105 lines
2.5 KiB
Julia
105 lines
2.5 KiB
Julia
module Engine
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export Construction, mprod
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import Subscripts
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using LinearAlgebra
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using AbstractAlgebra
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using Groebner
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# --- primitve elements ---
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mutable struct Point{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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## [to do] constructor argument never needed?
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Point{T}(vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing) where T = new(vec)
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end
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coordnames(_::Point) = [:xₚ, :yₚ, :zₚ]
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function buildvec(pt::Point, coordqueue)
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pt.coords = splice!(coordqueue, 1:3)
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coordring = parent(coordqueue[1])
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pt.vec = [one(coordring), dot(pt.coords, pt.coords), pt.coords...]
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end
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mutable struct Sphere{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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Sphere{T}(vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing) where T = new(vec)
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end
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coordnames(_::Sphere) = [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
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function buildvec(sph::Sphere, coordqueue)
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sph.coords = splice!(coordqueue, 1:5)
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sph.vec = sph.coords
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end
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# --- primitive relations ---
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abstract type Relation{T} end
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mprod(v, w) = v[1]*w[2] + w[1]*v[2] - dot(v[3:end], w[3:end])
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struct LiesOn{T} <: Relation{T}
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pt::Point{T}
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sph::Sphere{T}
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end
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struct AlignsWithBy{T} <: Relation{T}
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sph_v::Sphere{T}
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sph_w::Sphere{T}
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cos_angle::T
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end
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# --- constructions ---
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mutable struct Construction{T}
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points::Vector{Point{T}}
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spheres::Vector{Sphere{T}}
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Construction{T}(; points = Point{T}[], spheres = Sphere{T}[]) where T = new{T}(points, spheres)
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end
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function Base.push!(ctx::Construction{T}, elem::Point{T}) where T
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push!(ctx.points, elem)
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end
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function Base.push!(ctx::Construction{T}, elem::Sphere{T}) where T
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push!(ctx.spheres, elem)
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end
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function realize(ctx::Construction{T}) where T
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# collect variable names
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allcoordnames = Symbol[]
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elements = vcat(ctx.points, ctx.spheres)
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for (index, elem) in enumerate(elements)
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subscript = Subscripts.sub(string(index))
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append!(allcoordnames,
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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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# construct coordinate ring
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coordring, coordqueue = polynomial_ring(parent_type(T)(), allcoordnames)
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# construct coordinate vectors
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for elem in elements
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buildvec(elem, coordqueue)
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end
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end
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end
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# ~~~ sandbox setup ~~~
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a = Engine.Point{Rational{Int64}}()
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b = Engine.Point{Rational{Int64}}()
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s = Engine.Sphere{Rational{Int64}}()
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ctx = Engine.Construction{Rational{Int64}}(points = [a])
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Engine.push!(ctx, b)
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Engine.push!(ctx, s) |