Part A: the triples in L_delta, delta = 0..4
  ok   delta = 0: [-z^5 - z^4 + x^3, -y^3*z + x*y^2, -y^4 + x*z^2] lies in L_delta: True; local length 36 (ds), 36 (stable at N = 9, 10); 36 + delta = 36
  ok   delta = 1: [-y^5 + y^3*z + x^3, z^4 + x*y^2, -y^3*z + x*z^2] lies in L_delta: True; local length 37 (ds), 37 (stable at N = 10, 11); 36 + delta = 37
  ok   delta = 2: [y^5 - z^4 + x^3, -y*z^3 - z^4 + x*y^2, -y^2*z^2 + y*z^3 + x*z^2] lies in L_delta: True; local length 38 (ds), 38 (stable at N = 10, 11); 36 + delta = 38
  ok   delta = 3: [y^5 - z^4 + x^3, y^5 - y*z^3 + x*y^2, -y*z^3 + z^4 + x*z^2] lies in L_delta: True; local length 39 (ds), 39 (stable at N = 10, 11); 36 + delta = 39
  ok   delta = 4: [-z^4 + x^3, y^4*z + x*y^2, -y^5 + x*z^2] lies in L_delta: True; local length 40 (ds), 40 (stable at N = 10, 11); 36 + delta = 40
Part H: L^2 = N L and L'^2 = L L' for the five monomial models; two nonsquare-Q examples
  ok   delta = 0: (x m^2)^2 = (xQ)(x m^2) for Q = S_2: True; (g (y,z)^(4-d))^2 = K g (y,z)^(4-d): True; L^2 = N L: True
  ok   delta = 1: (x m^2)^2 = (xQ)(x m^2) for Q = S_2: True; (g (y,z)^(4-d))^2 = K g (y,z)^(4-d): True; L^2 = N L: True
  ok   delta = 2: (x m^2)^2 = (xQ)(x m^2) for Q = S_2: True; (g (y,z)^(4-d))^2 = K g (y,z)^(4-d): True; L^2 = N L: True
  ok   delta = 3: (x m^2)^2 = (xQ)(x m^2) for Q = S_2: True; (g (y,z)^(4-d))^2 = K g (y,z)^(4-d): True; L^2 = N L: True
  ok   delta = 4: (x m^2)^2 = (xQ)(x m^2) for Q = S_2: True; (g (y,z)^(4-d))^2 = K g (y,z)^(4-d): True; L^2 = N L: True
  ok   G = X^3 + 2*X^2*Y - X^2*Z + X*Y*Z + 3*X*Z^2: S_1 Q = S_3 (True) and S_2 Q = S_4 (True)
  ok   G = X*Y*Z: S_1 Q = S_3 (True) and S_2 Q = S_4 (True)
Part C
   (1,3,6,4,5,2), generic pencil: attempt 1 used (local lengths of the attempts made: [40]); the triple:
      f_1 = -3*x^5 - 2*x^4*y - 5*x^3*y^2 + 4*x^2*y^3 + 3*x*y^4 - 5*y^5 - 2*x^4*z + x^3*y*z + 2*x^2*y^2*z + 2*x*y^3*z - 3*y^4*z + x^3*z^2 - 5*x^2*y*z^2 - 4*x*y^2*z^2 - 4*y^3*z^2 + 5*x*y*z^3 - 4*y^2*z^3 - 5*y*z^4 + 2*z^5 - 4*y^4 - 1838/77*y^3*z - 2938/231*y^2*z^2 - 802/77*y*z^3 + 862/231*z^4 - 2*x^3 - 5*x^2*y - 5*x^2*z + 4*x*y*z + x*z^2
      f_2 = 5*x^5 - 5*x^4*y - 2*x^3*y^2 - 2*x^2*y^3 - 4*x*y^4 + y^5 + 2*x^4*z - 4*x^3*y*z + 5*x^2*y^2*z - 4*x*y^3*z - 2*y^4*z - 2*x^3*z^2 + 5*x^2*y*z^2 + 3*x*y^2*z^2 + 4*x^2*z^3 + 2*x*y*z^3 - 3*y^2*z^3 + 3*x*z^4 + 3*y*z^4 + z^5 - 3*y^4 - 2757/154*y^3*z - 1469/154*y^2*z^2 - 1203/154*y*z^3 + 431/154*z^4 - 3*x^3 + 3*x^2*y + x*y^2 + 2*x*y*z - 3*x*z^2
      f_3 = x^5 - x^4*y - 4*x^3*y^2 - 5*x^2*y^3 + 4*x*y^4 - 5*x^4*z - 3*x^3*y*z + 2*x^2*y^2*z + 3*x*y^3*z + 3*y^4*z + 2*x^3*z^2 - 4*x^2*y*z^2 - 2*x*y^2*z^2 + 4*y^3*z^2 + 3*x^2*z^3 + 4*x*y*z^3 - 4*y^2*z^3 + 4*x*z^4 - 3*y*z^4 + 5*z^5 + 2*y^4 + 919/77*y^3*z + 1469/231*y^2*z^2 + 401/77*y*z^3 - 431/231*z^4 - x^3 + 3*x*y^2 + 2*x^2*z + x*y*z
  ok   (1,3,6,4,5,2), generic pencil: H = [1, 3, 6, 4, 5, 2], closed True, f_i in Ann(M) True, deg gcd K = 4, CI local length 40 (stable pair N = 10, 11; attempt 1) <= 40
   (1,3,6,4,5,2), secant <Y^5,Z^5>: attempt 1 used (local lengths of the attempts made: [38]); the triple:
      f_1 = -3*x^5 - 4*x^4*y + x^3*y^2 + 5*x^2*y^3 + 5*x*y^4 - 5*y^5 - 3*x^4*z - 5*x^2*y^2*z - 2*x*y^3*z - 3*x^3*z^2 + 5*x^2*y*z^2 + x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 + 3*y^2*z^3 + 4*x*z^4 + y*z^4 + 5*z^5 - y^3*z - 2*y^2*z^2 - 4*y*z^3 - 3*x^3 + 5*x^2*y + 4*x*z^2
      f_2 = -x^5 - 5*x^4*y + 5*x^3*y^2 + x^2*y^3 - 4*x*y^4 + 2*y^5 - x^4*z - x^3*y*z - 2*x^2*y^2*z - 5*y^4*z - 5*x^3*z^2 - 3*x^2*y*z^2 + 5*x*y^2*z^2 - y^3*z^2 + x^2*z^3 - 3*x*y*z^3 - 3*y^2*z^3 - 3*x*z^4 + 5*y*z^4 + 3*z^5 + y^3*z + 2*y^2*z^2 - 5*y*z^3 - 2*x^3 - 2*x^2*y + 3*x*y^2 - 3*x^2*z - 4*x*y*z + 2*x*z^2
      f_3 = 4*x^5 + 2*x^4*y - 3*x^3*y^2 - x^2*y^3 + 5*x*y^4 - x^4*z + 3*x^3*y*z - 3*x^2*y^2*z - 3*x*y^3*z + 5*y^4*z + 4*x^3*z^2 - 5*x^2*y*z^2 - 5*x*y^2*z^2 - 2*y^3*z^2 + x^2*z^3 - x*y*z^3 + 4*y^2*z^3 + 4*x*z^4 + y*z^4 - z^5 + 4*y^3*z + y^2*z^2 + 2*y*z^3 + 2*x^3 - 5*x^2*y - 2*x^2*z - 3*x*y*z
  ok   (1,3,6,4,5,2), secant <Y^5,Z^5>: H = [1, 3, 6, 4, 5, 2], closed True, f_i in Ann(M) True, deg gcd K = 2, CI local length 38 (stable pair N = 10, 11; attempt 1) <= 38
   (1,3,6,4,5,2), tangent <Y^5,Y^4Z>: attempt 1 used (local lengths of the attempts made: [38]); the triple:
      f_1 = -5*x^5 + 5*x^4*y - 3*x^3*y^2 + 5*x^2*y^3 + 3*x*y^4 + 4*y^5 + 2*x^4*z - 4*x^3*y*z - x^2*y^2*z - 3*y^4*z - 4*x^3*z^2 - 3*x^2*y*z^2 + x*y^2*z^2 - 3*y^3*z^2 - x^2*z^3 + 2*x*y*z^3 - 3*y^2*z^3 - 2*x*z^4 + y*z^4 - 2*z^5 + y^2*z^2 - 4*y*z^3 - 3*z^4 + 5*x^3 + x^2*y - 3*x*y^2 - 3*x^2*z - 3*x*y*z - 4*x*z^2
      f_2 = x^5 + 4*x^4*y - 2*x^3*y^2 - 3*x*y^4 + 2*y^5 - 3*x^4*z - x^3*y*z - 5*x^2*y^2*z - x*y^3*z + 4*y^4*z + 4*x^3*z^2 - 2*x^2*y*z^2 - x*y^2*z^2 - 4*y^3*z^2 + x^2*z^3 + 3*x*y*z^3 + 3*y^2*z^3 + 3*x*z^4 + 4*y*z^4 - 5*z^5 + y^2*z^2 + 2*y*z^3 - 4*z^4 + 3*x^3 - 5*x^2*y + 3*x*y^2 + 4*x^2*z - 5*x*y*z - 5*x*z^2
      f_3 = -2*x^5 - 4*x^4*y - 4*x^2*y^3 - 4*x*y^4 + 2*y^5 + 4*x^4*z - 2*x^3*y*z - 4*x*y^3*z + 3*y^4*z + 5*x^2*y*z^2 + 5*x*y^2*z^2 + 4*y^3*z^2 + x^2*z^3 - 4*x*y*z^3 - 5*y^2*z^3 + 5*x*z^4 + 5*y*z^4 + 5*z^5 + 4*y^2*z^2 + 3*y*z^3 + 3*z^4 + 3*x^3 + 4*x^2*y + 3*x*y^2 - x*y*z - x*z^2
  ok   (1,3,6,4,5,2), tangent <Y^5,Y^4Z>: H = [1, 3, 6, 4, 5, 2], closed True, f_i in Ann(M) True, deg gcd K = 2, CI local length 38 (stable pair N = 10, 11; attempt 1) <= 38
   (1,3,6,4,5,2), <Y^5, Y^2Z^3 + Z^5>: attempt 1 used (local lengths of the attempts made: [37]); the triple:
      f_1 = -5*x^5 - 5*x^4*y + x^3*y^2 - x^2*y^3 + 2*x*y^4 + 2*y^5 + 5*x^4*z - 5*x^3*y*z + 4*x^2*y^2*z - 2*x*y^3*z - 2*y^4*z - 2*x^3*z^2 + x^2*y*z^2 + x*y^2*z^2 + 5*y^3*z^2 + x^2*z^3 + x*y*z^3 + 5*y^2*z^3 - 4*y*z^4 - 5*z^5 - 4*y^3*z - 2*y^2*z^2 + 1/5*z^4 + 2*x^3 + 2*x^2*y + 3*x*y^2 + 3*x^2*z + x*y*z + x*z^2
      f_2 = 5*x^5 + 4*x^4*y + 4*x^3*y^2 - 2*x^2*y^3 - x*y^4 - 3*y^5 + 5*x^4*z + 5*x^3*y*z + 2*x^2*y^2*z + 4*x*y^3*z - x^3*z^2 + 2*x^2*y*z^2 + x*y^2*z^2 - 2*y^3*z^2 + x^2*z^3 + 3*x*y*z^3 - y^2*z^3 - 5*x*z^4 + y*z^4 - 3*z^5 + 2*y^3*z + 5*y^2*z^2 - 1/2*z^4 + 2*x^3 - 3*x^2*y + 2*x^2*z + 4*x*y*z - 2*x*z^2
      f_3 = 2*x^5 - 4*x^4*y + x^3*y^2 + 5*x*y^4 - 3*x^4*z - 2*x^3*y*z - 2*x*y^3*z + 3*y^4*z + 5*x^3*z^2 + 5*x^2*y*z^2 - x*y^2*z^2 - y^3*z^2 + 4*x^2*z^3 - 4*x*y*z^3 - 3*y^2*z^3 - 5*x*z^4 + 5*y*z^4 + 3*z^5 + 4*y^3*z + y^2*z^2 - 1/10*z^4 - 4*x^3 + 3*x^2*y - 4*x*y^2 - 3*x^2*z + 3*x*y*z - x*z^2
  ok   (1,3,6,4,5,2), <Y^5, Y^2Z^3 + Z^5>: H = [1, 3, 6, 4, 5, 2], closed True, f_i in Ann(M) True, deg gcd K = 1, CI local length 37 (stable pair N = 10, 11; attempt 1) <= 37
   (1,3,6,4,4,3), p general: attempt 1 used (local lengths of the attempts made: [40]); the triple:
      f_1 = 5*x^4*y - 5*x^3*y^2 + 4*x^2*y^3 + 2*x*y^4 - 3*y^5 - 4*x^3*y*z - 5*x^2*y^2*z + 2*x*y^3*z - 4*y^4*z + 3*x^3*z^2 + x^2*y*z^2 - 2*x*y^2*z^2 - y^3*z^2 + 4*x^2*z^3 - 5*x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 + 2*y*z^4 - 5*y^4 - 5*y^3*z + 10*y^2*z^2 - 5/2*y*z^3 + 5/2*z^4 + x^3 + 4*x^2*y - 4*x*y^2 - x^2*z - 2*x*y*z - 2*x*z^2
      f_2 = -5*x^5 - x^4*y + x^3*y^2 - 2*x^2*y^3 + 2*x*y^4 - 4*y^5 - 2*x^4*z + x^3*y*z - 2*x^2*y^2*z - 5*x*y^3*z + y^4*z + 3*x^3*z^2 + 4*x^2*y*z^2 + 5*x*y^2*z^2 + 5*y^3*z^2 + 4*x^2*z^3 + 4*x*y*z^3 - 2*y^2*z^3 - 4*x*z^4 - 3*y*z^4 - 5*z^5 + 3*y^4 + 3*y^3*z - 6*y^2*z^2 + 3/2*y*z^3 - 3/2*z^4 - 5*x^3 - 3*x*y^2 - 3*x^2*z + 4*x*y*z + x*z^2
      f_3 = 5*x^5 + 5*x^4*y - 3*x^3*y^2 + 5*x*y^4 - 3*y^5 - x^3*y*z - x^2*y^2*z - 5*x*y^3*z + 3*y^4*z - 3*x^3*z^2 - x^2*y*z^2 - 4*x*y^2*z^2 - 4*y^3*z^2 + 5*x^2*z^3 + 5*x*y*z^3 + 5*y^2*z^3 - 4*x*z^4 - 2*y*z^4 + 2*y^4 + 2*y^3*z - 4*y^2*z^2 + y*z^3 - z^4 + 2*x^3 + 3*x^2*y + 3*x*y^2 + 4*x^2*z + 4*x*y*z + 2*x*z^2
  ok   (1,3,6,4,4,3), p general: H = [1, 3, 6, 4, 4, 3], closed True, f_i in Ann(M) True, deg gcd K = 4, CI local length 40 (stable pair N = 10, 11; attempt 1) <= 40
   (1,3,6,4,4,3), p = y^4: attempt 1 used (local lengths of the attempts made: [40]); the triple:
      f_1 = -2*x^5 - 2*x^4*y + x^3*y^2 - 2*x^2*y^3 + 5*y^5 + 3*x^4*z - 4*x^3*y*z - 2*x^2*y^2*z + 4*x*y^3*z - 3*y^4*z + 3*x^2*y*z^2 + 3*x*y^2*z^2 - 5*y^3*z^2 - 5*x^2*z^3 + 5*x*y*z^3 + 5*x*z^4 + 2*y*z^4 + 2*z^5 + y^4 - 5*x^3 - 4*x^2*y - 2*x^2*z + 3*x*y*z - x*z^2
      f_2 = 5*x^5 + 5*x^4*y + 3*x^3*y^2 - x^2*y^3 - y^5 + 4*x^4*z + 4*x^3*y*z + x^2*y^2*z - 5*x*y^3*z + 4*y^4*z - 4*x^3*z^2 - 2*x^2*y*z^2 - 5*y^3*z^2 + 2*x^2*z^3 - 3*x*y*z^3 + y^2*z^3 + 4*x*z^4 + 5*y*z^4 - 3*z^5 - 2*y^4 - 3*x^3 + 2*x^2*y - x*y^2 - 5*x^2*z + 5*x*y*z - 5*x*z^2
      f_3 = 3*x^5 - x^4*y + x^2*y^3 + 3*x*y^4 - 5*y^5 + 2*x^4*z - 4*x^3*y*z + 4*x^2*y^2*z + 5*x*y^3*z + y^4*z - 2*x^3*z^2 - 3*x^2*y*z^2 + 4*y^3*z^2 + 4*x*y*z^3 - 5*y^2*z^3 - 3*x*z^4 + 5*y*z^4 - 2*z^5 + 3*y^4 - 3*x^3 + 3*x^2*y + x*y^2 + 3*x^2*z - 2*x*y*z - 2*x*z^2
  ok   (1,3,6,4,4,3), p = y^4: H = [1, 3, 6, 4, 4, 3], closed True, f_i in Ann(M) True, deg gcd K = 4, CI local length 40 (stable pair N = 10, 11; attempt 1) <= 40
   (1,3,6,4,4,3), p = y^2 z^2: attempt 1 used (local lengths of the attempts made: [40]); the triple:
      f_1 = -x^5 - 3*x^4*y + x^3*y^2 + 2*x^2*y^3 + 2*x*y^4 + 2*y^5 + x^4*z - 2*x^3*y*z - x^2*y^2*z - 2*x*y^3*z - y^4*z + 2*x^3*z^2 - 5*x^2*y*z^2 - 5*x*y^2*z^2 - 3*y^3*z^2 + 3*x^2*z^3 - 2*y^2*z^3 + 4*x*z^4 - 3*y*z^4 + z^5 - 2*y^2*z^2 + 4*x^3 + 5*x^2*y + 2*x*y^2 + 2*x^2*z - 2*x*y*z + 5*x*z^2
      f_2 = 4*x^5 + 2*x^4*y + 2*x^3*y^2 + 2*x^2*y^3 - 2*x^4*z - 2*x^3*y*z + 5*x^2*y^2*z - 3*x*y^3*z + y^4*z + 3*x^3*z^2 - 5*x^2*y*z^2 + 2*x*y^2*z^2 + 4*y^3*z^2 - 5*x^2*z^3 + 5*y^2*z^3 + 2*x*z^4 + 2*y*z^4 + 4*z^5 - y^2*z^2 - 3*x^3 + x^2*y - 5*x*y^2 - 5*x^2*z + 5*x*y*z + 4*x*z^2
      f_3 = -4*x^5 - 2*x^4*y - 2*x^2*y^3 - x*y^4 + 5*y^5 + 4*x^4*z - 4*x^3*y*z + 5*x^2*y^2*z - 4*x*y^3*z - 2*y^4*z - x^3*z^2 - 3*x^2*y*z^2 + 5*x*y^2*z^2 + 3*y^3*z^2 - 3*x^2*z^3 + 4*x*y*z^3 - 2*y^2*z^3 - x*z^4 - 3*y*z^4 + 2*z^5 + 2*y^2*z^2 - 4*x^3 - x^2*y - 4*x^2*z + 5*x*y*z - x*z^2
  ok   (1,3,6,4,4,3), p = y^2 z^2: H = [1, 3, 6, 4, 4, 3], closed True, f_i in Ann(M) True, deg gcd K = 4, CI local length 40 (stable pair N = 10, 11; attempt 1) <= 40
   (1,3,6,4,4,3), p = y^3 z: attempt 1 used (local lengths of the attempts made: [40]); the triple:
      f_1 = 3*x^5 - 5*x^4*y + 4*x^3*y^2 + 3*x^2*y^3 + x*y^4 - 3*y^5 - 2*x^4*z + 2*x^3*y*z + 3*x^2*y^2*z + 5*x*y^3*z + 2*x^3*z^2 + 3*x^2*y*z^2 - 5*x*y^2*z^2 + y^3*z^2 + 5*x*y*z^3 + 2*y^2*z^3 + 5*y*z^4 + 5*z^5 + 5*y^3*z - 5*x^3 - x^2*y - 5*x*y^2 + x^2*z - 4*x*y*z + 4*x*z^2
      f_2 = 5*x^5 + 2*x^4*y + 4*x^3*y^2 - 5*x*y^4 - 2*y^5 - 2*x^4*z + 4*x^3*y*z + 2*x^2*y^2*z - x*y^3*z - 5*y^4*z - 4*x^3*z^2 - 3*x^2*y*z^2 + 2*y^3*z^2 - 3*x^2*z^3 - 3*y^2*z^3 - x*z^4 - 2*y*z^4 - 3*z^5 - 5*y^3*z + 2*x^3 + 3*x^2*y - 2*x*y^2 + 4*x^2*z + 2*x*y*z - 2*x*z^2
      f_3 = -3*x^5 + 3*x^4*y - 4*x^3*y^2 - 4*x^2*y^3 + 3*x*y^4 + 4*y^5 + 5*x^4*z + 5*x^3*y*z - 4*x^2*y^2*z - 5*x*y^3*z + 4*y^4*z + x^3*z^2 - 2*x^2*y*z^2 - 4*x*y^2*z^2 - 4*y^3*z^2 - 2*x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 - 2*x*z^4 - 2*y*z^4 + z^5 - 4*y^3*z - 5*x^3 + 4*x^2*y - 3*x*y^2 - 3*x^2*z - 2*x*y*z + 3*x*z^2
  ok   (1,3,6,4,4,3), p = y^3 z: H = [1, 3, 6, 4, 4, 3], closed True, f_i in Ann(M) True, deg gcd K = 4, CI local length 40 (stable pair N = 10, 11; attempt 1) <= 40
   (1,3,6,5,5,1), general G, general binary top: attempt 1 used (local lengths of the attempts made: [36]); the triple:
      f_1 = x^5 + 4*x^4*y - 3*x^3*y^2 - 4*x^2*y^3 + 3*x*y^4 + 5*y^5 + 2*x^4*z - 5*x^3*y*z - x^2*y^2*z - 3*x*y^3*z + 2*y^4*z + 5*x^3*z^2 + 2*x^2*y*z^2 - x*y^2*z^2 + 5*y^3*z^2 - x^2*z^3 - y^2*z^3 + y*z^4 - z^5 + 4*y^4 + 2*y^3*z - 5*y^2*z^2 + 794/23*y*z^3 + 589/46*z^4 + 5*x^2*y + x*y^2 - 5*x*y*z - 5/2*x*z^2
      f_2 = -3*x^5 - x^4*y + x^3*y^2 + 5*x^2*y^3 - 5*x*y^4 + 5*y^5 - x^4*z - 4*x^3*y*z + 5*x^2*y^2*z + 2*y^4*z - x^3*z^2 + 2*x^2*y*z^2 + x*y^2*z^2 - 2*y^3*z^2 - 2*x^2*z^3 + 3*x*y*z^3 + 3*y^2*z^3 - 4*x*z^4 - 2*z^5 + 2*y^4 - 3*y^2*z^2 + 352/23*y*z^3 + 265/46*z^4 - 5*x^3 - 4*x^2*y + 4*x*y^2 - x^2*z - 4*x*y*z + 8*x*z^2
      f_3 = -5*x^5 + x^4*y - 2*x^3*y^2 - 2*x^2*y^3 - 5*x*y^4 - 2*y^5 + 3*x^4*z - 3*x^3*y*z - 2*x^2*y^2*z + 5*x*y^3*z - 5*x^3*z^2 - 3*x^2*y*z^2 - 2*x*y^2*z^2 + 3*y^3*z^2 + 5*x*y*z^3 + y^2*z^3 + 2*x*z^4 - 2*y*z^4 - z^5 + y^3*z - 3*y^2*z^2 - 25/23*y*z^3 + 41/23*z^4 - 5*x^3 + 2*x^2*y - x*y^2 + 5*x^2*z + 4*x*y*z + 14/3*x*z^2
  ok   (1,3,6,5,5,1), general G, general binary top: H = [1, 3, 6, 5, 5, 1], closed True, f_i in Ann(M) True, deg gcd K = 0, CI local length 36 (stable pair N = 9, 10; attempt 1) <= 36
   (1,3,6,5,5,1), general G, top Y^5: attempt 1 used (local lengths of the attempts made: [37]); the triple:
      f_1 = -x^5 + 5*x^4*y - 4*x^3*y^2 - x^2*y^3 - 3*x*y^4 - y^5 + 5*x^4*z - 5*x^3*y*z + x*y^3*z - y^4*z - 2*x^3*z^2 + 3*x^2*y*z^2 - 5*x*y^2*z^2 - 2*y^3*z^2 + x^2*z^3 + 5*x*y*z^3 + 4*y^2*z^3 + 4*x*z^4 - 2*y*z^4 - 4*z^5 + 5*y*z^3 - 3*z^4 + 4*x^3 - 3*x^2*y + 2*x*y^2 - 3*x*y*z - 3/2*x*z^2
      f_2 = -3*x^5 + 5*x^4*y + x^3*y^2 - 3*x^2*y^3 - 3*x*y^4 - 4*y^5 + x^4*z + 5*x^3*y*z + 3*x^2*y^2*z - 5*x*y^3*z + 2*y^4*z - x^3*z^2 + x^2*y*z^2 - 4*x*y^2*z^2 - 5*y^3*z^2 - 5*x^2*z^3 - 3*x*y*z^3 - 4*y^2*z^3 + 2*x*z^4 + 5*y*z^4 + 5*y^3*z + 5*y^2*z^2 + 3*y*z^3 - 2*z^4 - 5*x^3 - 2*x^2*y - 2*x*y^2 + x^2*z + 2*x*y*z + 19/3*x*z^2
      f_3 = x^5 + 3*x^4*y - x^3*y^2 + x^2*y^3 - 4*x^4*z - x^2*y^2*z - x*y^3*z + 5*y^4*z - 5*x^3*z^2 + 2*x^2*y*z^2 + 5*y^3*z^2 + 5*x^2*z^3 - 3*x*y*z^3 + 3*x*z^4 - 2*y*z^4 + 5*z^5 + 5*y^3*z + 2*y^2*z^2 - y*z^3 + z^4 - 4*x^3 - 3*x^2*y + 4*x*y^2 + 3*x^2*z - x*y*z + 43/6*x*z^2
  ok   (1,3,6,5,5,1), general G, top Y^5: H = [1, 3, 6, 5, 5, 1], closed True, f_i in Ann(M) True, deg gcd K = 1, CI local length 37 (stable pair N = 10, 11; attempt 1) <= 37
   (1,3,6,5,4,2), general G, D_4 = p^perp, generic D_5: attempt 1 used (local lengths of the attempts made: [40]); the triple:
      f_1 = -2*x^5 - 3*x^4*y + 4*x^3*y^2 - 2*x^2*y^3 + x*y^4 + y^5 - 3*x^3*y*z - 4*x^2*y^2*z - x*y^3*z - y^4*z + 4*x^3*z^2 - 3*x^2*y*z^2 - 5*y^3*z^2 - x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 + x*z^4 - y*z^4 + 3*y^4 + 4*y^3*z + y^2*z^2 + 3*y*z^3 + 5*z^4 - 5*x^3 - 3*x^2*y + 4*x*y^2 + 5*x*y*z + 37/6*x*z^2
      f_2 = 2*x^5 + 2*x^4*y - 3*x^3*y^2 - 5*x^2*y^3 + 3*x*y^4 + 4*y^5 - 3*x^4*z + 4*x^3*y*z + x^2*y^2*z + 2*x*y^3*z - 5*y^4*z + 2*x^3*z^2 + 2*x^2*y*z^2 - 3*x*y^2*z^2 - 5*y^3*z^2 - 4*x^2*z^3 + 3*x*y*z^3 - y^2*z^3 - 4*x*z^4 + 3*y*z^4 - 3*z^5 + 4*y^4 + 16/3*y^3*z + 4/3*y^2*z^2 + 4*y*z^3 + 20/3*z^4 - 2*x^3 - x^2*y - 2*x*y^2 + x^2*z - 4*x*y*z + 11/3*x*z^2
      f_3 = 4*x^5 + x^4*y + 4*x^3*y^2 + 2*x^2*y^3 - x*y^4 - 3*y^5 + x^3*y*z - x^2*y^2*z + 5*x*y^3*z - 3*y^4*z + 2*x^3*z^2 - 3*x^2*y*z^2 - 2*x*y^2*z^2 + y^3*z^2 + 4*x^2*z^3 - x*y*z^3 + 5*y^2*z^3 - 4*x*z^4 + 3*z^5 - 4*y^4 - 16/3*y^3*z - 4/3*y^2*z^2 - 4*y*z^3 - 20/3*z^4 + 5*x^3 - 5*x^2*y - 4*x*y^2 + 5*x^2*z + 2*x*y*z - 1/3*x*z^2
  ok   (1,3,6,5,4,2), general G, D_4 = p^perp, generic D_5: H = [1, 3, 6, 5, 4, 2], closed True, f_i in Ann(M) True, deg gcd K = 4, CI local length 40 (stable pair N = 10, 11; attempt 1) <= 40
   (1,3,6,5,4,2), general G, D_5 = <Y^5, Z^5>: attempt 1 used (local lengths of the attempts made: [38]); the triple:
      f_1 = -5*x^5 - 4*x^4*y - 2*x^3*y^2 - 2*x*y^4 - 2*y^5 + 5*x^4*z - 2*x^3*y*z + 2*x^2*y^2*z + 5*x*y^3*z + 5*y^4*z + 2*x^3*z^2 - x^2*y*z^2 + 3*x*y^2*z^2 + 4*y^3*z^2 + 3*x^2*z^3 + 2*x*y*z^3 - x*z^4 + 4*z^5 + 3*y^2*z^2 + 3*y*z^3 - x^3 + 3*x*y^2 + x^2*z - 4*x*y*z + 2*x*z^2
      f_2 = 5*x^5 - 3*x^4*y + 3*x^3*y^2 - 3*x^2*y^3 + 4*x*y^4 - y^5 + 3*x^4*z - 3*x^3*y*z - x^2*y^2*z + 3*x*y^3*z - 4*y^4*z - 4*x^3*z^2 + 2*x^2*y*z^2 - x*y^2*z^2 + 4*y^3*z^2 + x^2*z^3 - 2*x*y*z^3 + 5*y^2*z^3 + 3*x*z^4 + 5*y*z^4 - 4*z^5 + 5*y^3*z - y^2*z^2 - 2*y*z^3 + 4*x^3 + 2*x^2*y + x*y^2 + 3*x^2*z - 2*x*y*z - 4*x*z^2
      f_3 = 3*x^5 + 3*x^4*y - 2*x^3*y^2 + x^2*y^3 - x*y^4 - 5*y^5 + 5*x^4*z + 5*x^3*y*z + 5*x^2*y^2*z + 4*x*y^3*z - y^4*z + x^3*z^2 + 5*x^2*y*z^2 - 3*x*y^2*z^2 + y^3*z^2 + x^2*z^3 + x*y*z^3 + y^2*z^3 - 2*x*z^4 - 2*y*z^4 + 5*z^5 - 3*y^3*z - 5*y^2*z^2 + 3*y*z^3 - x^3 + 4*x^2*y - 2*x*y^2 - 4*x^2*z + 3*x*y*z - 7/2*x*z^2
  ok   (1,3,6,5,4,2), general G, D_5 = <Y^5, Z^5>: H = [1, 3, 6, 5, 4, 2], closed True, f_i in Ann(M) True, deg gcd K = 2, CI local length 38 (stable pair N = 10, 11; attempt 1) <= 38
   (1,3,6,5,3,3), general G, Gamma = 3 points of the line: attempt 1 used (local lengths of the attempts made: [39]); the triple:
      f_1 = 4*x^5 - 2*x^4*y + 5*x^3*y^2 + 3*x*y^4 - 2*y^5 - 5*x^4*z - 5*x*y^3*z - 3*y^4*z - x^3*z^2 + 3*x^2*y*z^2 - x*y^2*z^2 - 4*y^3*z^2 + x^2*z^3 + 5*x*y*z^3 - 3*x*z^4 + 5*y*z^4 - 2*z^5 + 2*y^3*z - y^2*z^2 - y*z^3 + 5*x^3 - x^2*y + 5*x*y^2 + 5*x^2*z + x*y*z - 17/6*x*z^2
      f_2 = 4*x^5 - 4*x^4*y - 5*x^3*y^2 + 4*x^2*y^3 + x*y^4 - 3*y^5 - 5*x^4*z + 5*x^3*y*z + 4*x^2*y^2*z + x*y^3*z - 3*y^4*z + 2*x^3*z^2 - 3*x^2*y*z^2 - x*y^2*z^2 - 3*y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 + 4*y^2*z^3 - 5*x*z^4 + y*z^4 + 5*z^5 + 3*y^3*z + 5*y^2*z^2 - 8*y*z^3 - 3*x^3 + 4*x^2*y - 3*x^2*z + 4*x*y*z - 4/3*x*z^2
      f_3 = 5*x^5 + 5*x^4*y + 5*x^3*y^2 - 4*x^2*y^3 - 4*x*y^4 + y^5 - 2*x^4*z + 3*x^3*y*z - 4*x^2*y^2*z + x*y^3*z + 2*y^4*z - 3*x^3*z^2 + 5*x*y^2*z^2 - y^3*z^2 - 5*x^2*z^3 - 4*y^2*z^3 + 3*x*z^4 + y*z^4 - 5*z^5 - 4*y^2*z^2 + 4*y*z^3 + 5*x^3 + 2*x^2*y + x*y^2 - 3*x^2*z + x*y*z - 15/2*x*z^2
  ok   (1,3,6,5,3,3), general G, Gamma = 3 points of the line: H = [1, 3, 6, 5, 3, 3], closed True, f_i in Ann(M) True, deg gcd K = 3, CI local length 39 (stable pair N = 10, 11; attempt 1) <= 39
   (1,3,6,5,3,3), general G, Gamma = triple point of the line: attempt 1 used (local lengths of the attempts made: [39]); the triple:
      f_1 = -4*x^5 + 2*x^3*y^2 + 5*x^2*y^3 + 4*x*y^4 - 5*y^5 - 4*x^4*z + x^3*y*z + 2*x^2*y^2*z - 5*x*y^3*z + 4*y^4*z + x^3*z^2 + 2*x^2*y*z^2 + x*y^2*z^2 - y^3*z^2 - x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 + 5*x*z^4 + 2*y*z^4 - z^5 + 3*y*z^3 + 2*z^4 + 3*x^3 + 4*x^2*y - 3*x*y^2 - x^2*z - 6*x*z^2
      f_2 = -2*x^4*y + 5*x^2*y^3 - 4*x*y^4 + 2*y^5 - x^3*y*z + 2*x^2*y^2*z - x*y^3*z + 5*y^4*z - x^3*z^2 - 5*x^2*y*z^2 - 4*x*y^2*z^2 + 2*y^3*z^2 + 5*x^2*z^3 + 5*x*y*z^3 - 4*x*z^4 + y*z^4 + y*z^3 + z^4 - x^3 + 4*x^2*y + x*y^2 + 3*x^2*z - 2*x*y*z - 1/3*x*z^2
      f_3 = 3*x^5 - 4*x^4*y + 3*x^2*y^3 + 2*x*y^4 + 4*y^5 - 2*x^4*z + 5*x^3*y*z + 3*x^2*y^2*z - 4*x*y^3*z + y^4*z + x^3*z^2 + 3*x^2*y*z^2 + 3*x*y^2*z^2 + 2*y^3*z^2 + x^2*z^3 - 3*x*y*z^3 - 2*y^2*z^3 - 4*x*z^4 + y*z^4 - 2*z^5 - 3*y*z^3 - 3*z^4 + x^3 - 2*x^2*y - x*y^2 + 3*x^2*z - 4*x*y*z + 2*x*z^2
  ok   (1,3,6,5,3,3), general G, Gamma = triple point of the line: H = [1, 3, 6, 5, 3, 3], closed True, f_i in Ann(M) True, deg gcd K = 3, CI local length 39 (stable pair N = 10, 11; attempt 1) <= 39
   (1,3,6,5,5,1), G = XYZ, general binary top: attempt 1 used (local lengths of the attempts made: [36]); the triple:
      f_1 = -4*x^5 + x^4*y - 4*x^3*y^2 - 5*x^2*y^3 + x*y^4 + 5*y^5 - x^4*z + 4*x^3*y*z - 2*x^2*y^2*z - y^4*z - x^3*z^2 + 2*x^2*y*z^2 - 5*x*y^2*z^2 - 5*y^3*z^2 + x^2*z^3 - 5*y^2*z^3 + 2*x*z^4 + 3*y*z^4 - 3*z^5 + 4*y^4 - 2*y^3*z + 4*y^2*z^2 - 2172/143*y*z^3 - 192/143*z^4 - 2*x^3 - 5*x^2*y + 4*x*y^2 + x*z^2
      f_2 = 4*x^5 - x^4*y + 5*x^3*y^2 - 3*x*y^4 - y^5 + 5*x^4*z - 5*x^3*y*z - x^2*y^2*z + 4*x*y^3*z + 3*y^4*z - x^3*z^2 - 3*x^2*y*z^2 - 3*x*y^2*z^2 - 3*y^3*z^2 - 5*x^2*z^3 + 4*x*y*z^3 + y^2*z^3 - 5*x*z^4 + 4*y*z^4 + 3*z^5 + 2*y^3*z - 4*y^2*z^2 + 148/143*y*z^3 - 28/143*z^4 - 5*x^3 + 2*x^2*y + 4*x*y^2 + 3*x^2*z + x*z^2
      f_3 = x^4*y + 2*x^3*y^2 + 2*x^2*y^3 + 3*x*y^4 - 3*y^5 + 2*x^4*z - x^3*y*z + 5*x^2*y^2*z + 5*x*y^3*z + 2*y^4*z - 4*x^3*z^2 + 5*y^3*z^2 - 2*x^2*z^3 - 2*x*y*z^3 + 5*y^2*z^3 - 5*x*z^4 + 5*y*z^4 + z^5 + 5*y^4 - 4*y^3*z + 3*y^2*z^2 - 2501/143*y*z^3 - 503/286*z^4 - 2*x^3 - 5*x^2*y - x*y^2 - 4*x^2*z + x*z^2
  ok   (1,3,6,5,5,1), G = XYZ, general binary top: H = [1, 3, 6, 5, 5, 1], closed True, f_i in Ann(M) True, deg gcd K = 0, CI local length 36 (stable pair N = 9, 10; attempt 1) <= 36
   (1,3,6,5,5,1), G = XYZ, top Y^5: attempt 2 used (local lengths of the attempts made: [38, 37]); the triple:
      f_1 = 5*x^5 - 3*x^4*y + 5*x^2*y^3 + x*y^4 + 3*y^5 - 4*x^4*z - 3*y^4*z + 2*x^3*z^2 + 2*x^2*y*z^2 + 2*x*y^2*z^2 + 4*y^3*z^2 - 3*x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 + 5*x*z^4 + 4*y*z^4 + 2*z^5 - y^3*z - 2*y^2*z^2 - y*z^3 + 2*z^4 - x^3 + x^2*y - x*y^2 - 4*x^2*z - 5*x*z^2
      f_2 = -x^5 + 3*x^4*y + x^3*y^2 - 2*x^2*y^3 + 4*x*y^4 + 2*x^4*z + x^2*y^2*z - 2*x*y^3*z - y^4*z - 4*x^3*z^2 - x^2*y*z^2 + 3*x*y^2*z^2 + 5*y^3*z^2 + 4*x^2*z^3 - 5*x*y*z^3 + 3*y^2*z^3 + 4*z^5 - 3*y^2*z^2 + 2*y*z^3 + 4*z^4 + 4*x^3 - 4*x^2*y - 3*x*y^2 + x^2*z - 4*x*z^2
      f_3 = -3*x^5 + 5*x^4*y - 5*x^3*y^2 + 5*x^2*y^3 + 5*x*y^4 - 4*y^5 - 4*x^4*z - 2*x^3*y*z + x^2*y^2*z + x*y^3*z + 2*y^4*z - 2*x^3*z^2 - 4*x^2*y*z^2 - 3*x*y^2*z^2 - 5*y^3*z^2 + 4*x^2*z^3 + 4*x*y*z^3 + 4*y^2*z^3 - 2*x*z^4 - 4*y*z^4 + 5*z^5 + y^3*z - y^2*z^2 + 2*y*z^3 - 4*z^4 + 5*x^3 - 5*x^2*y + 5*x*y^2 - 3*x^2*z - 5*x*z^2
  ok   (1,3,6,5,5,1), G = XYZ, top Y^5: H = [1, 3, 6, 5, 5, 1], closed True, f_i in Ann(M) True, deg gcd K = 1, CI local length 37 (stable pair N = 10, 11; attempt 2) <= 37
   (1,3,6,5,4,2), G = XYZ, D_4 = p^perp, generic D_5: attempt 1 used (local lengths of the attempts made: [40]); the triple:
      f_1 = -x^5 + 4*x^4*y + 3*x^3*y^2 - 3*x^2*y^3 - 4*x*y^4 + 2*y^5 + 5*x^4*z - 4*x^3*y*z + x^2*y^2*z + 4*x*y^3*z + y^4*z - x^3*z^2 - x*y^2*z^2 - y^3*z^2 + x^2*z^3 + 3*x*y*z^3 + 5*y^2*z^3 + 3*x*z^4 - 5*y*z^4 + z^5 - 2*y^4 - y^3*z - 4*y^2*z^2 + 5*y*z^3 + 3*z^4 - 5*x^3 + 4*x^2*y + 5*x^2*z - 3*x*z^2
      f_2 = 2*x^5 - 4*x^4*y + 5*x^3*y^2 + x^2*y^3 + 4*x*y^4 - y^5 - x^4*z + 3*x^3*y*z + 5*x^2*y^2*z - 5*x*y^3*z + y^4*z + 3*x^2*y*z^2 - x*y^2*z^2 - 4*y^3*z^2 - 4*x^2*z^3 - 2*x*y*z^3 + 2*x*z^4 - 5*y*z^4 - 3*z^5 + 5*y^4 + 5/2*y^3*z + 10*y^2*z^2 - 25/2*y*z^3 - 15/2*z^4 - 2*x^3 - 5*x^2*y - x*y^2 - 3*x^2*z + 2*x*z^2
      f_3 = -x^5 + 2*x^3*y^2 - 3*x^2*y^3 - 3*x*y^4 + 4*y^5 - 4*x^4*z + x^3*y*z - 3*x*y^3*z + 2*y^4*z - 4*x^3*z^2 - 5*x^2*y*z^2 - 3*x*y^2*z^2 + 3*y^3*z^2 - 2*x^2*z^3 + 2*x*y*z^3 - 4*y^2*z^3 + 5*x*z^4 - y*z^4 + 2*z^5 - 3*y^4 - 3/2*y^3*z - 6*y^2*z^2 + 15/2*y*z^3 + 9/2*z^4 + 3*x^2*y - 5*x*y^2 + x^2*z + 5*x*z^2
  ok   (1,3,6,5,4,2), G = XYZ, D_4 = p^perp, generic D_5: H = [1, 3, 6, 5, 4, 2], closed True, f_i in Ann(M) True, deg gcd K = 4, CI local length 40 (stable pair N = 10, 11; attempt 1) <= 40
   (1,3,6,5,4,2), G = XYZ, D_5 = <Y^5, Z^5>: attempt 1 used (local lengths of the attempts made: [38]); the triple:
      f_1 = -4*x^5 - x^4*y + 5*x^3*y^2 - 2*x^2*y^3 + 3*x*y^4 - y^5 - x^3*y*z + 2*x*y^3*z - 4*y^4*z - 4*x^3*z^2 - 2*x^2*y*z^2 - y^3*z^2 + 4*x^2*z^3 - 3*x*y*z^3 - 3*y^2*z^3 + 2*x*z^4 + y*z^4 - 3*z^5 - 4*y^2*z^2 + y*z^3 + 4*x^3 + 4*x^2*y - 3*x*y^2 - 3*x^2*z - 5*x*z^2
      f_2 = -2*x^5 + x^4*y + x^3*y^2 + 5*x^2*y^3 - 4*x*y^4 - 4*y^5 + 4*x^4*z + 3*x^3*y*z - 3*x^2*y^2*z + 2*x*y^3*z + 4*y^4*z + 2*x^3*z^2 + 5*x^2*y*z^2 + 2*x*y^2*z^2 - y^3*z^2 - 2*x^2*z^3 + 4*y^2*z^3 + 2*x*z^4 - 4*y*z^4 - z^5 - y^3*z + 3*y^2*z^2 - y*z^3 + x^3 + 4*x^2*y - 5*x*y^2 + x^2*z + 5*x*z^2
      f_3 = 5*x^5 + 4*x^4*y - 5*x^3*y^2 + 3*x^2*y^3 + 4*x*y^4 + 4*y^5 + 2*x^3*y*z + 3*x*y^3*z + 2*y^4*z - 4*x^3*z^2 + 3*x^2*y*z^2 - 4*x*y^2*z^2 - 5*y^3*z^2 + 3*x^2*z^3 - 2*x*y*z^3 - x*z^4 + 4*y*z^4 + 5*z^5 - 4*y^3*z - 2*y^2*z^2 - 5*y*z^3 - 2*x^3 - 2*x^2*y + 5*x*y^2 + 5*x^2*z - 4*x*z^2
  ok   (1,3,6,5,4,2), G = XYZ, D_5 = <Y^5, Z^5>: H = [1, 3, 6, 5, 4, 2], closed True, f_i in Ann(M) True, deg gcd K = 2, CI local length 38 (stable pair N = 10, 11; attempt 1) <= 38
   (1,3,6,5,3,3), G = XYZ, Gamma = 3 points of the line: attempt 1 used (local lengths of the attempts made: [39]); the triple:
      f_1 = 2*x^5 - 2*x^4*y - 3*x^3*y^2 - 3*x^2*y^3 - x*y^4 + 3*y^5 + 2*x^4*z - x^3*y*z - 2*x^2*y^2*z + 2*y^4*z - 2*x^3*z^2 - 3*x^2*y*z^2 - 3*x*y^2*z^2 - 5*y^3*z^2 - 3*x^2*z^3 + 4*x*y*z^3 + 3*y^2*z^3 + x*z^4 - 4*y*z^4 - 2*z^5 + 3*y^3*z + 3*y^2*z^2 - 6*y*z^3 + 2*x^3 - 3*x^2*y - 5*x*y^2 + x^2*z - 2*x*z^2
      f_2 = 2*x^4*y + 3*x^3*y^2 + 5*x^2*y^3 + 5*y^5 - 2*x^4*z + 4*x^3*y*z + 2*x^2*y^2*z - 5*x*y^3*z - 5*y^4*z + 4*x^3*z^2 - 3*x^2*y*z^2 + 4*x*y^2*z^2 + 3*y^3*z^2 - 4*x^2*z^3 - 5*x*y*z^3 - 3*y^2*z^3 + x*z^4 - 5*y*z^4 + 5*z^5 - 3*y^2*z^2 + 3*y*z^3 + x^3 + 4*x^2*y + 2*x*y^2 - 4*x^2*z - 4*x*z^2
      f_3 = -3*x^5 - 2*x^4*y - x^3*y^2 + x^2*y^3 - 5*x*y^4 - 4*y^5 + 3*x^4*z + 3*x^2*y^2*z + 4*x*y^3*z + 4*y^4*z + 5*x^3*z^2 - 5*x^2*y*z^2 + x*y^2*z^2 + 3*y^3*z^2 + 2*x*y*z^3 - y^2*z^3 - 4*y*z^4 + 4*y^3*z + 3*y^2*z^2 - 7*y*z^3 - 3*x^3 - x^2*y - x*y^2 - x^2*z
  ok   (1,3,6,5,3,3), G = XYZ, Gamma = 3 points of the line: H = [1, 3, 6, 5, 3, 3], closed True, f_i in Ann(M) True, deg gcd K = 3, CI local length 39 (stable pair N = 10, 11; attempt 1) <= 39
   (1,3,6,5,3,3), G = XYZ, Gamma = triple point of the line: attempt 1 used (local lengths of the attempts made: [39]); the triple:
      f_1 = -2*x^5 - 4*x^4*y - 2*x^3*y^2 - 3*x^2*y^3 + 2*x*y^4 + y^5 - 4*x^4*z - 5*x^3*y*z - 4*x^2*y^2*z + 5*x*y^3*z + y^4*z - 5*x^3*z^2 - 5*x^2*y*z^2 + 4*x*y^2*z^2 + y^3*z^2 + 2*x^2*z^3 - x*y*z^3 + 5*y^2*z^3 + x*z^4 - 3*y*z^4 - 3*z^5 - y*z^3 + z^4 - 5*x^2*y + 2*x*y^2 + 3*x^2*z + 2*x*z^2
      f_2 = 4*x^5 - 2*x^4*y - 4*x^2*y^3 - 2*x*y^4 + 2*x^4*z - 2*x^3*y*z - 5*x^2*y^2*z + x*y^3*z + 3*y^4*z - 2*x^3*z^2 - 4*x^2*y*z^2 + x*y^2*z^2 + 5*y^3*z^2 + x^2*z^3 - 5*x*y*z^3 + y^2*z^3 - 2*x*z^4 - 3*y*z^4 - 3*z^5 + 4*y*z^3 - 4*z^4 + 4*x^3 - 4*x^2*y - 2*x*y^2 + 4*x^2*z + 3*x*z^2
      f_3 = 3*x^5 - 3*x^4*y - 4*x^3*y^2 - 4*x^2*y^3 - 5*x*y^4 - 4*y^5 - 4*x^4*z + 2*x^3*y*z - 4*x^2*y^2*z + 2*x*y^3*z - 2*y^4*z + 2*x^3*z^2 + 4*x^2*y*z^2 - 5*x*y^2*z^2 + 4*y^3*z^2 + 2*x^2*z^3 - x*y*z^3 - 3*y^2*z^3 - 3*x*z^4 - 4*y*z^4 + 3*z^5 - 2*y*z^3 - 5*z^4 + 3*x^3 - 4*x^2*y + x*y^2 + 2*x^2*z + 4*x*z^2
  ok   (1,3,6,5,3,3), G = XYZ, Gamma = triple point of the line: H = [1, 3, 6, 5, 3, 3], closed True, f_i in Ann(M) True, deg gcd K = 3, CI local length 39 (stable pair N = 10, 11; attempt 1) <= 39
total time 161.3 s
ALL CHECKS PASSED
