(b) U: F_6 = X Y^5, P_5 = lam X^3 Y^2 + mu X^2 Y^3 + X (nu Y^4 + sig Y^3 Z) + B_5, all lower tails symbolic
  ok   p_3 o P_5 = A Y^2 + B X Y modulo the conditions
  ok   T o Phi in T_{<=1} modulo the conditions (all tails symbolic)
  ok   p_3 kills D_5 = <Y^5, X Y^4> and X Y^5
  ok   the two conditions on p_3 are linear forms in (a, b, c); the cross product v of their coefficient rows solves both identically and is nonzero, and v = 0 forces dependent rows: a nonzero p_3 exists for every B_5
  ok   (a) Q_D = YZ, F_6 general, seed 0: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      N1 triple: 32 <= 36
  ok   (a) Q_D = YZ, F_6 general, seed 1: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      N1 triple: 32 <= 36
  ok   (a) Q_D = YZ, F_6 general, seed 2: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      N1 triple: 36 <= 36
  ok   (b) Q_D = Y^2, F_6 = X Y^5, seed 0: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      Pi = [y^2*z - 1/4*z^3]: nonzero, in z S_2
  ok   (b) Q_D = Y^2, F_6 = X Y^5, seed 1: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      Pi = [y^2*z - 1/8*z^3]: nonzero, in z S_2
  ok   (b) Q_D = Y^2, F_6 = X Y^5, seed 2: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      Pi = [y^2*z, y*z^2, z^3]: nonzero, in z S_2
  ok   (c) Q_D = Y^2, F_6 general binary, Y^4 in D_4, seed 0: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 3*y^5 + 6*y^4*z + 3*y^3*z^2 + 100*y^2*z^3 + 5*y*z^4 + 2*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 32 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 32 <= 40
  ok   (c) Q_D = Y^2, F_6 general binary, Y^4 in D_4, seed 1: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 3*y^5 + 7*y^4*z + 7*y^3*z^2 + 320/3*y^2*z^3 + 3*y*z^4 + z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 32 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 32 <= 40
  ok   (c) Q_D = Y^2, F_6 general binary, Y^4 in D_4, seed 2: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = y^5 + 7*y^4*z + 3*y^3*z^2 + 200/3*y^2*z^3 + 4*y*z^4 + 6*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 37 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 37 <= 40
  ok   (c) Q_D = Y^2, F_6 = Y^6 + Z^6, non-binary D_4, seed 0: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 6*y^5 - 28*y^4*z + 54*y^3*z^2 - 53*y^2*z^3 + 33*y*z^4 - 18*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 35 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 35 <= 40
  ok   (c) Q_D = Y^2, F_6 = Y^6 + Z^6, non-binary D_4, seed 1: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 6*y^5 - 27*y^4*z + 54*y^3*z^2 - 54*y^2*z^3 + 27*y*z^4 - 12*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 35 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 35 <= 40
  ok   (c) Q_D = Y^2, F_6 = Y^6 + Z^6, non-binary D_4, seed 2: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 3*y^5 - 10*y^4*z + 15*y^3*z^2 - 13*y^2*z^3 + 9*y*z^4 - 7*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 39 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 39 <= 40
  ok   (c) Q_D = Y^2, F_6 = Y^5 Z, seed 0: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 2*y^5 + y^3*z^2 + 3*y^2*z^3 + y*z^4 + 5*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 36 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 36 <= 40
  (c) Q_D = Y^2, F_6 = Y^5 Z: no consistent draw
  ok   (c) Q_D = Y^2, F_6 = Y^5 Z, seed 2: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 3*y^5 + 2*y^3*z^2 + 3*y^2*z^3 + 5*y*z^4 + 2*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 40 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 40 <= 40
  ok   (c) Q_D = Y^2, F_6 = Y^6, seed 0: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      x T_5, z T_5 in I (T_5 = 3*y^5 + 6*y^4*z + 6*y^3*z^2 + 2*y^2*z^3 + 6*y*z^4 + 5*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 36 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 36 <= 40
  ok   (c) Q_D = Y^2, F_6 = Y^6, seed 1: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      x T_5, z T_5 in I (T_5 = 3*y^5 + 3*y^4*z + y^3*z^2 + y^2*z^3 + 3*y*z^4 + 5*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 36 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 36 <= 40
  ok   (c) Q_D = Y^2, F_6 = Y^6, seed 2: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      x T_5, z T_5 in I (T_5 = 6*y^5 + 4*y^4*z + 3*y^3*z^2 + 2*y^2*z^3 + 2*y*z^4 + 5*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 40 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 40 <= 40
  ok   (c) Q_D = Y^2, F_6 = Z^6, seed 0: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 4*y^5 + y^4*z + 2*y^3*z^2 + 5*y^2*z^3 + 7*y*z^4 + 4*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 35 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 35 <= 40
  ok   (c) Q_D = Y^2, F_6 = Z^6, seed 1: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = 6*y^5 + y^4*z + 7*y^3*z^2 + 6*y^2*z^3 + 5*y*z^4 + 3*z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 35 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 35 <= 40
  ok   (c) Q_D = Y^2, F_6 = Z^6, seed 2: closed, H = [1, 3, 5, 5, 4, 2, 1]
  ok      a binary quartic p_4 lies in I*_4 (dim 1)
  ok      coordinate change consistent
  ok      x T_5, y T_5 in I (T_5 = y^5 + 2*y^4*z + 7*y^3*z^2 + 5*y^2*z^3 + 3*y*z^4 + z^5, coprime to p_4)
  ok      tau = 0: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau
  ok      tau = 3: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 39 <= 40
  ok      tau = -5: colength 21, H = [1, 3, 5, 5, 4, 2, 1], q, v in I_tau; CI (q, w_tau, v) local length 39 <= 40
  accepted samples: 20 of 20
  ok   all samples accepted
time 39.9 s
ALL CHECKS PASSED
