engine-proto/Engine.jl

@@ -263,22 +263,9 @@ println("Two points on a sphere: ", freedom, " degrees of freedom")
 
 # --- test rational cut ---
 
-cut_coeffs = [
-  1 1 1 0 0 0 1 1 1 1 1;
-  2 1 1 0 0 0 1 2 1 1 1;
-  1 2 0 0 0 0 1 1 0 1 2
-]
-cut = [
-  sum(vcat(cf[1:3] .* a.coords, cf[4:6] .* b.coords, cf[7:end] .* (s.coords - [0, 0, 0, 0, 1])))
-  for cf in eachrow(cut_coeffs)
-]
-cut_ideal_ab_s = Generic.Ideal(base_ring(ideal_ab_s), [gens(ideal_ab_s); cut])
-cut_freedom = Engine.dimension(cut_ideal_ab_s)
-println("Two points on a sphere, after cut: ", cut_freedom, " degrees of freedom")
-if cut_freedom == 0
 coordring = base_ring(ideal_ab_s)
 vbls = Variable.(symbols(coordring))
-  cut_system = System([eqns_ab_s; cut], variables = vbls)
+##cut_system = CompiledSystem(System([eqns_ab_s; cut], variables = vbls))
 ##cut_result = HomotopyContinuation.solve(cut_system)
 ##println("non-singular solutions:")
 ##for soln in solutions(cut_result)
@@ -290,6 +277,7 @@ if cut_freedom == 0
 ##end
 
 # test a random witness set
+system = CompiledSystem(System(eqns_ab_s, variables = vbls))
 max_slope = 2
 binom = Binomial(2max_slope, 1/2)
 Random.seed!(6071)
@@ -307,7 +295,7 @@ if cut_freedom == 0
   display(cut_matrix)
   display(cut_offset)
   cut_subspace = LinearSubspace(cut_matrix, cut_offset)
-    wtns = witness_set(System(eqns_ab_s, variables = vbls), cut_subspace)
+  wtns = witness_set(system, cut_subspace)
   append!(samples, solution.(filter(isreal, results(wtns))))
 end
 println("witness solutions:")
@@ -326,4 +314,3 @@ if cut_freedom == 0
     println("center at origin: r² = $(round(1/k_sq, digits = 6)); x² + y² + z² = $(round(sum_sq, digits = 6))")
   end
 end
-end