Part A: the quintic conditions
  ok   secant: {Phi5 : z o Phi5 in D_4} = span of [X^5, X^4*Y, X^4*Z, X^3*Y^2, X^2*Y^3, X*Y^4, Y^5, Y^4*Z]
  ok   tangent: {Phi5 : z o Phi5 in D_4} = span of [X^5, X^4*Y, X^4*Z, X^3*Y^2, X^3*Y*Z, X^2*Y^3, X*Y^4, Y^5]
  ok   secant: x y o Phi5 = 4*p1*XX^3 + 6*p2*XX^2*YY + 6*p3*XX*YY^2 + 4*p4*YY^3; modulo <X^3, Y^3> it is v = 6 p2 X^2Y + 6 p3 XY^2
  ok   tangent: y^2 o Phi5 = 2*p2*XX^3 + 6*p3*XX^2*YY + 12*p4*XX*YY^2 + 20*p5*YY^3; modulo E0 it is v = 12 p4 XY^2 + 20 p5 Y^3
Part B: criterion vs direct closedness
   secant, piece v = 0: closed True, criterion True, H = [1, 3, 6, 5, 2, 2, 1]; perturbed: closed False, criterion False
   secant, piece v = 0: closed True, criterion True, H = [1, 3, 6, 5, 2, 2, 1]; perturbed: closed False, criterion False
   secant, piece v != 0: closed True, criterion True, H = [1, 3, 6, 5, 2, 2, 1]; perturbed: closed False, criterion False
   secant, piece v != 0: closed True, criterion True, H = [1, 3, 6, 5, 2, 2, 1]; perturbed: closed False, criterion False
   tangent, piece v = 0: closed True, criterion True, H = [1, 3, 6, 5, 2, 2, 1]; perturbed: closed False, criterion False
   tangent, piece v = 0: closed True, criterion True, H = [1, 3, 6, 5, 2, 2, 1]; perturbed: closed False, criterion False
   tangent, piece v != 0: closed True, criterion True, H = [1, 3, 6, 5, 2, 2, 1]; perturbed: closed False, criterion False
   tangent, piece v != 0: closed True, criterion True, H = [1, 3, 6, 5, 2, 2, 1]; perturbed: closed False, criterion False
  ok   criterion = direct closedness, H = (1,3,6,5,2,2,1) on all random members
Part C: one member of each family with a short complete intersection
   secant, v = 0: D_3 = [X^3, Y^3, 3*X^3 - 3*X^2*Y - 3*X*Y^2 + X^2*Z - 3*X*Y*Z - Y^2*Z + 2*X*Z^2 - 3*Y*Z^2 + 2*Z^3, 2*X^3 - 2*X^2*Y - 2*X*Y^2 + 3*Y^3 - X^2*Z - X*Y*Z - 2*Y^2*Z + 3*X*Z^2 - 2*Y*Z^2 - 2*Z^3, -2*X^3 - X^2*Y + 2*X*Y^2 - 2*Y^3 - X^2*Z + 3*X*Z^2 + Z^3], Phi5 = -X^5 + X^4*Y + X*Y^4 + X^4*Z + 2*Y^4*Z: closed True, H = [1, 3, 6, 5, 2, 2, 1]; complete intersection of local length 29 (stable at N = 8)
      random.seed(100), attempt 0 used; generators: [9*x^7 - 3*x^6*y + 2*x^4*y^3 + 6*x^2*y^5 - 2*x*y^6 + 3*y^7 + 2*x^5*y*z - 3*x^3*y^3*z - 4*x^2*y^4*z - 9*x*y^5*z + 3*y^6*z + 6*x^5*z^2 + 4*x^3*y^2*z^2 + x^2*y^3*z^2 - 2*x*y^4*z^2 + 9*y^5*z^2 - 2*x^4*z^3 - 2*x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*x*y^3*z^3 - 2*y^4*z^3 + x^3*z^4 - 2*x^2*y*z^4 - 6*x*y^2*z^4 - 3*x^2*z^5 - 4*x*y*z^5 + 4*y^2*z^5 - 2*x*z^6 - 3*y*z^6 - 9*z^7 + 130337/10800*x^6 + 3*x^5*y - 6*x^4*y^2 + 6*x^3*y^3 + 4*x^2*y^4 - x*y^5 - 3*y^6 + 4*x^5*z + 2*x^2*y^3*z + 6*x*y^4*z - 2*x^4*z^2 + 6*x^3*y*z^2 - x^2*y^2*z^2 + 2*x*y^3*z^2 - 9*y^4*z^2 - 3*x^3*z^3 + 6*x^2*y*z^3 + 2*x*y^2*z^3 + y^3*z^3 - 3*x^2*z^4 + 4*x*y*z^4 + 3*y^2*z^4 - x*z^5 + 2*y*z^5 - 3*z^6 - 1001/25*x^5 + 6*x^4*y + 3*x^3*y^2 - 3*x^2*y^3 + 6*x*y^4 - 6*x^4*z - 6*x^2*y^2*z - 6*x^3*z^2 + 2*x^2*y*z^2 + 3*x*y^2*z^2 + y^3*z^2 + 3*x^2*z^3 - 9*x*y*z^3 + 4*y^2*z^3 + 6*y*z^4 - 2*z^5 - 9/2*x^4 - x^3*y + 9*x^2*y^2 + 2*y^4 + 6*x^2*z^2 + 9*x*y*z^2 + 2*x*z^3 + y*z^3 + 2*z^4 + 530*x^2*y - 72*x*y^2 + 220*x^2*z - 2166*x*y*z - 6*y^2*z + 3*x*z^2 + 6*y*z^2, -x^7 + 9*x^6*y + 3*x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + 9*x^6*z - 9*x^5*y*z + 6*x^4*y^2*z - 2*x^2*y^4*z + 3*x*y^5*z - 6*x^5*z^2 - 6*x^3*y^2*z^2 + y^5*z^2 - 4*x^4*z^3 - 4*x^3*y*z^3 + 3*x^2*y^2*z^3 - 6*x*y^3*z^3 - 4*y^4*z^3 - 2*x^3*z^4 + 9*x^2*y*z^4 + 2*x*y^2*z^4 + 3*y^3*z^4 + 2*x*y*z^5 + 2*y^2*z^5 + 4*y*z^6 - 778001/32400*x^6 - 2*x^5*y + 6*x^4*y^2 + 3*x^3*y^3 - x^2*y^4 + 6*x^5*z - 9*x^4*y*z - 6*x^3*y^2*z + 3*x^2*y^3*z + 2*x*y^4*z - 9*y^5*z - 2*x^3*y*z^2 - 2*x^2*y^2*z^2 - 2*y^4*z^2 + 3*x^3*z^3 - 3*x^2*y*z^3 + 3*y^3*z^3 + 2*x^2*z^4 - 9*x*y*z^4 + 6*y^2*z^4 + 2*x*z^5 + 115403/2700*x^5 - 4*x^3*y^2 - 9*x^2*y^3 + x*y^4 - x^4*z - 2*x^3*y*z - 9*x^2*y^2*z + 9*x*y^3*z - 6*y^4*z + 6*x^3*z^2 - 2*x*y^2*z^2 + 9*x^2*z^3 - x*y*z^3 + 3*y^2*z^3 - 6*y*z^4 + 6*z^5 + x^2*y^2 - 85066/45*x*y^3 + 3*y^4 - 6*x^3*z + 9*x^2*y*z - 2*x^2*z^2 + 2*x*y*z^2 + 2*y^2*z^2 - 6*x*z^3 - 6*y*z^3 + 431*x^2*y + 102*x*y^2 - 1080*x^2*z + 3486*x*y*z + 4*y^2*z + 2*x*z^2, -3*x^7 - 9*x^6*y + 6*x^5*y^2 + 6*x^4*y^3 + x^2*y^5 + x*y^6 - 2*y^7 - 2*x^6*z - 2*x^5*y*z + 6*x^4*y^2*z + 2*x*y^5*z - 2*y^6*z + 2*x^3*y^2*z^2 - 6*x^2*y^3*z^2 - 4*y^5*z^2 + 6*x^4*z^3 - 4*x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*y^4*z^3 - 2*x^3*z^4 + 3*x*y^2*z^4 - 4*y^3*z^4 - 6*x^2*z^5 - 2*x*y*z^5 + 4*y^2*z^5 - 3*x*z^6 + 3*x^5*y - 3*x^4*y^2 - 3*x^3*y^3 + 6*x^2*y^4 + 6*x^5*z + 3*x^2*y^3*z - 6*y^5*z + 6*x^4*z^2 + x^3*y*z^2 - 6*x^2*y^2*z^2 - 4*x*y^3*z^2 - y^4*z^2 + 4*x^3*z^3 + 9*x^2*y*z^3 + 9*x*y^2*z^3 - 4*y^3*z^3 - 3*x^2*z^4 + 2*x*y*z^4 + y*z^5 + 3*z^6 + 17923/450*x^5 + 3*x^4*y + 4*x^3*y^2 + 6*x^2*y^3 - y^5 - x^3*y*z - x*y^3*z + 3*y^4*z + 6*x^3*z^2 + 9*x*y^2*z^2 + 2*y^3*z^2 - 6*x^2*z^3 + 9*x*y*z^3 + 2*y*z^4 - 4*z^5 - 12/5*x^4 - 9*x^3*y - 4*x^2*y^2 - 25381/10*x*y^3 - 3*y^4 + 2*x^3*z - 4*x*y^2*z + 9*x^2*z^2 - x*y*z^2 + 2*y^2*z^2 + 9*y*z^3 - 1218*x^2*y - 90*x*y^2 + 668*x^2*z - 3240*x*y*z + 4*x*z^2 + 4*y*z^2 - 6*z^3]
   secant, v != 0: D_3 = [X^3, Y^3, 8*X^3 + 6*X^2*Y - 6*X*Y^2 + 8*Y^3, -X^3 + X^2*Y + X*Y^2 + 2*Y^3 + X*Y*Z + Y^2*Z - 3*X*Z^2 + Y*Z^2 + Z^3, 2*X^3 + X^2*Y + 2*X*Y^2 - 2*X^2*Z + 3*X*Y*Z - 2*Y^2*Z + Y*Z^2 - 2*Z^3], Phi5 = -X^5 + 2*X^4*Y + X^3*Y^2 - X^2*Y^3 + 2*X*Y^4 + 2*Y^5 - X^4*Z + Y^4*Z: closed True, H = [1, 3, 6, 5, 2, 2, 1]; complete intersection of local length 33 (stable at N = 10)
      random.seed(102), attempt 0 used; generators: [-6*x^7 - 3*x^6*y + 9*x^4*y^3 + x^3*y^4 - x*y^6 - 6*y^7 + 6*x^6*z + 6*x^5*y*z - 6*x^4*y^2*z + 6*x^3*y^3*z + 3*x*y^5*z + 3*x^4*y*z^2 - 2*x^3*y^2*z^2 - 6*x^2*y^3*z^2 - 4*x*y^4*z^2 + 2*y^5*z^2 + 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 2*y^4*z^3 + 2*x^3*z^4 - 9*x*y^2*z^4 + 6*y^3*z^4 + 9*x^2*z^5 + x*y*z^5 + 6*y^2*z^5 + 6*x*z^6 - 2*y*z^6 + 4*z^7 - 2*x^5*y - 2*x^3*y^3 + 6*x^2*y^4 + x*y^5 - 3*y^6 - 6*x^5*z - 6*x^2*y^3*z - 4*x*y^4*z + 2*y^5*z + 2*x^4*z^2 - 2*x^3*y*z^2 - 6*x^2*y^2*z^2 - 2*x*y^3*z^2 + 4*y^4*z^2 - 6*x^2*y*z^3 - 6*x*y^2*z^3 - 4*y^3*z^3 - 2*x^2*z^4 + 4*x*y*z^4 + 2*y^2*z^4 - 3*x*z^5 - 2*y*z^5 - 3*x^4*y - x^2*y^3 + 4*x*y^4 - 6*x^3*y*z - 4*x*y^3*z + 6*y^4*z - 3*x^3*z^2 - 6*x*y^2*z^2 - 2*y^3*z^2 + 6*x^2*z^3 + 9*x*z^4 - 3*z^5 - 118/15*x^4 + 79/20*x^3*y - 3*x^2*y^2 + 2*x*y^3 + 3*y^4 - x^2*y*z - 6*y^3*z + 2*x^2*z^2 - 2*x*y*z^2 + 9*y^2*z^2 - x*z^3 - y*z^3 + 40*x*y^2 + 204*x^2*z - 120*x*y*z + 9*x*z^2 + 4*y*z^2 - 6*z^3, -3*x^7 - x^6*y - 3*x^5*y^2 + 6*x^4*y^3 - 4*x^3*y^4 + 9*x^2*y^5 - 2*y^7 + 3*x^6*z - 4*x^5*y*z + 4*x^2*y^4*z - 6*x*y^5*z - 3*y^6*z - 3*x^5*z^2 + 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 + 6*x*y^4*z^2 + 2*x^4*z^3 + 2*x^3*y*z^3 + 3*x^2*y^2*z^3 + x*y^3*z^3 - 6*y^4*z^3 + 6*x^3*z^4 - 6*x*y^2*z^4 - 6*y^3*z^4 - 2*x^2*z^5 + 3*y^2*z^5 + 9*x*z^6 + 2*y*z^6 + 3*z^7 - 64537/7200*x^6 - 6*x^5*y + 3*x^4*y^2 - 4*x^2*y^4 - 6*x*y^5 + 2*x^4*y*z - 4*x^3*y^2*z - 3*x^2*y^3*z - 6*y^5*z - 3*x^4*z^2 - 4*x^3*y*z^2 - 4*x^2*y^2*z^2 - 6*y^4*z^2 + 3*x^2*y*z^3 + 9*x*y^2*z^3 + 6*y^3*z^3 + 6*x^2*z^4 + 6*x*y*z^4 + 3*x*z^5 - 6*y*z^5 - 2*z^6 - x^4*y - 4*x^2*y^3 - 6*x^4*z + 4*x^3*y*z + 6*x^2*y^2*z + 4*y^4*z + 6*x^3*z^2 - 2*x^2*y*z^2 + 6*x*y^2*z^2 + 4*y^3*z^2 + 2*x^2*z^3 - 3*x*y*z^3 + 6*y^2*z^3 - 2*x*z^4 - 2*z^5 + 3*x^2*y^2 - 3*x^3*z - 3*x^2*y*z + 2*x*y^2*z + 4*y^3*z - 2*x*y*z^2 - 6*y^2*z^2 - 4*x*z^3 + 59*x^2*z + 26*x*y*z + 6*x*z^2 - 2*y*z^2 + 9*z^3, 6*x^5*y^2 + 3*x^4*y^3 - 3*x^3*y^4 + 3*x^2*y^5 - 6*x*y^6 + y^7 - 6*x^4*y^2*z + 6*x^3*y^3*z + 2*x^2*y^4*z - 4*x*y^5*z - y^6*z + 6*x^5*z^2 - 2*x^4*y*z^2 - 2*x^3*y^2*z^2 + 6*x^2*y^3*z^2 - 4*x*y^4*z^2 - 4*y^5*z^2 - 3*x^4*z^3 + 2*x^3*y*z^3 + 2*x^2*y^2*z^3 - 9*y^4*z^3 - 6*x^3*z^4 + 6*x^2*y*z^4 + 9*x*y^2*z^4 + 2*x*y*z^5 - 9*x*z^6 - 6*y*z^6 + 9*z^7 - 2*x^5*y + 6*x^4*y^2 - 4*x^2*y^4 + 6*y^6 + 2*x^4*y*z - 4*x*y^4*z + 3*y^5*z - 9*x^4*z^2 + 3*x^3*y*z^2 + 2*x^2*y^2*z^2 - 6*x*y^3*z^2 + 2*x^3*z^3 + 4*x*y^2*z^3 - 3*y^3*z^3 + 9*x*y*z^4 + 3*y^2*z^4 + 9*y*z^5 + 4*z^6 + 24769/1800*x^5 + 3*x^4*y - 3*x^3*y^2 - 4*y^5 + 4*x^3*y*z - 4*x*y^3*z - 2*y^4*z + x^2*y*z^2 + 4*x*y^2*z^2 + 3*y^3*z^2 - 6*x^2*z^3 - 9*x*y*z^3 + 2*y^2*z^3 + 2*x*z^4 + y*z^4 + 3/5*x^4 + 6361/20*x^3*y - 6*x^2*y^2 - 6*x*y^3 - 2*x^3*z + x^2*y*z + 6*x*y^2*z - 2*y^3*z - 2*x^2*z^2 - 9*y^2*z^2 - 6*x*z^3 + 6*y*z^3 + 2*z^4 - 36*x^2*z + 18*x*y*z - 3*x*z^2 + 9*y*z^2 + z^3]
   tangent, v = 0: D_3 = [X^3, X^2*Y, X^3 - 2*X^2*Y - 2*Y^3 - X^2*Z + 2*X*Y*Z - Y^2*Z + 3*X*Z^2 - 3*Z^3, -X^3 - 2*X^2*Y - 3*X*Y^2 + Y^3 - 2*X^2*Z - Y^2*Z + 3*X*Z^2 - 2*Y*Z^2, 3*X^3 - X^2*Y + 2*X*Y^2 - 2*X^2*Z + 3*X*Y*Z - 2*Y^2*Z - 3*Y*Z^2], Phi5 = 2*X^5 - X^4*Y + 2*X^3*Y^2 + 2*X^4*Z - X^3*Y*Z: closed True, H = [1, 3, 6, 5, 2, 2, 1]; complete intersection of local length 29 (stable at N = 8)
      random.seed(101), attempt 0 used; generators: [-6*x^7 - 2*x^6*y + 6*x^5*y^2 - 6*x^3*y^4 + 9*x^2*y^5 + 6*x^6*z + 9*x^3*y^3*z - 6*x^2*y^4*z - 9*x*y^5*z + 4*y^6*z + 6*x^5*z^2 - 3*x^3*y^2*z^2 - x^2*y^3*z^2 - 3*x*y^4*z^2 - 9*x^4*z^3 - 3*x^3*y*z^3 + 9*x^2*y^2*z^3 - x*y^3*z^3 - 3*y^4*z^3 + 4*x^2*y*z^4 + 3*x*y^2*z^4 - 4*y^3*z^4 + 2*x^2*z^5 - 2*x*y*z^5 - 6*x*z^6 - 6*z^7 + 8177/33000*x^5*y + 2*x^4*y^2 - 9*x*y^5 + 3*x^4*y*z + 2*x^2*y^3*z - 4*y^5*z - 2*x^4*z^2 - 6*x^3*y*z^2 - 6*x^2*y^2*z^2 + 2*x*y^3*z^2 - 4*y^4*z^2 + x^3*z^3 + 6*x^2*y*z^3 + 6*x*y^2*z^3 - 3*y^3*z^3 + 9*x^2*z^4 - 2*x*y*z^4 - 6*y^2*z^4 + 3*x*z^5 - 3*y*z^5 - 6*z^6 - 3907/4400*x^5 - 12899/2200*x^4*y - x^3*y^2 + 2*x*y^4 + 3*x^4*z + 6*x^3*y*z - 2*x^2*y^2*z - 3*x*y^3*z - 6*y^4*z - 2*x^3*z^2 - 9*x*y^2*z^2 - 6*y^3*z^2 + x^2*z^3 - 6*y^2*z^3 + 2*x*z^4 - 2*y*z^4 + 2*z^5 - 21/10*x^3*y - 2*x^2*y^2 - 9*x*y^3 + 6*x^2*y*z - 9*x*y^2*z - 2*y^3*z - 2*x^2*z^2 + 9*y^2*z^2 + 3*z^4 + 18*x*y^2 - 6*y^3 + 14*x^2*z - 2*y^2*z - 6*x*z^2 - 3*y*z^2 - z^3, 6*x^7 + 6*x^6*y - 3*x^5*y^2 + 2*x^4*y^3 + 6*x^2*y^5 + 4*x*y^6 - y^7 + 3*x^6*z + 6*x^5*y*z + x^4*y^2*z - 9*x^3*y^3*z + 2*x^2*y^4*z + 6*y^6*z + 6*x^5*z^2 + 4*x^4*y*z^2 - 3*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - 9*x*y^4*z^2 - y^5*z^2 - 6*x^2*y^2*z^3 + 2*x*y^3*z^3 - 2*y^4*z^3 + 4*x^3*z^4 - 6*x^2*y*z^4 + 2*x*y^2*z^4 + 6*x^2*z^5 + 2*x*y*z^5 + 2*y*z^6 + 3*z^7 - 75563/22000*x^5*y + 9*x^4*y^2 - 2*x^3*y^3 + 9*y^6 + 2*x^5*z + 6*x^3*y^2*z - x^2*y^3*z + 2*x*y^4*z - 3*y^5*z + 6*x^4*z^2 - 6*x^3*y*z^2 + 2*x^2*y^2*z^2 - y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 - 2*x*y^2*z^3 - y^3*z^3 + 2*x^2*z^4 - 9*y^2*z^4 - 6*y*z^5 + 2*z^6 + 757/4400*x^5 - 19141/2200*x^4*y - 3*x^3*y^2 - 9*x*y^4 + 3*x*y^3*z + 2*x^3*z^2 + 3*x^2*y*z^2 + 3*x*y^2*z^2 - 6*y^3*z^2 - 6*x^2*z^3 - 6*x*y*z^3 - y^2*z^3 - 2*x*z^4 - 108/55*x^4 + 909/110*x^3*y + 4*x^2*y^2 - 4*x*y^3 + 4*y^4 + 3*x^3*z + 2*x*y^2*z - 6*y^3*z + 6*x*y*z^2 + 2*y^2*z^2 + 4*x*z^3 + 4*y*z^3 - 2*z^4 + 2*y^3 + 648/11*x^2*z + 1638/11*x*y*z + 3*x*z^2 - 9*y*z^2 - 6*z^3, 6*x^7 - 3*x^6*y + 2*x^5*y^2 + 6*x^3*y^4 + x^2*y^5 - 9*x*y^6 + 3*x^5*y*z + 3*x^4*y^2*z + 3*x^2*y^4*z - x*y^5*z - 4*y^6*z - 9*x^5*z^2 + 3*x^4*y*z^2 + 3*x^2*y^3*z^2 + 6*x*y^4*z^2 + 3*y^5*z^2 + 2*x^4*z^3 + 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 2*x*y^3*z^3 + 3*y^4*z^3 - 2*x^3*z^4 - x*y^2*z^4 - 4*y^3*z^4 - 3*y^2*z^5 + 6*x*z^6 + 2*y*z^6 - z^7 + 16197/5500*x^5*y + x^3*y^3 + x^2*y^4 - 6*x*y^5 + y^6 + 6*x^5*z + 3*x^3*y^2*z + 6*x^2*y^3*z - 4*x*y^4*z - 2*x^4*z^2 - 2*x^3*y*z^2 + 6*x^2*y^2*z^2 + 2*x*y^3*z^2 + 6*y^4*z^2 - 6*x^2*y*z^3 - 6*x*y^2*z^3 - 2*y^3*z^3 - 4*x^2*z^4 - 3*y^2*z^4 - 4*z^6 + 5251/2200*x^5 - 25413/4400*x^4*y + 3*x^3*y^2 + 2*x^2*y^3 - 4*x*y^4 + 6*x^4*z + 6*x^2*y^2*z + 6*x*y^3*z + 2*y^4*z - 4*x^3*z^2 - 6*x^2*y*z^2 - 6*x*y^2*z^2 + 3*y^3*z^2 - 4*x^2*z^3 + 6*x*y*z^3 - 4*y^2*z^3 - 2*x*z^4 - 2*y*z^4 + 18/11*x^4 - 423/55*x^3*y - 4*x^2*y^2 - 9*x*y^3 + 9*y^4 + 3*x^3*z + 4*x^2*y*z - 6*x*y^2*z + 6*y^3*z - 2*x^2*z^2 + 2*x*y*z^2 + 6*y^2*z^2 - y*z^3 + 4*y^3 + 360/11*x^2*z + 492/11*x*y*z + 3*y^2*z + 6*y*z^2 - 3*z^3]
   tangent, v != 0: D_3 = [X^3, X^2*Y, -4*X^3 + 12*X^2*Y - 24*X*Y^2 + 20*Y^3, 3*X^3 + 2*X^2*Y - 2*Y^3 - 3*X^2*Z - 3*X*Y*Z + Y^2*Z - 2*X*Z^2 + 3*Y*Z^2 - 3*Z^3, -3*X^3 - 2*X^2*Y + 2*X*Y^2 + Y^3 - 3*X^2*Z - 2*X*Y*Z - Y^2*Z + X*Z^2 - 2*Y*Z^2 + 2*Z^3], Phi5 = X^5 - X^4*Y - 2*X^3*Y^2 + 2*X^2*Y^3 - 2*X*Y^4 + Y^5 + X^4*Z: closed True, H = [1, 3, 6, 5, 2, 2, 1]; complete intersection of local length 31 (stable at N = 9)
      random.seed(103), attempt 0 used; generators: [3*x^7 + x^6*y + 2*x^5*y^2 - 9*x^4*y^3 + 6*x^3*y^4 + 3*x^2*y^5 - 6*x*y^6 - 3*x^6*z + 2*x^4*y^2*z + 6*x^3*y^3*z - 6*x^2*y^4*z + 9*x*y^5*z - 2*y^6*z - 2*x^5*z^2 - 6*x^4*y*z^2 - x^3*y^2*z^2 + 4*x^2*y^3*z^2 + x*y^4*z^2 + 6*y^5*z^2 - 4*x^4*z^3 - 4*x^2*y^2*z^3 - 3*x*y^3*z^3 - 3*y^4*z^3 + 3*x^2*y*z^4 - 3*x*y^2*z^4 - 2*x^2*z^5 + 2*x*y*z^5 - 6*y^2*z^5 - 9*x*z^6 + 3*y*z^6 - 2*x^6 - 15097/11250*x^5*y + 6*x^3*y^3 + 4*x*y^5 + 3*y^6 + 2*x^4*y*z - 2*x^2*y^3*z - 6*y^5*z - 2*x^2*y^2*z^2 - 9*y^4*z^2 + 2*x^3*z^3 - 6*y^3*z^3 + 3*x^2*z^4 - 6*y^2*z^4 + 6*x*z^5 - 6*z^6 + 2973/500*x^5 + 917/4500*x^4*y - 3*x^3*y^2 - x^2*y^3 - 6*x*y^4 - 2*y^5 + x^4*z - 9*x^3*y*z + 4*x^2*y^2*z + 4*x^3*z^2 + 2*x^2*y*z^2 - x*y^2*z^2 - 2*y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 + 6*y^2*z^3 - 3*x*z^4 - 4*y*z^4 + 2*z^5 + 11*x^3*y - x*y^3 + y^4 - 6*x^3*z - 4*x^2*y*z + 3*x*y^2*z + 2*y^3*z - 6*x*z^3 - 6*y*z^3 - 9*z^4 - 55/3*x^2*z + 138*x*y*z + 3*y^2*z + 2*x*z^2 + 2*z^3, 3*x^7 - 9*x^6*y + 6*x^5*y^2 + 4*x^4*y^3 + 2*x^3*y^4 + 6*x^2*y^5 - 6*x*y^6 - 9*y^7 - 9*x^6*z + 2*x^5*y*z + 3*x^4*y^2*z - x^2*y^4*z + 3*y^6*z - 3*x^5*z^2 - 9*x^4*y*z^2 - 6*x^3*y^2*z^2 - 3*x^2*y^3*z^2 + 6*x*y^4*z^2 + 6*x^3*y*z^3 - 3*x^2*y^2*z^3 - 4*y^4*z^3 - 6*x^3*z^4 + 4*x^2*y*z^4 + 9*x*y^2*z^4 - 3*y^3*z^4 + 6*y^2*z^5 - 4*x*z^6 + 4*y*z^6 + 2*z^7 + 9*x^6 - 10321/750*x^5*y - 6*x^2*y^4 + 6*x*y^5 + 6*y^6 - 4*x^5*z - 2*x^4*y*z - x^3*y^2*z + 6*x*y^4*z + 4*x^4*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 - 6*y^4*z^2 - 3*x^2*y*z^3 + 3*y^3*z^3 + 9*x^2*z^4 + x*y*z^4 - y^2*z^4 - 6*y*z^5 - 4*z^6 - 44401/2250*x^5 - 3*x^3*y^2 + 3*x*y^4 + 6*y^5 - 6*x^4*z + 4*x^3*y*z - 6*x*y^3*z - 3*x^2*y*z^2 - 2*x*y^2*z^2 - 2*x*y*z^3 - 2*y^2*z^3 + 2*x*z^4 + 2*y*z^4 - 6*z^5 + 1/5*x^4 + 3*x^2*y^2 - y^4 - 6*x^3*z - 4*x^2*y*z - 3*x*y^2*z + 6*y^3*z + 4*x^2*z^2 - 2*x*y*z^2 + 3*x*z^3 - 6*y*z^3 + 2*z^4 + 15*x*y^2 + 4*y^3 - 288*x*y*z - 3*x*z^2 - 2*y*z^2 + 6*z^3, 2*x^6*y - 9*x^5*y^2 + 2*x^4*y^3 - 6*x^3*y^4 + 4*x^2*y^5 + 6*x*y^6 - 2*y^7 + 2*x^6*z + x^5*y*z + 3*x^4*y^2*z + 9*x^3*y^3*z - 9*x^2*y^4*z - 9*x*y^5*z - 6*y^6*z + 2*x^5*z^2 - 4*x^4*y*z^2 + 3*x^3*y^2*z^2 - 3*x^2*y^3*z^2 - 2*x*y^4*z^2 - 3*x^4*z^3 - 6*x^2*y^2*z^3 + 6*x*y^3*z^3 + 2*x^3*z^4 + 3*x^2*y*z^4 - 2*y^3*z^4 + 2*x^2*z^5 - 9*y^2*z^5 + 2*x*z^6 + 6*y*z^6 - 2*z^7 + 6787/1250*x^5*y - 2*x*y^5 - 3*y^6 - 6*x^3*y^2*z - 3*x^2*y^3*z + 3*x*y^4*z + y^5*z + 4*x^4*z^2 + 4*x^3*y*z^2 + 9*x^2*y^2*z^2 + 2*y^4*z^2 + 6*x*y^2*z^3 + 2*x^2*z^4 - y^2*z^4 - 2*x*z^5 - 9*y*z^5 + 4*z^6 - 11359/500*x^5 + 326/375*x^4*y - 3*x^3*y^2 - 2*x^2*y^3 - 2*x*y^4 - 2*x^3*y*z - 6*x^2*y^2*z + y^4*z - 6*x^3*z^2 + 9*x*y^2*z^2 - 2*y^3*z^2 - 6*x^2*z^3 + 6*x*y*z^3 + 3*x*z^4 - 9*y*z^4 + 2*z^5 + 4*x*y^3 - 6*y^4 - 2*x^3*z + x^2*y*z - y^3*z + x*y*z^2 - 6*x*z^3 + 3*z^4 + 236/3*x^2*z - 98*x*y*z - y^2*z + x*z^2 + 3*y*z^2 - 3*z^3]
  ok   each of the four families has a member in a complete intersection of local length < 40
total time 881.1 s
ALL CHECKS PASSED
