diff --git a/engine-proto/engine.jl b/engine-proto/engine.jl
new file mode 100644
index 0000000..df75fbe
--- /dev/null
+++ b/engine-proto/engine.jl
@@ -0,0 +1,105 @@
+module Engine
+
+export Construction, mprod
+
+import Subscripts
+using LinearAlgebra
+using AbstractAlgebra
+using Groebner
+
+# --- primitve elements ---
+
+mutable struct Point{T}
+  coords::Union{Vector{MPolyRingElem{T}}, Nothing}
+  vec::Union{Vector{MPolyRingElem{T}}, Nothing}
+  
+  ## [to do] constructor argument never needed?
+  Point{T}(vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing) where T = new(vec)
+end
+
+coordnames(_::Point) = [:xₚ, :yₚ, :zₚ]
+
+function buildvec(pt::Point, coordqueue)
+  pt.coords = splice!(coordqueue, 1:3)
+  coordring = parent(coordqueue[1])
+  pt.vec = [one(coordring), dot(pt.coords, pt.coords), pt.coords...]
+end
+
+mutable struct Sphere{T}
+  coords::Union{Vector{MPolyRingElem{T}}, Nothing}
+  vec::Union{Vector{MPolyRingElem{T}}, Nothing}
+  
+  Sphere{T}(vec::Union{Vector{MPolyRingElem{T}}, Nothing} = nothing) where T = new(vec)
+end
+
+coordnames(_::Sphere) = [:rₛ, :sₛ, :xₛ, :yₛ, :zₛ]
+
+function buildvec(sph::Sphere, coordqueue)
+  sph.coords = splice!(coordqueue, 1:5)
+  sph.vec = sph.coords
+end
+
+# --- primitive relations ---
+
+abstract type Relation{T} end
+
+mprod(v, w) = v[1]*w[2] + w[1]*v[2] - dot(v[3:end], w[3:end])
+
+struct LiesOn{T} <: Relation{T}
+  pt::Point{T}
+  sph::Sphere{T}
+end
+
+struct AlignsWithBy{T} <: Relation{T}
+  sph_v::Sphere{T}
+  sph_w::Sphere{T}
+  cos_angle::T
+end
+
+# --- constructions ---
+
+mutable struct Construction{T}
+  points::Vector{Point{T}}
+  spheres::Vector{Sphere{T}}
+  
+  Construction{T}(; points = Point{T}[], spheres = Sphere{T}[]) where T = new{T}(points, spheres)
+end
+
+function Base.push!(ctx::Construction{T}, elem::Point{T}) where T
+  push!(ctx.points, elem)
+end
+
+function Base.push!(ctx::Construction{T}, elem::Sphere{T}) where T
+  push!(ctx.spheres, elem)
+end
+
+function realize(ctx::Construction{T}) where T
+  # collect variable names
+  allcoordnames = Symbol[]
+  elements = vcat(ctx.points, ctx.spheres)
+  for (index, elem) in enumerate(elements)
+    subscript = Subscripts.sub(string(index))
+    append!(allcoordnames,
+      [Symbol(name, subscript) for name in coordnames(elem)]
+    )
+  end
+  
+  # construct coordinate ring
+  coordring, coordqueue = polynomial_ring(parent_type(T)(), allcoordnames)
+  
+  # construct coordinate vectors
+  for elem in elements
+    buildvec(elem, coordqueue)
+  end
+end
+
+end
+
+# ~~~ sandbox setup ~~~
+
+a = Engine.Point{Rational{Int64}}()
+b = Engine.Point{Rational{Int64}}()
+s = Engine.Sphere{Rational{Int64}}()
+ctx = Engine.Construction{Rational{Int64}}(points = [a])
+Engine.push!(ctx, b)
+Engine.push!(ctx, s)
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