diff --git a/engine-proto/Engine.jl b/engine-proto/Engine.jl
index 41d3ed7..38ed672 100644
--- a/engine-proto/Engine.jl
+++ b/engine-proto/Engine.jl
@@ -261,7 +261,7 @@ println("Two points on a sphere: ", Engine.dimension(ideal_ab_s), " degrees of f
 # --- test rational cut ---
 
 cut = [
-  sum(vcat(a.coords, (s.coords - [0, 0, 0, 0, 1])))
+  sum(vcat([1, 1, 1] .* a.coords, [1, 1, 1, 1, 1] .* (s.coords - [0, 0, 0, 0, 1])))
   sum(vcat([2, 1, 1] .* a.coords, [1, 2, 1, 1, 1] .* (s.coords - [0, 0, 0, 0, 1])))
   sum(vcat([1, 2, 0] .* a.coords, [1, 1, 0, 1, 2] .* (s.coords - [0, 0, 0, 0, 1])))
 ]