Part 421: H = (1,3,5,4,4,2,1), F secant Y^6+Z^6 (d2 = yz) or tangent Y^5 Z (d2 = z^2); F5 = X W4 + G5 with d2 o W4 = 0
  ok   secant: d2 o F = 0 and d2 o W4 = 0
  ok   secant, l = c_z y - c_y z: d2-component of u3 o G5 vanishes identically
  ok   secant, l = c_z y - c_y z: u o Phi in T_{<=1} identically (all tails symbolic)
  ok   secant: u3 kills the derivatives y o F, z o F (= D_5)
  ok   secant, c_y = c_z = 0: l = y: d2-component in the ideal (c_y, c_z)
  ok   secant, c_y = c_z = 0: l = y: u o Phi in T_{<=1} modulo (c_y, c_z)
  ok   tangent: d2 o F = 0 and d2 o W4 = 0
  ok   tangent, l = c_z y - c_y z: d2-component of u3 o G5 vanishes identically
  ok   tangent, l = c_z y - c_y z: u o Phi in T_{<=1} identically (all tails symbolic)
  ok   tangent: u3 kills the derivatives y o F, z o F (= D_5)
  ok   tangent, c_y = c_z = 0: l = y: d2-component in the ideal (c_y, c_z)
  ok   tangent, c_y = c_z = 0: l = y: u o Phi in T_{<=1} modulo (c_y, c_z)
Part 421p (sanity): F = Y^6, W4 = z h3: W4 o Y^6 = 0, W4 o (anything of degree <= 5) has degree <= 1
  ok   W4 = z (y^3 + y^2*z + 7*z^3): W4 o Y^6 = 0
  ok   W4 = z (y^3 - z^3): W4 o Y^6 = 0
Part 331: H = (1,3,5,4,3,3,1), pure F = Y^6: h sampled in z C[y,z]_2 (h o Y^6 = 0), U = {G in C[Y,Z]_4 : h o G = 0}, z o B5 in U,
          F5 = alpha X Y^4 + B5: then h o B5 = c Y^2 and T = h - (c/360) y^4 lies in (I : m^2)  [h sampled after random.seed(11)]
  ok   h = 3*y*z^2 + z^3: dim U = 3
  ok      h o B5 has no YZ, Z^2 terms modulo the conditions h o (z o B5) = 0
  ok      T o Phi in T_{<=1} modulo the conditions (all tails symbolic)
  ok   h = 3*y^2*z + 3*y*z^2: dim U = 3
  ok      h o B5 has no YZ, Z^2 terms modulo the conditions h o (z o B5) = 0
  ok      T o Phi in T_{<=1} modulo the conditions (all tails symbolic)
  ok   h = y*z^2 + 3*z^3: dim U = 3
  ok      h o B5 has no YZ, Z^2 terms modulo the conditions h o (z o B5) = 0
  ok      T o Phi in T_{<=1} modulo the conditions (all tails symbolic)
  ok   h = z^3: dim U = 3
  ok      h o B5 has no YZ, Z^2 terms modulo the conditions h o (z o B5) = 0
  ok      T o Phi in T_{<=1} modulo the conditions (all tails symbolic)
Part 322: H = (1,3,5,4,3,2,2), gcd h of J_4 of degree three: one operator u = h + w4 for both sextic lifts
          h symbolic: h = y z (a y + b z) (secant), h = z^2 (a y + b z) (tangent), a, b indeterminates; all tails symbolic
  ok   secant, h = a*y^2*z + b*y*z^2: h kills nu_4(Gamma), nu_5(Gamma), nu_6(Gamma) identically in (a, b)
  ok   secant: the 2 x 2 minors of h o : C[Y,Z]_4 -> C[Y,Z]_1 generate an ideal with radical (a, b): rank 2, so U = ker(h o), for all (a, b) != (0, 0)
  ok   secant: u o F, u o T in T_{<=1} modulo the closedness conditions, identically in (a, b) and the tails
  ok   secant: the cubic part of u is h, a nonzero binary cubic for (a, b) != (0, 0)
  ok   tangent, h = a*y*z^2 + b*z^3: h kills nu_4(Gamma), nu_5(Gamma), nu_6(Gamma) identically in (a, b)
  ok   tangent: the 2 x 2 minors of h o : C[Y,Z]_4 -> C[Y,Z]_1 generate an ideal with radical (a, b): rank 2, so U = ker(h o), for all (a, b) != (0, 0)
  ok   tangent: u o F, u o T in T_{<=1} modulo the closedness conditions, identically in (a, b) and the tails
  ok   tangent: the cubic part of u is h, a nonzero binary cubic for (a, b) != (0, 0)
total time 0.3 s
ALL CHECKS PASSED
