbol, Symbol][n]
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T = [Int64, Int64, Symbol, Symbol][n]
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subsets = Set{T}.([
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targets = Set{T}.([
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[
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[
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[1, 3, 5],
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[1, 3, 5],
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[2, 3, 4],
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[2, 3, 4],
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@ -98,7 +99,7 @@ function test(n = 1)
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[:b, :z, :t14]
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[:b, :z, :t14]
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]
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]
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][n])
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][n])
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problem = HittingSetProblem(subsets)
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problem = HittingSetProblem(targets)
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if isa(problem, HittingSetProblem{T})
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if isa(problem, HittingSetProblem{T})
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println("Correct type")
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println("Correct type")
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else
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else
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Block a user