minor corrections

euler-newton.jl

@@ -8,11 +8,12 @@ module EulerNewton
   function en_step(H, x, t, step_size)
 
     # Predictor step
-    vars = variables(H(t))
+    vars = variables(H(1))
     # Jacobian of H evaluated at (x,t)
     JH = [jh(vars=>x) for jh in differentiate(H(t), vars)]
-    # ∂H/∂t is the same as γG-F=H(1)-H(0) for our choice of homotopy
+    # ∂H/∂t = γG-F = H(1)-H(0) for our homotopy; it doesn't depend on t
-    Δx = JH \ -[gg(vars=>x) for gg in H(1)-H(0)]
+    δH_δt = [dh(vars=>x) for dh in H(1)-H(0)]
+    Δx = JH \ -δH_δt
     xh = x + Δx * step_size
 
     # Corrector step

solve.jl

@@ -66,7 +66,7 @@ end
 #  F = [x*y - 1, x^2 + y^2 - 4]
 #  T = [x*y - 1, x^2 + y^2 - 2]
 
-R = random_system(5, 5)
+R = random_system(3, 5)
 println("System: ", R)
 (G, roots)=start_system(R)
 println("Number of roots: ", length(roots))