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6349f298ae |
engine-proto
@ -1,3 +1,5 @@
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include("HittingSet.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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@ -6,6 +8,24 @@ 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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# 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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# 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.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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@ -23,8 +43,6 @@ mutable struct Point{T} <: Element{T}
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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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function buildvec!(pt::Point)
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function buildvec!(pt::Point)
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coordring = parent(pt.coords[1])
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coordring = parent(pt.coords[1])
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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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@ -43,8 +61,6 @@ mutable struct Sphere{T} <: Element{T}
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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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function buildvec!(sph::Sphere)
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function buildvec!(sph::Sphere)
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coordring = parent(sph.coords[1])
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coordring = parent(sph.coords[1])
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sph.vec = sph.coords
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sph.vec = sph.coords
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@ -130,10 +146,6 @@ function realize(ctx::Construction{T}) where T
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end
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end
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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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@ -150,16 +162,14 @@ function realize(ctx::Construction{T}) where T
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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)
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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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vcat(
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eqns = vcat(
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equation.(ctx.relations),
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equation.(ctx.relations),
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[elem.rel for elem in ctx.elements if !isnothing(elem.rel)]
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[elem.rel for elem in ctx.elements if !isnothing(elem.rel)]
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)
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)
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Generic.Ideal(coordring, eqns)
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end
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end
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end
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end
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@ -172,22 +182,26 @@ a = Engine.Point{CoeffType}()
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s = Engine.Sphere{CoeffType}()
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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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eqns_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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Engine.push!(ctx, b)
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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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eqns_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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Engine.AlignsWithBy{CoeffType}(
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Engine.AlignsWithBy{CoeffType}(
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spheres[n],
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spheres[n],
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spheres[mod1(n+1, length(spheres))],
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spheres[mod1(n+1, length(spheres))],
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-1//1
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CoeffType(-1//1)
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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_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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