engine-proto/Engine.jl

@@ -263,38 +263,26 @@ 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_result = HomotopyContinuation.solve(cut_system)
-  ##println("non-singular solutions:")
-  ##for soln in solutions(cut_result)
-  ##  display(soln)
-  ##end
-  ##println("singular solutions:")
-  ##for sing in singular(cut_result)
-  ##  display(sing.solution)
-  ##end
+coordring = base_ring(ideal_ab_s)
+vbls = Variable.(symbols(coordring))
+##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)
+##  display(soln)
+##end
+##println("singular solutions:")
+##for sing in singular(cut_result)
+##  display(sing.solution)
+##end
 
-  # test a random witness set
-  max_slope = 2
-  binom = Binomial(2max_slope, 1/2)
-  Random.seed!(6071)
-  samples = []
-  for _ in 1:3
+# 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)
+samples = []
+for _ in 1:3
   cut_matrix = rand(binom, freedom, length(gens(coordring))) .- max_slope
   ##cut_matrix = [
   ##  1 1 1 1 0 1 1 0 1 1 0;
@@ -307,11 +295,11 @@ 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:")
-  for soln in samples
+end
+println("witness solutions:")
+for soln in samples
   display([vbls round.(soln, digits = 6)])
   k_sq = abs2(soln[1])
   if abs2(soln[end-2]) > 1e-12
@@ -325,5 +313,4 @@ if cut_freedom == 0
     sum_sq = sum(soln[[4, 7, 10]] .^ 2)
     println("center at origin: r² = $(round(1/k_sq, digits = 6)); x² + y² + z² = $(round(sum_sq, digits = 6))")
   end
-  end
 end