--- E: F = Y^6 + Z^6, D_4 = <Y^4, Z^4, Y^2Z^2, Y^3Z>, J_4 = C y z^3 (triple root at [Y]), d = y - 4z, seed 1
  ok   closed, H(I) = [1, 3, 5, 5, 4, 2, 1]
  ok   binary case, I*_3 = x^2 S_1 + x<yz, z^2>
  ok   gamma_f = 0
  ok   after the shear: H = [1, 3, 5, 5, 4, 2, 1], f cubic part 0 in x^2 S_1
  ok   D_6 = C F, F = Y^6 + Z^6 binary
  ok   J_4 != 0 (dim 1)
  ok   P in I of order 4, binary part of p_4 = p = (2) * y * z^3
  ok   d = y - 4*z, d o F = 6*Y^5 - 24*Z^5 is zero or not a fifth power
  ok   T_5 = y^5 - 3*y^4*z + 4*y^3*z^2 + y^2*z^3 + 1/4*z^5 in (d o F)^perp, coprime to p
  ok   x T_5, d T_5 in I (sextics orthogonal to F)
  ok   lambda has kernel C d
  ok   (i): x phi(m), m^2 phi(m) in I
  ok   (ii): every syzygy sum c_i m_i = 0 (dim 1) gives sum c_i phi(m_i) in I, and d | sum lambda(l_i) c_i
  ok   bad stratum: theta_yz(Y) = theta_z2(Y) = 0 (theta = [0, 2*y*z^3 - z^4]), every p in J_4 vanishes at [Y]
  ok   E = C p_4 meets x^2 S_2 + x bS_1 W_2 only in 0
  ok   I = N + C f + sum C K_mi + sum C u_k: 63 = 57 + 6
  ok   m = z e, e = 3/8*y - 2*z, lambda(e) = 1, phi(m) = T_5 (order 5, leading form coprime to p)
  ok   tau = 0: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); equals I; H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok   tau = 1: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = 1: certified local length 39 (ds 39, stabilized 39 at N=11) in [21, 40]
  ok   tau = -2: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = -2: certified local length 39 (ds 39, stabilized 39 at N=11) in [21, 40]
  ok   tau = 7/3: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = 7/3: certified local length 39 (ds 39, stabilized 39 at N=11) in [21, 40]
  ok   tau symbolic (QQ[tau]): rank 63 = 63, closed under x,y,z over QQ(tau), Hermite pivots units (flat over C[tau]): True
  ok      CI over QQ(t) (generic tau): ds local length 39 in [21, 40]
  ..   unslid CI (f, P, K_m): ds 45, stabilized (45, 13) (information: -1 = infinite)
--- E: F = Y^6 + Z^6, D_4 = <Y^4, Z^4, Y^2Z^2, Y^3Z>, J_4 = C y z^3 (triple root at [Y]), d = y - 4z, seed 2
  ok   closed, H(I) = [1, 3, 5, 5, 4, 2, 1]
  ok   binary case, I*_3 = x^2 S_1 + x<yz, z^2>
  ok   gamma_f = 0
  ok   after the shear: H = [1, 3, 5, 5, 4, 2, 1], f cubic part 0 in x^2 S_1
  ok   D_6 = C F, F = Y^6 + Z^6 binary
  ok   J_4 != 0 (dim 1)
  ok   P in I of order 4, binary part of p_4 = p = (6) * y * z^3
  ok   d = y - 4*z, d o F = 6*Y^5 - 24*Z^5 is zero or not a fifth power
  ok   T_5 = -2*y^5 - 3*y^3*z^2 + 4*y^2*z^3 - y*z^4 - 1/2*z^5 in (d o F)^perp, coprime to p
  ok   x T_5, d T_5 in I (sextics orthogonal to F)
  ok   lambda has kernel C d
  ok   (i): x phi(m), m^2 phi(m) in I
  ok   (ii): every syzygy sum c_i m_i = 0 (dim 1) gives sum c_i phi(m_i) in I, and d | sum lambda(l_i) c_i
  ok   bad stratum: theta_yz(Y) = theta_z2(Y) = 0 (theta = [-1/6*y^3*z + 1/2*y^2*z^2 + 2*y*z^3, 1/3*y^3*z + 3/2*y^2*z^2 + 2*y*z^3 - z^4]), every p in J_4 vanishes at [Y]
  ok   E = C p_4 meets x^2 S_2 + x bS_1 W_2 only in 0
  ok   I = N + C f + sum C K_mi + sum C u_k: 63 = 57 + 6
  ok   m = z e, e = -5/12*y + 2*z, lambda(e) = 1, phi(m) = T_5 (order 5, leading form coprime to p)
  ok   tau = 0: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); equals I; H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok   tau = 1: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = 1: certified local length 37 (ds 37, stabilized 37 at N=11) in [21, 40]
  ok   tau = -2: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = -2: certified local length 37 (ds 37, stabilized 37 at N=11) in [21, 40]
  ok   tau = 7/3: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = 7/3: certified local length 37 (ds 37, stabilized 37 at N=11) in [21, 40]
  ok   tau symbolic (QQ[tau]): rank 63 = 63, closed under x,y,z over QQ(tau), Hermite pivots units (flat over C[tau]): True
  ok      CI over QQ(t) (generic tau): ds local length 37 in [21, 40]
  ..   unslid CI (f, P, K_m): ds 37, stabilized (37, 11) (information: -1 = infinite)
  ok   E: F = Y^6 + Z^6, D_4 = <Y^4, Z^4, Y^2Z^2, Y^3Z>, J_4 = C y z^3 (triple root at [Y]), d = y - 4z: at least one accepted algebra (2)
--- F: F = (Y+Z)^6, D_5 = <L^5, Y^5>, D_4 = <L^4, Y^4, Z^4, Y^2Z^2>, d = y - z, seed 1
  ok   closed, H(I) = [1, 3, 5, 5, 4, 2, 1]
  ok   binary case, I*_3 = x^2 S_1 + x<yz, z^2>
  ok   gamma_f = 0
  ok   after the shear: H = [1, 3, 5, 5, 4, 2, 1], f cubic part 0 in x^2 S_1
  ok   D_6 = C F, F = Y^6 + 6*Y^5*Z + 15*Y^4*Z^2 + 20*Y^3*Z^3 + 15*Y^2*Z^4 + 6*Y*Z^5 + Z^6 binary
  ok   J_4 != 0 (dim 1)
  ok   P in I of order 4, binary part of p_4 = p = (5) * z * (y - z) * y * (y + z)
  ok   F = L^6 and d(L) = 0: d o F = 0
  ok   T_5 = -4*y^5 - 3*y^4*z - 3*y^3*z^2 + 2*y^2*z^3 + y*z^4 + 3*z^5 in (d o F)^perp, coprime to p
  ok   x T_5, d T_5 in I (sextics orthogonal to F)
  ok   lambda has kernel C d
  ok   (i): x phi(m), m^2 phi(m) in I
  ok   (ii): every syzygy sum c_i m_i = 0 (dim 1) gives sum c_i phi(m_i) in I, and d | sum lambda(l_i) c_i
  ok   bad stratum: theta_yz(Y) = theta_z2(Y) = 0 (theta = [y^2*z^2 - y*z^3, 1/12*y^3*z + y*z^3 - 13/12*z^4]), every p in J_4 vanishes at [Y]
  ok   E = C p_4 meets x^2 S_2 + x bS_1 W_2 only in 0
  ok   I = N + C f + sum C K_mi + sum C u_k: 63 = 57 + 6
  ok   m = z e, e = -16/5*y + 3*z, lambda(e) = 1, phi(m) = T_5 (order 5, leading form coprime to p)
  ok   tau = 0: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); equals I; H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok   tau = 1: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = 1: certified local length 36 (ds 36, stabilized 36 at N=11) in [21, 40]
  ok   tau = -2: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = -2: certified local length 36 (ds 36, stabilized 36 at N=11) in [21, 40]
  ok   tau = 7/3: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = 7/3: certified local length 36 (ds 36, stabilized 36 at N=11) in [21, 40]
  ok   tau symbolic (QQ[tau]): rank 63 = 63, closed under x,y,z over QQ(tau), Hermite pivots units (flat over C[tau]): True
  ok      CI over QQ(t) (generic tau): ds local length 36 in [21, 40]
  ..   unslid CI (f, P, K_m): ds 38, stabilized (38, 12) (information: -1 = infinite)
--- F: F = (Y+Z)^6, D_5 = <L^5, Y^5>, D_4 = <L^4, Y^4, Z^4, Y^2Z^2>, d = y - z, seed 2
  ok   closed, H(I) = [1, 3, 5, 5, 4, 2, 1]
  ok   binary case, I*_3 = x^2 S_1 + x<yz, z^2>
  ok   gamma_f = 0
  ok   after the shear: H = [1, 3, 5, 5, 4, 2, 1], f cubic part 0 in x^2 S_1
  ok   D_6 = C F, F = Y^6 + 6*Y^5*Z + 15*Y^4*Z^2 + 20*Y^3*Z^3 + 15*Y^2*Z^4 + 6*Y*Z^5 + Z^6 binary
  ok   J_4 != 0 (dim 1)
  ok   P in I of order 4, binary part of p_4 = p = (4) * z * (y - z) * y * (y + z)
  ok   F = L^6 and d(L) = 0: d o F = 0
  ok   T_5 = -y^5 - 3*y^4*z + 2*y^3*z^2 - y^2*z^3 - y*z^4 + 2*z^5 in (d o F)^perp, coprime to p
  ok   x T_5, d T_5 in I (sextics orthogonal to F)
  ok   lambda has kernel C d
  ok   (i): x phi(m), m^2 phi(m) in I
  ok   (ii): every syzygy sum c_i m_i = 0 (dim 1) gives sum c_i phi(m_i) in I, and d | sum lambda(l_i) c_i
  ok   bad stratum: theta_yz(Y) = theta_z2(Y) = 0 (theta = [-3/2*y^3*z - y^2*z^2 + 2*y*z^3, -5/6*y^3*z + y^2*z^2 - y*z^3 + 1/3*z^4]), every p in J_4 vanishes at [Y]
  ok   E = C p_4 meets x^2 S_2 + x bS_1 W_2 only in 0
  ok   I = N + C f + sum C K_mi + sum C u_k: 63 = 57 + 6
  ok   m = z e, e = 5/2*y - 3*z, lambda(e) = 1, phi(m) = T_5 (order 5, leading form coprime to p)
  ok   tau = 0: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); equals I; H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok   tau = 1: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = 1: certified local length 35 (ds 35, stabilized 35 at N=10) in [21, 40]
  ok   tau = -2: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = -2: certified local length 35 (ds 35, stabilized 35 at N=10) in [21, 40]
  ok   tau = 7/3: span is an ideal, colength 21 (ideal: 21), contains f, P, K_m + tau phi(m); H(I_tau) = [1, 3, 5, 5, 4, 2, 1] (H_A: True)
  ok      CI (f, P, K_m + tau phi(m)), tau = 7/3: certified local length 35 (ds 35, stabilized 35 at N=10) in [21, 40]
  ok   tau symbolic (QQ[tau]): rank 63 = 63, closed under x,y,z over QQ(tau), Hermite pivots units (flat over C[tau]): True
  ok      CI over QQ(t) (generic tau): ds local length 35 in [21, 40]
  ..   unslid CI (f, P, K_m): ds 38, stabilized (38, 12) (information: -1 = infinite)
  ok   F: F = (Y+Z)^6, D_5 = <L^5, Y^5>, D_4 = <L^4, Y^4, Z^4, Y^2Z^2>, d = y - z: at least one accepted algebra (2)
  ok   accepted samples 4 of 4
accepted samples: 4
107 checks, total time 1568.8 s
ALL CHECKS PASSED
