--- A: F = (Y+2Z)^6, D_5 = <L^5, X Y^4 + Z^5>, d general (d(L)=0), 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 = 1/64*Y^6 + 3/16*Y^5*Z + 15/16*Y^4*Z^2 + 5/2*Y^3*Z^3 + 15/4*Y^2*Z^4 + 3*Y*Z^5 + Z^6 binary
  ok   J_4 != 0 (dim 2)
  ok   P in I of order 4, binary part of p_4 = p = (1/2) * z * y * (2*y - z) * (6*y + 5*z)
  ok   F = L^6 and d(L) = 0: d o F = 0
  ok   T_5 = -3*y^5 + 4*y^4*z - 2*y^2*z^3 - y*z^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   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 = -21/5*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 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 35, stabilized (35, 10) (information)
--- A: F = (Y+2Z)^6, D_5 = <L^5, X Y^4 + Z^5>, d general (d(L)=0), 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 = 1/64*Y^6 + 3/16*Y^5*Z + 15/16*Y^4*Z^2 + 5/2*Y^3*Z^3 + 15/4*Y^2*Z^4 + 3*Y*Z^5 + Z^6 binary
  ok   J_4 != 0 (dim 2)
  ok   P in I of order 4, binary part of p_4 = p = z * y * (y + 2*z) * (2*y - z)
  ok   F = L^6 and d(L) = 0: d o F = 0
  ok   T_5 = -4*y^5 - 3*y^4*z - 4*y^3*z^2 + 4*y^2*z^3 + 4*y*z^4 + 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   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 = -17/3*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 35, stabilized (35, 10) (information)
  ok   A: F = (Y+2Z)^6, D_5 = <L^5, X Y^4 + Z^5>, d general (d(L)=0): at least one accepted algebra (2)
--- B: F general binary, D_4 = S_2 o F + X Y^3, d = 3y + 5z, 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 = 1/3*Y^6 + 2/3*Y^5*Z - 1/3*Y^3*Z^3 + 1/3*Y*Z^5 + Z^6 binary
  ok   J_4 != 0 (dim 2)
  ok   P in I of order 4, binary part of p_4 = p = (1/270) * (810*y^4 + 1620*y^3*z + 490*y^2*z^2 + 27000*y*z^3 - 1473*z^4)
  ok   d = 3*y + 5*z, d o F = 28/3*Y^5 + 10*Y^4*Z - 5*Y^3*Z^2 - 3*Y^2*Z^3 + 25/3*Y*Z^4 + 31*Z^5 is zero or not a fifth power
  ok   T_5 = -4*y^5 - 3*y^3*z^2 - 3*y*z^4 + 245/186*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   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 = -19/15*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 32 (ds 32, stabilized 32 at N=9) 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 32 (ds 32, stabilized 32 at N=9) 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 32 (ds 32, stabilized 32 at N=9) 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 32 in [21, 40]
  ..   unslid CI (f, P, K_m): ds 32, stabilized (32, 9) (information)
--- B: F general binary, D_4 = S_2 o F + X Y^3, d = 3y + 5z, 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 = 1/3*Y^6 + 2/3*Y^5*Z - 1/3*Y^3*Z^3 + 1/3*Y*Z^5 + Z^6 binary
  ok   J_4 != 0 (dim 2)
  ok   P in I of order 4, binary part of p_4 = p = (1/324) * (324*y^4 + 1620*y^3*z - 950*y^2*z^2 + 17280*y*z^3 - 933*z^4)
  ok   d = 3*y + 5*z, d o F = 28/3*Y^5 + 10*Y^4*Z - 5*Y^3*Z^2 - 3*Y^2*Z^3 + 25/3*Y*Z^4 + 31*Z^5 is zero or not a fifth power
  ok   T_5 = -2*y^5 - 4*y^4*z - y^3*z^2 - 2*y^2*z^3 + 4*y*z^4 + 189/310*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   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 = -2/3*y - 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 32 (ds 32, stabilized 32 at N=9) 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 32 (ds 32, stabilized 32 at N=9) 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 32 (ds 32, stabilized 32 at N=9) 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 32 in [21, 40]
  ..   unslid CI (f, P, K_m): ds 32, stabilized (32, 9) (information)
  ok   B: F general binary, D_4 = S_2 o F + X Y^3, d = 3y + 5z: at least one accepted algebra (2)
--- C: F = Y^6 + Z^6, D_4 binary <Y^4, Z^4, Y^2Z^2, Y^3 Z>, d = y - 4z, seed 4
  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 = (5) * 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^4*z - 4*y^3*z^2 + 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   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 = 1/8*y - 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 35, stabilized (35, 10) (information)
  ok   C: F = Y^6 + Z^6, D_4 binary <Y^4, Z^4, Y^2Z^2, Y^3 Z>, d = y - 4z: at least one accepted algebra (1)
--- D: F = Y^5 Z, D_4 = S_2 o F + Z^4 + X Y^3, 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^5*Z binary
  ok   J_4 != 0 (dim 2)
  ok   P in I of order 4, binary part of p_4 = p = y * (5*y + 4*z) * z^2
  ok   d = y + z, d o F = Y^5 + 5*Y^4*Z is zero or not a fifth power
  ok   T_5 = -4*y^5 + 4*y^4*z - 3*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   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 = 11/5*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 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 35, stabilized (35, 10) (information)
--- D: F = Y^5 Z, D_4 = S_2 o F + Z^4 + X Y^3, 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^5*Z binary
  ok   J_4 != 0 (dim 2)
  ok   P in I of order 4, binary part of p_4 = p = y * (3*y + 4*z) * z^2
  ok   d = y + z, d o F = Y^5 + 5*Y^4*Z is zero or not a fifth power
  ok   T_5 = y^5 - y^4*z - y^3*z^2 + y^2*z^3 - 2*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   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 = -10/3*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 35, stabilized (35, 10) (information)
  ok   D: F = Y^5 Z, D_4 = S_2 o F + Z^4 + X Y^3, d = y + z: at least one accepted algebra (2)
  ok   accepted samples 7 of 7
accepted samples: 7
180 checks, total time 238.4 s
ALL CHECKS PASSED
