diff --git a/engine-proto/Engine.Algebraic.jl b/engine-proto/Engine.Algebraic.jl
index ca39967..380cee1 100644
--- a/engine-proto/Engine.Algebraic.jl
+++ b/engine-proto/Engine.Algebraic.jl
@@ -197,7 +197,8 @@ function realize(ctx::Construction{T}) where T
     push!(eqns, sum(elt.vec[2] for elt in Iterators.flatten((ctx.points, ctx.spheres))) - n_elts)
   end
   
-  (Generic.Ideal(coordring, eqns), eqns)
+  ## [test] (Generic.Ideal(coordring, eqns), eqns)
+  (nothing, eqns)
 end
 
 end
\ No newline at end of file
diff --git a/engine-proto/Engine.jl b/engine-proto/Engine.jl
index 7ddf72d..49011c6 100644
--- a/engine-proto/Engine.jl
+++ b/engine-proto/Engine.jl
@@ -61,21 +61,18 @@ CoeffType = Rational{Int64}
 ##freedom = Engine.dimension(ideal_tan_sph)
 ##println("Three mutually tangent spheres: $freedom degrees of freedom")
 
-p = Engine.Point{CoeffType}()
-q = Engine.Point{CoeffType}()
-a = Engine.Sphere{CoeffType}()
-b = Engine.Sphere{CoeffType}()
-p_on_a = Engine.LiesOn{CoeffType}(p, a)
-p_on_b = Engine.LiesOn{CoeffType}(p, b)
-q_on_a = Engine.LiesOn{CoeffType}(q, a)
-q_on_b = Engine.LiesOn{CoeffType}(q, b)
+points = [Engine.Point{CoeffType}() for _ in 1:3]
+spheres = [Engine.Sphere{CoeffType}() for _ in 1:2]
 ctx_joined = Engine.Construction{CoeffType}(
-  elements = Set([p, q, a, b]),
-  relations= Set([p_on_a, p_on_b, q_on_a, q_on_b])
+  elements = Set([points; spheres]),
+  relations= Set([
+    Engine.LiesOn{CoeffType}(pt, sph)
+    for pt in points for sph in spheres
+  ])
 )
 ideal_joined, eqns_joined = Engine.realize(ctx_joined)
 freedom = Engine.dimension(ideal_joined)
-println("Two points on two spheres: $freedom degrees of freedom")
+println("$(length(points)) points on $(length(spheres)) spheres: $freedom degrees of freedom")
 
 # --- test rational cut ---