Part Q: Q5 on (1,3,5,4,5,2,1), D_4 = C[Y,Z]_4, D_5 = <Y^5, Z^5>, D_6 = C Y^6
  ok   p = y z (y - z)(y + z)(y - 2z) (e0 = 1), graded: closed with H True; z-multiples in (I:m^2) True; v6(Y) = 0; colength I_0 = 21, I_t = 21; triple in I_t True; local length 41 <= 41
  ok   p = y z (y - z)(y + z)(y - 2z) (e0 = 1), seed 1: closed with H True; z-multiples in (I:m^2) True; v6(Y) = -1/5; colength I_0 = 21, I_t = 21; triple in I_t True; local length 41 <= 41
  ok   p = y z (y - z)(y + z)(y - 2z) (e0 = 1), seed 2: closed with H True; z-multiples in (I:m^2) True; v6(Y) = -1/10; colength I_0 = 21, I_t = 21; triple in I_t True; local length 41 <= 41
  ok   p = y z (y - z)(y + z)(y - 2z) (e0 = 1), seed 3: closed with H True; z-multiples in (I:m^2) True; v6(Y) = 1/15; colength I_0 = 21, I_t = 21; triple in I_t True; local length 41 <= 41
  ok   p = y z^2 (y - z)(y + z) (e0 = 2), graded: closed with H True; z-multiples in (I:m^2) True; v6(Y) = 0; colength I_0 = 21, I_t = 21; triple in I_t True; local length 42 (outside (b): e0 >= 2 and v6(Y) = 0; info only)
  ok   p = y z^2 (y - z)(y + z) (e0 = 2), seed 1: closed with H True; z-multiples in (I:m^2) True; v6(Y) = 1/12; colength I_0 = 21, I_t = 21; triple in I_t True; local length 41 <= 41
  ok   p = y z^2 (y - z)(y + z) (e0 = 2), seed 2: closed with H True; z-multiples in (I:m^2) True; v6(Y) = 0; colength I_0 = 21, I_t = 21; triple in I_t True; local length 42 (outside (b): e0 >= 2 and v6(Y) = 0; info only)
  ok   p = y z^2 (y - z)(y + z) (e0 = 2), seed 3: closed with H True; z-multiples in (I:m^2) True; v6(Y) = -1/30; colength I_0 = 21, I_t = 21; triple in I_t True; local length 41 <= 41
Part Q(a): D_6 = C F, F a general binary sextic, D_5 = S_1 o F; p general in J_5, w a quartic killing F with gcd(w, p) = 1: <= 40
  J_5 has dimension 4, the quartics killing F dimension 2; gcd(p, w) = 1, gcd(p, b) = 1, gcd(p, r) = 1
  ok   (a) graded: closed with H True; w in (I:m^2): True; colength I_t = 21; triple in I_t: True; local length 40 <= 40
  ok   (a) seed 1: closed with H True; w in (I:m^2): True; colength I_t = 21; triple in I_t: True; local length 40 <= 40
  ok   (a) seed 2: closed with H True; w in (I:m^2): True; colength I_t = 21; triple in I_t: True; local length 40 <= 40
Part M: MC on (1,3,5,5,4,2,1), I*_3 = x^2 S_1 + <xyz, xz^2>, D_3 = C[Y,Z]_3 + C X Y^2
  ok   D_4 = <Y^4, Y^3 Z, Y^2 Z^2, X Y^3>, D_6 = Y^6, graded: closed with H True; dim{T} = 5, xT, yT in I: True; (tau, colength, H(S/I_tau), q in I_tau) = [(0, 21, [1, 3, 5, 5, 4, 2, 1], True), (3, 21, [1, 3, 5, 5, 4, 2, 1], True), (-5, 21, [1, 3, 5, 5, 4, 2, 1], True)]; I_0 = I: True
  ok   D_4 = <Y^4, Y^3 Z, Y^2 Z^2, X Y^3>, D_6 = Y^6, seed 1: closed with H True; dim{T} = 5, xT, yT in I: True; (tau, colength, H(S/I_tau), q in I_tau) = [(0, 21, [1, 3, 5, 5, 4, 2, 1], True), (3, 21, [1, 3, 5, 5, 4, 2, 1], True), (-5, 21, [1, 3, 5, 5, 4, 2, 1], True)]; I_0 = I: True
  ok   D_4 = <Y^4, Y^3 Z, Y^2 Z^2, X Y^3>, D_6 = Y^6, seed 2: closed with H True; dim{T} = 5, xT, yT in I: True; (tau, colength, H(S/I_tau), q in I_tau) = [(0, 21, [1, 3, 5, 5, 4, 2, 1], True), (3, 21, [1, 3, 5, 5, 4, 2, 1], True), (-5, 21, [1, 3, 5, 5, 4, 2, 1], True)]; I_0 = I: True
  ok   D_4 = <Y^4, Y^3 Z, Y^2 Z^2, Y Z^3>, D_6 = Y^5 Z, graded: closed with H True; dim{T} = 5, xT, yT in I: True; (tau, colength, H(S/I_tau), q in I_tau) = [(0, 21, [1, 3, 5, 5, 4, 2, 1], True), (3, 21, [1, 3, 5, 5, 4, 2, 1], True), (-5, 21, [1, 3, 5, 5, 4, 2, 1], True)]; I_0 = I: True
  ok   D_4 = <Y^4, Y^3 Z, Y^2 Z^2, Y Z^3>, D_6 = Y^5 Z, seed 1: closed with H True; dim{T} = 5, xT, yT in I: True; (tau, colength, H(S/I_tau), q in I_tau) = [(0, 21, [1, 3, 5, 5, 4, 2, 1], True), (3, 21, [1, 3, 5, 5, 4, 2, 1], True), (-5, 21, [1, 3, 5, 5, 4, 2, 1], True)]; I_0 = I: True
  ok   D_4 = <Y^4, Y^3 Z, Y^2 Z^2, Y Z^3>, D_6 = Y^5 Z, seed 2: closed with H True; dim{T} = 5, xT, yT in I: True; (tau, colength, H(S/I_tau), q in I_tau) = [(0, 21, [1, 3, 5, 5, 4, 2, 1], True), (3, 21, [1, 3, 5, 5, 4, 2, 1], True), (-5, 21, [1, 3, 5, 5, 4, 2, 1], True)]; I_0 = I: True
accepted samples: 15
total time 26.7 s
ALL CHECKS PASSED
