engine-proto/engine.jl

@@ -12,68 +12,46 @@ using Groebner
 abstract type Element{T} end
 
 mutable struct Point{T} <: Element{T}
-  coords::Vector{MPolyRingElem{T}}
+  coords::Union{Vector{MPolyRingElem{T}}, Nothing}
   vec::Union{Vector{MPolyRingElem{T}}, Nothing}
   rel::Nothing
   
   ## [to do] constructor argument never needed?
   Point{T}(
-    coords::Vector{MPolyRingElem{T}} = MPolyRingElem{T}[],
+    coords::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing,
     vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing
   ) where T = new(coords, vec, nothing)
 end
 
-##coordnames(_::Point) = [:xₚ, :yₚ, :zₚ]
+coordnames(_::Point) = [:xₚ, :yₚ, :zₚ]
 
-function buildvec!(pt::Point)
+function buildvec(pt::Point, coordqueue)
-  coordring = parent(pt.coords[1])
+  coordring = parent(coordqueue[1])
+  pt.coords = splice!(coordqueue, 1:3)
   pt.vec = [one(coordring), dot(pt.coords, pt.coords), pt.coords...]
 end
 
 mutable struct Sphere{T} <: Element{T}
-  coords::Vector{MPolyRingElem{T}}
+  coords::Union{Vector{MPolyRingElem{T}}, Nothing}
   vec::Union{Vector{MPolyRingElem{T}}, Nothing}
   rel::Union{MPolyRingElem{T}, Nothing}
   
-  ## [to do] constructor argument never needed?
   Sphere{T}(
-    coords::Vector{MPolyRingElem{T}} = MPolyRingElem{T}[],
+    coords::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing,
     vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing,
     rel::Union{MPolyRingElem{T}, Nothing} = nothing
   ) where T = new(coords, vec, rel)
 end
 
-##coordnames(_::Sphere) = [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
+coordnames(_::Sphere) = [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
 
-function buildvec!(sph::Sphere)
+function buildvec(sph::Sphere, coordqueue)
-  coordring = parent(sph.coords[1])
+  coordring = parent(coordqueue[1])
+  sph.coords = splice!(coordqueue, 1:5)
   sph.vec = sph.coords
   sph.rel = mprod(sph.coords, sph.coords) + one(coordring)
 end
 
-const coordnames = IdDict{Symbol, Vector{Union{Symbol, Nothing}}}(
-  nameof(Point) => [nothing, nothing, :xₚ, :yₚ, :zₚ],
-  nameof(Sphere) => [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
-)
-
-coordname(elem::Element, index) = coordnames[nameof(typeof(elem))][index]
-
-function pushcoordname!(coordnamelist, indexed_elem::Tuple{Any, Element}, coordindex)
-  elemindex, elem = indexed_elem
-  name = coordname(elem, coordindex)
-  if !isnothing(name)
-    subscript = Subscripts.sub(string(elemindex))
-    push!(coordnamelist, Symbol(name, subscript))
-  end
-end
-
-function takecoord!(coordlist, indexed_elem::Tuple{Any, Element}, coordindex)
-  elem = indexed_elem[2]
-  if !isnothing(coordname(elem, coordindex))
-    push!(elem.coords, popfirst!(coordlist))
-  end
-end
-
 # --- primitive relations ---
 
 abstract type Relation{T} end
@@ -121,38 +99,22 @@ function Base.push!(ctx::Construction{T}, rel::Relation{T}) where T
 end
 
 function realize(ctx::Construction{T}) where T
-  # collect coordinate names
+  # collect variable names
   coordnamelist = Symbol[]
   elemenum = enumerate(ctx.elements)
-  for coordindex in 1:5
+  for (index, elem) in elemenum
-    for indexed_elem in elemenum
+    subscript = Subscripts.sub(string(index))
-      pushcoordname!(coordnamelist, indexed_elem, coordindex)
+    append!(coordnamelist,
-    end
+      [Symbol(name, subscript) for name in coordnames(elem)]
+    )
   end
   
-  display(collect(elemenum))
-  display(coordnamelist)
-  println()
-  
   # construct coordinate ring
   coordring, coordqueue = polynomial_ring(parent_type(T)(), coordnamelist, ordering = :degrevlex)
   
-  # retrieve coordinates
-  for (_, elem) in elemenum
-    empty!(elem.coords)
-  end
-  for coordindex in 1:5
-    for indexed_elem in elemenum
-      takecoord!(coordqueue, indexed_elem, coordindex)
-    end
-  end
-  
   # construct coordinate vectors
   for (_, elem) in elemenum
-    buildvec!(elem)
+    buildvec(elem, coordqueue)
-    display(elem.coords)
-    display(elem.vec)
-    println()
   end
   
   # turn relations into equations

engine-proto/hitting-set.jl

@@ -1,110 +0,0 @@
-module HittingSet
-
-HittingSetProblem{T} = Pair{Set{T}, Vector{Pair{T, Set{Set{T}}}}}
-
-# `subsets` should be a collection of Set objects
-function HittingSetProblem(subsets, chosen = Set())
-  wholeset = union(subsets...)
-  T = eltype(wholeset)
-  unsorted_moves = [
-    elt => Set(filter(s -> elt ∉ s, subsets))
-    for elt in wholeset
-  ]
-  moves = sort(unsorted_moves, by = pair -> length(pair.second))
-  Set{T}(chosen) => moves
-end
-
-function Base.display(problem::HittingSetProblem{T}) where T
-  println("HittingSetProblem{$T}")
-  
-  chosen = problem.first
-  println(" {", join(string.(chosen), ", "), "}")
-  
-  moves = problem.second
-  for (choice, missed) in moves
-    println(" | ", choice)
-    for s in missed
-      println(" | | {", join(string.(s), ", "), "}")
-    end
-  end
-  println()
-end
-
-function solve(pblm::HittingSetProblem{T}, maxdepth = Inf) where T
-  problems = Dict(pblm)
-  println(typeof(problems))
-  while length(first(problems).first) < maxdepth
-    subproblems = typeof(problems)()
-    for (chosen, moves) in problems
-      if isempty(moves)
-        return chosen
-      else
-        for (choice, missed) in moves
-          to_be_chosen = union(chosen, Set([choice]))
-          if isempty(missed)
-            return to_be_chosen
-          elseif !haskey(subproblems, to_be_chosen)
-            push!(subproblems, HittingSetProblem(missed, to_be_chosen))
-          end
-        end
-      end
-    end
-    problems = subproblems
-  end
-  problems
-end
-
-function test(n = 1)
-  T = [Int64, Int64, Symbol, Symbol][n]
-  subsets = Set{T}.([
-    [
-      [1, 3, 5],
-      [2, 3, 4],
-      [1, 4],
-      [2, 3, 4, 5],
-      [4, 5]
-    ],
-    # example from Amit Chakrabarti's graduate-level algorithms class (CS 105)
-    # notes by Valika K. Wan and Khanh Do Ba, Winter 2005
-    # https://www.cs.dartmouth.edu/~ac/Teach/CS105-Winter05/
-    [
-      [1, 3], [1,    4], [1,    5],
-      [1, 3], [1, 2, 4], [1, 2, 5],
-      [4, 3], [   2, 4], [   2, 5],
-      [6, 3], [6,    4], [      5]
-    ],
-    [
-      [:w, :x, :y],
-      [:x, :y, :z],
-      [:w, :z],
-      [:x, :y]
-    ],
-    # Wikipedia showcases this as an example of a problem where the greedy
-    # algorithm performs especially poorly
-    [
-      [:a, :x, :t1],
-      [:a, :y, :t2],
-      [:a, :y, :t3],
-      [:a, :z, :t4],
-      [:a, :z, :t5],
-      [:a, :z, :t6],
-      [:a, :z, :t7],
-      [:b, :x, :t8],
-      [:b, :y, :t9],
-      [:b, :y, :t10],
-      [:b, :z, :t11],
-      [:b, :z, :t12],
-      [:b, :z, :t13],
-      [:b, :z, :t14]
-    ]
-  ][n])
-  problem = HittingSetProblem(subsets)
-  if isa(problem, HittingSetProblem{T})
-    println("Correct type")
-  else
-    println("Wrong type: ", typeof(problem))
-  end
-  problem
-end
-
-end