=== R3: B = V(m_X^2) + [Y]; D_3 = <X^3,X^2Y,X^2Z,Y^3>, D_5 = <X^5,Y^5>, D_4 = <X^4,Y^4,X^3L>, L in {Y, Z}
--- R3 L=Y
  ok   R3 L=Y: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R3 L=Y: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 57 eliminated with constant pivots; residual equations:
       (1/1470) * (50*P_510^2*P_501 + 630*P_510*P_060*G_301 - 1323*P_060*G_130*G_031 - 8820*P_060*G_301*H_120 - 350*P_510^2*H_111 - 210*P_501*P_320 + 4410*P_060*G_111 + 1470*P_320*H_111)
       (2/21) * (-9*P_501*P_060*G_301 - 63*P_060*G_301*H_111 - 10*P_510^2*H_102 + 126*P_060*G_102 + 42*P_320*H_102)
       (1/210) * (-189*P_060*G_031^2 - 1260*P_060*G_301*H_021 - 100*P_510^2*H_012 + 1260*P_060*G_012 + 420*P_320*H_012)
       (2/7) * (-21*P_060*G_301*H_012 - 5*P_510^2*H_003 + 63*P_060*G_003 + 21*P_320*H_003)
  ok   R3 L=Y: on {P_060 != 0} the residual equations are triangular in ['G_111', 'G_102', 'G_012', 'G_003'] with diagonal (const)*P_060: a graph (irreducible)
  ok   R3 L=Y: on {P_060 = 0}: each equation is (-5*P_510^2 + 21*P_320) times a linear form; components {c = 0} and {linear forms ['-1/147*P_501 + 1/21*H_111', '4/21*H_102', '2/21*H_012', '2/7*H_003'] = 0}
  ok   R3 L=Y, component W1 (P_060 != 0): a point of the component (residual equations vanish)
      timing: member+triples 0.6 s, stabilization 0.3 s
  ok   R3 L=Y, component W1 (P_060 != 0) anchor (A): fixed {'P_060': 1}, solved ['G_111', 'G_102', 'G_012', 'G_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 40 (ds), stabilization (40, 13)
      anchor generators: {'P': 'X^7 + Y^6 + 2*X*Y^3 - 4*Y^3*Z + 2*X*Y^2 - X*Y*Z + Y^2*Z + 2*X*Z^2 + Z^3', 'G': 'Y^5 + X*Y^2 - 2*Y^2*Z', 'H': 'X^3*Y - X*Y^2 + X*Y*Z + Y^2*Z - X*Z^2 + Y*Z^2'}
      anchor triple: ['x^8 + 2*x^7*y + 3*x^6*y^2 - 3*x^5*y^3 - x^4*y^4 + 2*x^3*y^5 - 3*x^2*y^6 - x*y^7 + 3*y^8 + 2*x^7*z + 2*x^5*y^2*z - 2*x^4*y^3*z - 3*x^3*y^4*z - 3*x*y^6*z + y^7*z + 2*x^6*z^2 - 2*x^5*y*z^2 + 2*x^4*y^2*z^2 + 3*x^3*y^3*z^2 - x^2*y^4*z^2 + 3*x*y^5*z^2 + y^6*z^2 + 2*x^5*z^3 - 3*x^4*y*z^3 + 2*x^3*y^2*z^3 + 3*x^2*y^3*z^3 + y^5*z^3 + 3*x^4*z^4 - 2*x^3*y*z^4 - 3*x^2*y^2*z^4 + x*y^3*z^4 + 3*x^3*z^5 + x*y^2*z^5 + y^3*z^5 + 3*x^2*z^6 - 2*x*y*z^6 + 2*y^2*z^6 + 2*x*z^7 - 2*y*z^7 - 3*z^8 + 1417/5040*x^7 - 2*x^6*y + x^5*y^2 - 2*x^4*y^3 + 3*x^3*y^4 + 3*x^2*y^5 + 2*x*y^6 - 2*y^7 + 2*x^4*y^2*z + x^3*y^3*z - x^2*y^4*z + x*y^5*z - y^6*z - 2*x^5*z^2 + x^3*y^2*z^2 + 2*x^2*y^3*z^2 - x*y^4*z^2 + y^5*z^2 + x^4*z^3 + 3*x^3*y*z^3 + 2*y^4*z^3 - x^3*z^4 - x^2*y*z^4 - 3*x*y^2*z^4 + 3*y^3*z^4 - 2*x^2*z^5 - y^2*z^5 + 2*y*z^6 + 3*z^7 + 3*x^5*y + x^4*y^2 + x^3*y^3 - x^2*y^4 + x*y^5 - 2*y^6 - x^5*z + x^4*y*z - 2*x^3*y^2*z - 2*x^2*y^3*z - x*y^4*z + 3*y^5*z - 3*x^4*z^2 + x^3*y*z^2 - x^2*y^2*z^2 + 2*x*y^3*z^2 + 2*y^4*z^2 - x^3*z^3 - 2*x^2*y*z^3 - 3*x*y^2*z^3 - 2*x^2*z^4 - 3*x*y*z^4 - 3*y^2*z^4 - 2*y*z^5 + 2*z^6 - 2*x^4*y - 3*x^3*y^2 - 3*x^2*y^3 - 3*x*y^4 + 1/15*y^5 + x^4*z - 2*x^3*y*z - 2*x^2*y^2*z + 3*x*y^3*z - 3*y^4*z + 3*x^3*z^2 + x^2*y*z^2 + y^3*z^2 - 3*x*y*z^3 - x*z^4 - 1/6*x^3*y - 2*x^2*y^2 - 2*x*y^3 + x^3*z - 3*x^2*y*z + x*y^2*z - y^3*z + x^2*z^2 - x*y*z^2 + x*z^3 + 3*y*z^3 - 2*z^4 + 2*x*y^2 - 3*x*y*z + 3*y^2*z + y*z^2 + z^3', '-3*x^8 - 2*x^7*y - x^6*y^2 - 3*x^5*y^3 + x^4*y^4 - 3*x^3*y^5 + 2*x^2*y^6 - 3*x*y^7 + x^7*z + 2*x^6*y*z - x^5*y^2*z - 3*x^4*y^3*z - 3*x^2*y^5*z + 2*x*y^6*z + y^7*z - 3*x^6*z^2 + 2*x^4*y^2*z^2 - 3*x^3*y^3*z^2 - 2*x^2*y^4*z^2 - x*y^5*z^2 - y^6*z^2 + x^5*z^3 + 2*x^4*y*z^3 + 3*x^3*y^2*z^3 + 3*x^2*y^3*z^3 + 2*y^5*z^3 + 3*x^4*z^4 + 3*x^3*y*z^4 - 2*x^2*y^2*z^4 - 2*x*y^3*z^4 + y^4*z^4 + 3*x^3*z^5 + 2*x^2*y*z^5 + y^3*z^5 - 2*x^2*z^6 + 3*x*y*z^6 + y^2*z^6 - 2*x*z^7 + y*z^7 + z^8 - 2117/5040*x^7 + 3*x^6*y - 2*x^5*y^2 - 3*x^3*y^4 - 2*x^2*y^5 + 2*y^7 + x^6*z - 3*x^5*y*z - 2*x^4*y^2*z - x^3*y^3*z - x*y^5*z - 2*y^6*z + 3*x^5*z^2 + 3*x^4*y*z^2 + 2*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - x*y^4*z^2 - y^5*z^2 + 2*x^2*y^2*z^3 - 3*y^4*z^3 + x^3*z^4 + 3*x*y^2*z^4 - x^2*z^5 + x*y*z^5 - 3*y^2*z^5 + 2*x*z^6 - 2*y*z^6 - 3*z^7 + 3*x^5*y - 2*x^4*y^2 - 2*x^3*y^3 + x^2*y^4 - x*y^5 + 3*y^6 + 3*x^5*z - 3*x^4*y*z + 3*x^3*y^2*z - x^2*y^3*z + 2*y^5*z + 3*x^4*z^2 + 3*x^3*y*z^2 - 2*x^2*y^2*z^2 - 2*x*y^3*z^2 - 3*y^4*z^2 + 2*x^3*z^3 + 3*x^2*y*z^3 - 2*x*y^2*z^3 - 3*y^3*z^3 - x^2*z^4 + 3*x*y*z^4 + 2*y^2*z^4 + x*z^5 - y*z^5 + 2*x^4*y - 2*x^3*y^2 + 2*x^2*y^3 - 1/12*y^5 + 3*x^4*z + 3*x^3*y*z + 2*x^2*y^2*z + 3*x*y^3*z - 3*x^3*z^2 + x^2*y*z^2 - 3*x*y^2*z^2 + 2*y^3*z^2 - x^2*z^3 + 2*x*y*z^3 + 3*y^2*z^3 - 2*x*z^4 + 13/6*x^3*y - x^2*y^2 - 2*x*y^3 + x^3*z + 2*x^2*y*z + 3*x*y^2*z + 2*y^3*z - 2*x^2*z^2 - x*y*z^2 + 2*y^2*z^2 + 2*x*z^3 - y*z^3 - 3*z^4 + 3*x*y^2 - x*y*z - y^2*z - 2*y*z^2 + 3*z^3', '-x^8 - 2*x^7*y - 2*x^6*y^2 - 2*x^5*y^3 - 3*x^4*y^4 - 2*x^3*y^5 - 2*x^2*y^6 - 2*x*y^7 - 3*y^8 - x^7*z - 2*x^5*y^2*z - 2*x^3*y^4*z - 2*x*y^6*z + 3*x^5*y*z^2 - x^4*y^2*z^2 + x^3*y^3*z^2 - 3*x^2*y^4*z^2 + 2*x*y^5*z^2 + x^5*z^3 - x^4*y*z^3 - 3*x^3*y^2*z^3 - 3*x^2*y^3*z^3 - 2*x^4*z^4 + 2*x^3*y*z^4 - 3*x^2*y^2*z^4 - 3*x*y^3*z^4 - 3*y^4*z^4 - 2*x^3*z^5 - 3*x^2*y*z^5 - x*y^2*z^5 - 3*y^3*z^5 + x^2*z^6 + 2*x*y*z^6 - y^2*z^6 + x*z^7 + 2*y*z^7 + 5/336*x^7 + 2*x^4*y^3 - 3*x^2*y^5 - x*y^6 - 2*y^7 - 2*x^6*z + 2*x^4*y^2*z + 3*x^3*y^3*z + x^2*y^4*z + x*y^5*z + y^6*z + 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 + y^5*z^2 - 3*x^4*z^3 - 3*x^3*y*z^3 + x*y^3*z^3 + 3*y^4*z^3 + 3*x^3*z^4 - x^2*y*z^4 + y^3*z^4 - x^2*z^5 - 2*x*y*z^5 + 3*y^2*z^5 - 2*x*z^6 - 3*y*z^6 - z^7 + 3*x^5*y - x^3*y^3 + 2*x^2*y^4 + 3*x*y^5 + x^5*z + 3*x^4*y*z - 2*x^3*y^2*z + 3*x^2*y^3*z - x*y^4*z + 2*x^2*y^2*z^2 - 3*x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 + 3*x^2*y*z^3 + 2*x*y^2*z^3 - 2*y^3*z^3 - 2*x^2*z^4 + x*y*z^4 + x*z^5 - 2*y*z^5 - 3*z^6 + 2*x^4*y + 2*x^3*y^2 + 2*x^2*y^3 + x*y^4 - 1/15*y^5 + x^4*z - 2*x^3*y*z - x^2*y^2*z + 3*x*y^3*z + 2*y^4*z + 3*x^3*z^2 - x^2*y*z^2 + 3*x*y^2*z^2 - 3*y^3*z^2 + x^2*z^3 + x*y*z^3 + y^2*z^3 + 3*x*z^4 + y*z^4 - 2*z^5 - 7/6*x^3*y - 3*x^2*y^2 - 2*x*y^3 + 3*x^3*z + 2*x^2*y*z + 3*x*y^2*z + 2*y^3*z - 3*x^2*z^2 + x*y*z^2 - 3*y^2*z^2 - 3*x*z^3 + y*z^3 - 2*z^4 - 2*x*y^2 - x*y*z - 3*y^2*z - 2*x*z^2 + 3*y*z^2 + 3*z^3']
  ok   R3 L=Y, component W2 (P_060 = 0 = c): a point of the component (residual equations vanish)
      timing: member+triples 0.6 s, stabilization 0.3 s
  ok   R3 L=Y, component W2 (P_060 = 0 = c) anchor (A): fixed {'P_060': 0}, solved ['P_320']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 13)
      anchor generators: {'P': 'X^7 - 2*X*Y^2 - 2*X*Y*Z - 2*X*Z^2 - Y*Z^2', 'G': 'Y^5 - X*Y^2 + Y^2*Z - 2*X*Z^2 + Z^3', 'H': 'X^3*Y - X*Y^2 - X*Y*Z - 2*Y^2*Z + 2*X*Z^2 + 2*Y*Z^2 - Z^3'}
      anchor triple: ['2*x^8 - 2*x^7*y - x^6*y^2 + 2*x^5*y^3 + 3*x^4*y^4 + 3*x^3*y^5 + 2*x^2*y^6 + x*y^7 + 2*y^8 + 2*x^7*z - 3*x^6*y*z + 2*x^5*y^2*z - 2*x^4*y^3*z - 3*x^3*y^4*z + 3*x*y^6*z + 2*x^6*z^2 + x^5*y*z^2 - x^4*y^2*z^2 + 3*x^3*y^3*z^2 + 2*x^2*y^4*z^2 - 2*y^6*z^2 - 2*x^5*z^3 - 2*x^4*y*z^3 - 3*x^3*y^2*z^3 + 3*x^2*y^3*z^3 - 2*x*y^4*z^3 - y^5*z^3 - 2*x^4*z^4 + 2*x^3*y*z^4 - x^2*y^2*z^4 - x*y^3*z^4 - y^4*z^4 - 2*x^3*z^5 + 2*x^2*y*z^5 + 2*x*y^2*z^5 + 2*y^3*z^5 + 2*x^2*z^6 - x*y*z^6 + 2*y^2*z^6 - x*z^7 - y*z^7 + 3*z^8 - 11/2520*x^7 - x^6*y - 2*x^5*y^2 - 2*x^4*y^3 + 3*x^3*y^4 + 3*x^2*y^5 + x*y^6 - y^7 - 3*x^6*z + 3*x^5*y*z - 3*x^4*y^2*z + x^3*y^3*z - x^2*y^4*z - 2*x*y^5*z - x^4*y*z^2 - x^3*y^2*z^2 + 2*x^2*y^3*z^2 - 3*x*y^4*z^2 + y^5*z^2 - 2*x^4*z^3 - 2*x^3*y*z^3 - x^2*y^2*z^3 - 3*x*y^3*z^3 - 3*y^4*z^3 + x^2*y*z^4 - 2*x*y^2*z^4 - 2*y^3*z^4 - 3*x^2*z^5 + x*y*z^5 + 3*y^2*z^5 + x*z^6 + 3*y*z^6 + 3*z^7 + 2*x^5*y - 2*x^4*y^2 - 3*x^3*y^3 + x^2*y^4 + 2*x*y^5 + 2*y^6 + 3*x^5*z - 3*x^3*y^2*z - 2*x^2*y^3*z - 3*x*y^4*z + 2*y^5*z + 2*x^3*y*z^2 - 3*x^2*y^2*z^2 - x*y^3*z^2 + y^4*z^2 + x^3*z^3 - y^3*z^3 + y^2*z^4 - 2*x*z^5 - 3*y*z^5 - 2*z^6 + x^4*y - x^3*y^2 + 2*x*y^4 - 1/60*y^5 - x^4*z - 3*x^3*y*z - 2*x^2*y^2*z + 2*x*y^3*z - 3*y^4*z + x^3*z^2 - 2*x^2*y*z^2 + 3*x*y^2*z^2 - 3*y^3*z^2 - x*y*z^3 + 2*y^2*z^3 + x*z^4 + 2*z^5 + 1/3*x^3*y + 3*x^2*y^2 - x*y^3 - 2*x^3*z + 3*x^2*y*z - 2*x*y^2*z + 3*x^2*z^2 + y^2*z^2 + 3*y*z^3 + 2*z^4 - 3*x*y^2 - 2*x*y*z + y^2*z - 3*y*z^2 - z^3', '2*x^8 - 3*x^7*y - 3*x^6*y^2 - 3*x^5*y^3 + 3*x^3*y^5 + 2*x*y^7 + 2*y^8 + 2*x^7*z + x^6*y*z + x^5*y^2*z - 2*x^4*y^3*z + 2*x^3*y^4*z + 2*x^2*y^5*z - 2*x*y^6*z + 3*y^7*z - 3*x^6*z^2 + 3*x^5*y*z^2 + x^4*y^2*z^2 + x^3*y^3*z^2 - 2*x^2*y^4*z^2 + x*y^5*z^2 - 3*x^4*y*z^3 - x^3*y^2*z^3 - 2*x^2*y^3*z^3 + 2*x*y^4*z^3 + y^5*z^3 - 2*x^4*z^4 + x^3*y*z^4 + x^2*y^2*z^4 - x*y^3*z^4 + 3*y^4*z^4 - 3*x^3*z^5 - x^2*y*z^5 - 2*x*y^2*z^5 - 2*y^3*z^5 - 3*x^2*z^6 + 3*x*y*z^6 - 2*y^2*z^6 + x*z^7 + y*z^7 - z^8 + 1/630*x^7 - x^6*y - 2*x^5*y^2 - x^3*y^4 + 3*x^2*y^5 - 2*x*y^6 - 3*y^7 + 3*x^6*z + 3*x^5*y*z - 2*x^4*y^2*z + 2*x*y^5*z + 2*y^6*z + 2*x^5*z^2 - 2*x^4*y*z^2 + x^3*y^2*z^2 - 2*x^2*y^3*z^2 - 2*x*y^4*z^2 - 3*y^5*z^2 - 3*x^4*z^3 - 3*x^2*y^2*z^3 + 2*x*y^3*z^3 + 3*y^4*z^3 + 3*x^3*z^4 - 2*x^2*y*z^4 + y^3*z^4 + 2*x*y*z^5 - 2*y^2*z^5 + 3*z^7 + x^5*y + 2*x^4*y^2 - 2*x^3*y^3 - x^2*y^4 + x*y^5 - 3*y^6 + 2*x^5*z + 3*x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z - 3*x*y^4*z + 2*y^5*z - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 - y^4*z^2 + 2*x^3*z^3 + 2*x^2*y*z^3 - x*y^2*z^3 + x^2*z^4 + 2*x*y*z^4 - y^2*z^4 + 2*x*z^5 + y*z^5 + 3*z^6 - x^4*y + 3*x^3*y^2 + x^2*y^3 + x*y^4 + 1/15*y^5 + x^4*z - 2*x^3*y*z - 3*x*y^3*z + 3*y^4*z - x^3*z^2 - 3*x^2*y*z^2 + 3*y^3*z^2 - 2*x^2*z^3 - x*y*z^3 - 3*y^2*z^3 - x*z^4 - 3*y*z^4 + z^5 - 1/6*x^3*y + 3*x*y^3 + 3*x^3*z - 3*x^2*y*z + 2*x*y^2*z - y^3*z + x^2*z^2 + 3*x*y*z^2 - y^2*z^2 + y*z^3 - 3*z^4 + 2*x*y^2 - 3*x*y*z + 3*y^2*z + x*z^2 + y*z^2 - z^3', '-x^8 - 2*x^7*y - x^6*y^2 + 3*x^4*y^4 + 3*x^3*y^5 + x^2*y^6 - 3*x*y^7 + 3*y^8 - 3*x^7*z + 3*x^6*y*z - x^5*y^2*z - 3*x^4*y^3*z - 3*x^3*y^4*z + 2*x^2*y^5*z - x*y^6*z + 2*y^7*z + 2*x^6*z^2 + 3*x^5*y*z^2 + x^4*y^2*z^2 + 3*x^3*y^3*z^2 + x*y^5*z^2 - x^5*z^3 + x^4*y*z^3 - x^3*y^2*z^3 - 2*x^2*y^3*z^3 - x*y^4*z^3 + y^5*z^3 + 3*x^4*z^4 - 2*x^3*y*z^4 + y^4*z^4 - 3*x^3*z^5 + x^2*y*z^5 + 3*x*y^2*z^5 - 3*y^3*z^5 + 3*x^2*z^6 - x*y*z^6 + 2*y^2*z^6 + y*z^7 + 1/504*x^7 - x^6*y + 3*x^5*y^2 + 3*x^4*y^3 + 2*x^2*y^5 - 2*x*y^6 + y^7 + 2*x^6*z - 2*x^5*y*z + x^3*y^3*z + x^2*y^4*z + 3*x*y^5*z + 2*y^6*z + 3*x^5*z^2 + 3*x^4*y*z^2 - x^3*y^2*z^2 + 2*x^2*y^3*z^2 + 3*x^4*z^3 - 3*x^3*y*z^3 + 3*x^2*y^2*z^3 - x*y^3*z^3 - x^3*z^4 + x^2*y*z^4 - x*y^2*z^4 + 2*y^3*z^4 + 3*x*y*z^5 + 2*y^2*z^5 + 3*x*z^6 - 2*y*z^6 + 3*z^7 - 2*x^4*y^2 + 2*x^3*y^3 + 2*x^2*y^4 - 3*y^6 - 2*x^5*z - x^4*y*z + 2*x^3*y^2*z + 2*x^2*y^3*z - y^5*z + 3*x^4*z^2 + x^3*y*z^2 + x^2*y^2*z^2 - 3*x*y^3*z^2 + y^4*z^2 + 2*x^3*z^3 + 3*x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 + 3*x^2*z^4 + 3*x*y*z^4 - 2*y^2*z^4 - 3*y*z^5 - x^4*y - 2*x^3*y^2 - x*y^4 + 1/30*y^5 + 3*x^4*z - x^3*y*z + 3*x^2*y^2*z - x*y^3*z + 2*y^4*z - 2*x^3*z^2 + 3*x^2*y*z^2 - x*y^2*z^2 + 3*y^3*z^2 + 2*x^2*z^3 - 3*x*y*z^3 - 3*y^2*z^3 + y*z^4 + z^5 + x^3*y + 3*x^2*y^2 + x*y^3 - x^3*z - 2*x*y^2*z + y^3*z - x^2*z^2 - 3*y^2*z^2 + 2*x*z^3 - 3*y*z^3 + z^4 + 3*x*y^2 + 2*x*y*z - 2*x*z^2 + y*z^2 - z^3']
  ok   R3 L=Y, component W3 (P_060 = 0, linear): a point of the component (residual equations vanish)
      timing: member+triples 0.3 s, stabilization 0.1 s
  ok   R3 L=Y, component W3 (P_060 = 0, linear) anchor (A): fixed {'P_060': 0}, solved ['P_501', 'H_102', 'H_012', 'H_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 37 (ds), stabilization (37, 11)
      anchor generators: {'P': 'X^7 - 7*X^5*Z + 2*X^3*Y^2 + 35/3*X^3*Z^2 - 2*X*Y^2*Z - 8/3*Y^3*Z - 35/9*X*Z^3 + 2*X*Y^2 - 2*X*Y*Z - Y^2*Z - X*Z^2 - 2*Y*Z^2', 'G': 'Y^5 + 2*X*Y^2 - X*Y*Z - 2*Y^2*Z - Y*Z^2 + 2*Z^3', 'H': 'X^3*Y - X*Y*Z - 2*Y^2*Z'}
      anchor triple: ['2*x^8 + 2*x^7*y - x^6*y^2 + 3*x^5*y^3 + x^4*y^4 - x^3*y^5 + 2*x*y^7 + 2*x^6*y*z - 3*x^5*y^2*z + 3*x^4*y^3*z - 2*x^2*y^5*z - 2*x*y^6*z + 2*x^6*z^2 - x^5*y*z^2 + 3*x^4*y^2*z^2 + 2*x^3*y^3*z^2 + x*y^5*z^2 + 2*y^6*z^2 + x^5*z^3 - 2*x^4*y*z^3 + x^3*y^2*z^3 - x^2*y^3*z^3 - 3*x*y^4*z^3 + 3*y^5*z^3 - 2*x^4*z^4 + 3*x^3*y*z^4 - 2*y^4*z^4 + 2*x^3*z^5 + 3*x*y*z^6 - 2*y^2*z^6 + 2*x*z^7 + 3*y*z^7 + 2*z^8 - 365/1512*x^7 - 3*x^5*y^2 + 3*x^4*y^3 - 3*x*y^6 + 3*x^6*z - 2*x^5*y*z - 2*x^4*y^2*z - x^2*y^4*z - 3*x*y^5*z + 2*y^6*z + 3*x^5*z^2 + 3*x^4*y*z^2 + 3*x^2*y^3*z^2 + 3*y^5*z^2 - 2*x^4*z^3 + 3*x^3*y*z^3 - x^2*y^2*z^3 + x*y^3*z^3 + y^4*z^3 - x^3*z^4 + x^2*y*z^4 + 3*x*y^2*z^4 + 2*x^2*z^5 + 2*x*y*z^5 + 2*y^2*z^5 + 3*x*z^6 + 2*y*z^6 - 2*z^7 + 433/756*x^6 - 2*x^5*y - x^4*y^2 + x^3*y^3 - 3*x^2*y^4 - 3*x*y^5 - 2*y^6 - x^5*z + x^4*y*z + x^3*y^2*z + x^2*y^3*z - 3*x*y^4*z - 3*y^5*z - 2*x^4*z^2 + 3*x^3*y*z^2 - 2*x^2*y^2*z^2 + 3*x^3*z^3 - x^2*y*z^3 + x*y^2*z^3 - y^3*z^3 - 3*x^2*z^4 - x*y*z^4 - 3*y^2*z^4 + 2*x*z^5 - y*z^5 + 3*z^6 - 443/1260*x^5 - x^4*y + x^3*y^2 - 2*x^2*y^3 - 1/6*y^5 + 3*x^4*z - 2*x^3*y*z - 2*x^2*y^2*z - x*y^3*z + 2*y^4*z + 2*x^3*z^2 - 3*x*y^2*z^2 + 3*y^3*z^2 - x^2*z^3 - 2*x*y*z^3 + 3*x*z^4 + y*z^4 + z^5 - 5/3*x^3*y - 2*x^2*y^2 - 3*x*y^3 - 2*x^3*z - x^2*y*z + 2*x*y^2*z - 3*y^3*z - 2*x^2*z^2 + x*y*z^2 - 3*y^2*z^2 - 2*x*z^3 + 3*y*z^3 - z^4 - 2*x*y^2 - 2*x*y*z - 2*y^2*z + x*z^2 + 3*y*z^2 + 2*z^3', '3*x^8 - 2*x^7*y + 3*x^6*y^2 - 3*x^5*y^3 - 2*x^4*y^4 + x^3*y^5 - 3*x^2*y^6 + x*y^7 - y^8 + x^7*z - 2*x^6*y*z - 3*x^5*y^2*z - 3*x^4*y^3*z + 2*x^3*y^4*z + x^2*y^5*z + x*y^6*z + y^7*z + 2*x^5*y*z^2 - x^4*y^2*z^2 - 2*x^3*y^3*z^2 + 2*x^2*y^4*z^2 - x*y^5*z^2 - y^6*z^2 + 2*x^5*z^3 + x^4*y*z^3 + 3*x^3*y^2*z^3 - x^2*y^3*z^3 + x*y^4*z^3 - 2*y^5*z^3 + 3*x^4*z^4 + 2*x^3*y*z^4 - 2*x^2*y^2*z^4 - y^4*z^4 - 3*x^3*z^5 + 3*x^2*y*z^5 - 3*y^3*z^5 + 2*x^2*z^6 + x*y*z^6 - 2*y^2*z^6 - z^8 - 13/756*x^7 + 3*x^5*y^2 - 3*x^4*y^3 + x^3*y^4 + 2*x^2*y^5 - 2*x*y^6 - y^7 - 3*x^6*z - 3*x^5*y*z + x^4*y^2*z + x^3*y^3*z + 2*x*y^5*z - y^6*z - 2*x^5*z^2 + x^4*y*z^2 - 3*x^3*y^2*z^2 - 2*x^2*y^3*z^2 - 3*x*y^4*z^2 + 2*y^5*z^2 + x^4*z^3 + 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*x*y^3*z^3 + x^3*z^4 + 2*x^2*y*z^4 + x*y^2*z^4 + 3*y^3*z^4 - x*y*z^5 + 2*y^2*z^5 - 3*x*z^6 + y*z^6 - 3*z^7 + 239/1260*x^6 + x^5*y - 2*x^4*y^2 + 3*x^3*y^3 - 2*x^2*y^4 + 2*x*y^5 + 3*y^6 - x^2*y^3*z + 2*x*y^4*z + 3*y^5*z + 3*x^4*z^2 + 2*x^3*y*z^2 + 3*x^2*y^2*z^2 - 3*x*y^3*z^2 + 3*y^4*z^2 + x^3*z^3 - 3*x^2*y*z^3 - 3*x*y^2*z^3 + 3*x*z^5 + y*z^5 - 2*z^6 - 19/36*x^5 + 2*x^4*y - 1/24*y^5 + x^4*z - 3*x^3*y*z - 2*x*y^3*z + 3*y^4*z + 3*x^2*y*z^2 - 3*x*y^2*z^2 - 2*x*y*z^3 + 2*y^2*z^3 - x*z^4 + 3*y*z^4 + 2*z^5 - 1/6*x^3*y + x^2*y^2 + 2*x*y^3 - 3*x^3*z + x^2*y*z - 2*y^3*z - x^2*z^2 - x*y*z^2 - y^2*z^2 - 2*x*z^3 + 2*y*z^3 + z^4 - x*y*z + x*z^2 - 2*y*z^2', '3*x^7*y - x^6*y^2 + 2*x^5*y^3 + 3*x^4*y^4 - 2*x^3*y^5 - 3*x^2*y^6 - 3*x*y^7 + 3*y^8 - x^6*y*z - 2*x^5*y^2*z - x^3*y^4*z + 2*x^2*y^5*z + 2*x*y^6*z - 3*y^7*z + x^6*z^2 + 3*x^5*y*z^2 + 3*x^4*y^2*z^2 - x^3*y^3*z^2 - 3*x^2*y^4*z^2 - y^6*z^2 + x^5*z^3 - x^4*y*z^3 + 3*x^2*y^3*z^3 - 3*x*y^4*z^3 + y^5*z^3 - 3*x^4*z^4 + x^3*y*z^4 - 3*x^2*y^2*z^4 - x*y^3*z^4 + 3*y^4*z^4 + x^3*z^5 - 3*x^2*y*z^5 - 3*x^2*z^6 + 3*x*y*z^6 - y^2*z^6 - 3*x*z^7 + 2*y*z^7 + 2*z^8 + 13/270*x^7 - 2*x^6*y - 3*x^5*y^2 - x^4*y^3 + x^2*y^5 + 2*x*y^6 - 2*x^6*z + x^5*y*z + x^4*y^2*z - 3*x^3*y^3*z + x^2*y^4*z - 2*x*y^5*z - y^6*z - 3*x^4*y*z^2 + 3*x^3*y^2*z^2 - x^2*y^3*z^2 + x*y^4*z^2 - 2*y^5*z^2 + 2*x^4*z^3 - x^3*y*z^3 - x^2*y^2*z^3 + 2*x*y^3*z^3 + 3*y^4*z^3 + 3*x^2*y*z^4 + y^3*z^4 + x^2*z^5 + 2*x*y*z^5 + 2*y^2*z^5 + 2*x*z^6 + 3*y*z^6 - z^7 - 395/756*x^6 + x^4*y^2 + 3*x^2*y^4 + 2*x*y^5 + 2*y^6 - 2*x^4*y*z + 2*x^2*y^3*z - 3*x*y^4*z - y^5*z + x^4*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 + 2*x*y*z^4 + x*z^5 + 3*y*z^5 + 16/105*x^5 - 3*x^4*y - 2*x^3*y^2 + 3*x^2*y^3 - 11/40*y^5 - 3*x^4*z - 2*x^3*y*z + 3*x^2*y^2*z + 3*x*y^3*z - 2*y^4*z - x^3*z^2 + x^2*y*z^2 - x*y^2*z^2 - y^3*z^2 + 2*x^2*z^3 - x*y*z^3 - 2*y^2*z^3 - x*z^4 - 3*y*z^4 + 2*z^5 + 5/6*x^3*y + x^2*y^2 - 3*x*y^3 + x^3*z - 3*x*y^2*z + 2*y^3*z + x^2*z^2 - 3*x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 - 3*y*z^3 - 3*z^4 + 3*x*y^2 + x*y*z + y^2*z - y*z^2 + 2*z^3']
--- R3 L=Z
  ok   R3 L=Z: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R3 L=Z: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 57 eliminated with constant pivots; residual equations:
       (-1/210) * (90*P_501*P_060*G_310 + 189*P_060*G_130*G_031 - 100*P_501^2*H_120 - 630*P_060*G_111 + 420*P_302*H_120)
       (-2/147) * (5*P_510*P_501^2 - 35*P_501^2*H_111 - 21*P_510*P_302 - 882*P_060*G_102 + 147*P_302*H_111)
       (-1/210) * (189*P_060*G_031^2 - 100*P_501^2*H_021 - 1260*P_060*G_012 + 420*P_302*H_021)
       (-2/21) * (-5*P_501^2*H_012 - 189*P_060*G_003 + 21*P_302*H_012)
  ok   R3 L=Z: on {P_060 != 0} the residual equations are triangular in ['G_111', 'G_102', 'G_012', 'G_003'] with diagonal (const)*P_060: a graph (irreducible)
  ok   R3 L=Z: on {P_060 = 0}: each equation is (-5*P_501^2 + 21*P_302) times a linear form; components {c = 0} and {linear forms ['-2/21*H_120', '2/147*P_510 - 2/21*H_111', '-2/21*H_021', '-2/21*H_012'] = 0}
  ok   R3 L=Z, component W1 (P_060 != 0): a point of the component (residual equations vanish)
      timing: member+triples 0.5 s, stabilization 0.3 s
  ok   R3 L=Z, component W1 (P_060 != 0) anchor (A): fixed {'P_060': 1}, solved ['G_111', 'G_102', 'G_012', 'G_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 40 (ds), stabilization (40, 13)
      anchor generators: {'P': 'X^7 + Y^6 - 2*X*Y^3 + 2*Y^3*Z + 2*X*Y^2 - X*Y*Z + 2*Y^2*Z + Y*Z^2', 'G': 'Y^5 - X*Y^2 + Y^2*Z', 'H': 'X^3*Z - 2*X*Y^2 + 2*Y^2*Z - 2*X*Z^2 - 2*Y*Z^2 - 2*Z^3'}
      anchor triple: ['-2*x^7*y - 2*x^6*y^2 - x^5*y^3 - 3*x^4*y^4 - 3*x^3*y^5 - x^2*y^6 - 3*y^8 - x^7*z + 2*x^5*y^2*z + 3*x^4*y^3*z + 2*x^3*y^4*z + x^2*y^5*z + 2*x*y^6*z - y^7*z + 3*x^6*z^2 + x^5*y*z^2 - 2*x^4*y^2*z^2 + 2*x^3*y^3*z^2 + 3*x*y^5*z^2 - y^6*z^2 - 2*x^5*z^3 - 2*x^4*y*z^3 + x^3*y^2*z^3 - 2*x^2*y^3*z^3 + 2*x*y^4*z^3 + 2*y^5*z^3 + x^4*z^4 - 2*x^3*y*z^4 + x^2*y^2*z^4 - 3*x*y^3*z^4 - 2*y^4*z^4 - x^2*y*z^5 - x*y^2*z^5 + y^3*z^5 + 3*x^2*z^6 - 3*x*y*z^6 + 2*y^2*z^6 - 17/40*x^7 - 2*x^6*y - 2*x^5*y^2 + 2*x^4*y^3 - 2*x^3*y^4 + 3*x*y^6 + 2*y^7 + 3*x^6*z - 2*x^5*y*z + 2*x^4*y^2*z - 2*x^3*y^3*z - x^2*y^4*z + x*y^5*z + 3*y^6*z + 2*x^5*z^2 - 3*x^4*y*z^2 - x^3*y^2*z^2 + 3*x^2*y^3*z^2 + 3*x*y^4*z^2 + 2*y^5*z^2 - 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*x*y^3*z^3 + 3*y^4*z^3 - x^2*y*z^4 - x*y^2*z^4 + 2*y^3*z^4 + 2*x^2*z^5 + 3*x*y*z^5 - 3*y^2*z^5 - 3*x*z^6 + 2*y*z^6 + z^7 + 2*x^5*y + 3*x^4*y^2 + x^3*y^3 + 2*x^2*y^4 + x*y^5 + 3*y^6 - 2*x^4*y*z + 3*x^3*y^2*z - x^2*y^3*z + x*y^4*z - y^5*z + 3*x^4*z^2 - 3*x^3*y*z^2 - 3*x^2*y^2*z^2 + 3*x*y^3*z^2 + 2*y^4*z^2 + x^3*z^3 + 2*x^2*y*z^3 + x*y^2*z^3 + 3*y^3*z^3 + 2*x^2*z^4 - y^2*z^4 + z^6 + x^4*y - 3*x^2*y^3 - x*y^4 + 1/60*y^5 - 3*x^4*z + x^3*y*z + x^2*y^2*z - 3*x*y^3*z - y^4*z + 2*x^3*z^2 + x^2*y*z^2 + x*y^2*z^2 - 2*y^3*z^2 + 2*x^2*z^3 - 2*x*y*z^3 + y^2*z^3 - 3*x*z^4 + 2*y*z^4 + 2*z^5 + 3*x^2*y^2 + x*y^3 + 16/3*x^3*z + y^3*z - 2*x^2*z^2 + x*y*z^2 - 2*y^2*z^2 - x*z^3 - 2*x*y^2 + 2*x*y*z - 3*y^2*z - x*z^2 + 2*y*z^2 + 2*z^3', '-x^8 + 3*x^7*y - 2*x^6*y^2 + 2*x^5*y^3 - x^4*y^4 + x^3*y^5 + 3*x^2*y^6 + 3*x*y^7 + 3*y^8 + 2*x^7*z - 3*x^6*y*z - x^5*y^2*z + 2*x^4*y^3*z - x^3*y^4*z + 2*x^2*y^5*z + 3*x*y^6*z + 3*y^7*z + x^5*y*z^2 - 3*x^4*y^2*z^2 - 2*x^3*y^3*z^2 - 3*x*y^5*z^2 + y^6*z^2 + 3*x^5*z^3 - 2*x^4*y*z^3 + 2*x^3*y^2*z^3 - 2*x^2*y^3*z^3 + 3*x*y^4*z^3 - 2*y^5*z^3 - x^4*z^4 - 3*x^3*y*z^4 - x^2*y^2*z^4 - x*y^3*z^4 - 3*y^4*z^4 - 2*x^3*z^5 - x^2*y*z^5 + 3*x*y^2*z^5 - 3*y^3*z^5 - x^2*z^6 + x*y*z^6 + x*z^7 - y*z^7 + 2*z^8 + 1/840*x^7 + 3*x^6*y + 3*x^3*y^4 - x^2*y^5 - 3*x*y^6 + y^7 + 2*x^6*z - x^5*y*z - 3*x^4*y^2*z - 2*x^3*y^3*z + 3*x^2*y^4*z + 2*x*y^5*z - 2*y^6*z + x^5*z^2 - x^4*y*z^2 - x^3*y^2*z^2 - x^2*y^3*z^2 + 2*x*y^4*z^2 - 2*y^5*z^2 - 2*x^4*z^3 + 2*x^3*y*z^3 + 3*x^2*y^2*z^3 - 3*x*y^3*z^3 - 3*y^4*z^3 + x^3*z^4 - 3*x^2*y*z^4 - 2*x*y^2*z^4 + 3*y^3*z^4 - 3*x^2*z^5 - 3*x*y*z^5 + 2*y^2*z^5 - 2*x*z^6 - 3*y*z^6 + 2*z^7 + x^5*y + x^4*y^2 + x^3*y^3 + 3*x^2*y^4 + 3*x*y^5 + x^5*z - x^3*y^2*z - x^2*y^3*z + x*y^4*z + 3*x^4*z^2 - 3*x^2*y^2*z^2 + 2*x*y^3*z^2 + y^4*z^2 + 2*x^3*z^3 + x^2*y*z^3 - x*y^2*z^3 - y^3*z^3 + 2*x^2*z^4 + 3*x*y*z^4 - 2*y^2*z^4 - 3*x*z^5 + 2*y*z^5 - 3*z^6 - 2*x^4*y - x^3*y^2 - x*y^4 + 1/20*y^5 + 3*x^4*z - 2*x^3*y*z - x^2*y^2*z - 3*x*y^3*z + 2*y^4*z + 2*x^3*z^2 + 2*x^2*y*z^2 + x*y^2*z^2 - 3*y^3*z^2 - x^2*z^3 + 3*x*y*z^3 - 2*y^2*z^3 - 3*x*z^4 - 3*y*z^4 - 2*z^5 - x^3*y - 3*x^2*y^2 + x*y^3 + 14/3*x^3*z + 3*x^2*y*z + x*y^2*z + y^3*z - x^2*z^2 - 2*x*y*z^2 - 2*x*z^3 - 3*y*z^3 + 3*z^4 - 2*x*y*z - 3*y^2*z + 2*x*z^2 + 2*y*z^2', '3*x^8 + 2*x^7*y + x^6*y^2 + 3*x^5*y^3 + 3*x^4*y^4 - x*y^7 - 3*y^8 - 2*x^7*z - x^6*y*z + 3*x^5*y^2*z - 2*x^4*y^3*z + x^3*y^4*z + 3*x^2*y^5*z - 3*x*y^6*z + 2*y^7*z - x^6*z^2 - 3*x^4*y^2*z^2 - x^3*y^3*z^2 + 3*x^2*y^4*z^2 + x*y^5*z^2 - 3*y^6*z^2 + 3*x^5*z^3 - 3*x^4*y*z^3 + 3*x^3*y^2*z^3 + 3*x^2*y^3*z^3 - 3*x*y^4*z^3 - 3*y^5*z^3 - 3*x^4*z^4 + x^3*y*z^4 - 2*x^2*y^2*z^4 + x*y^3*z^4 + 3*y^4*z^4 + 2*x^3*z^5 + x^2*y*z^5 + 2*y^3*z^5 + 3*x^2*z^6 - x*y*z^6 - y^2*z^6 - 2*x*z^7 - 3*z^8 + 233/840*x^7 + 3*x^6*y + 3*x^5*y^2 + 2*x^4*y^3 - 2*x^3*y^4 - 3*x*y^6 + 3*x^6*z - 2*x^5*y*z + 2*x^4*y^2*z - x^2*y^4*z - x*y^5*z - 3*y^6*z + 2*x^5*z^2 + x^4*y*z^2 - 2*x*y^4*z^2 + x^4*z^3 + 2*x^3*y*z^3 + x^2*y^2*z^3 - 3*x*y^3*z^3 + 2*y^4*z^3 - 2*x^3*z^4 + x^2*y*z^4 - x*y^2*z^4 - 2*y^3*z^4 + 3*x^2*z^5 - 3*x*y*z^5 - 3*y^2*z^5 - 3*x*z^6 - 2*y*z^6 - 2*z^7 + x^5*y + 2*x^3*y^3 + x^2*y^4 + x*y^5 - 2*y^6 + x^5*z + x^3*y^2*z + x^2*y^3*z - x*y^4*z + 3*y^5*z + 2*x^4*z^2 - x^3*y*z^2 + x*y^3*z^2 + 2*y^4*z^2 + 3*x^3*z^3 - 3*x^2*y*z^3 + x*y^2*z^3 - y^3*z^3 - 3*x^2*z^4 - 3*x*y*z^4 - 3*y^2*z^4 + 2*x*z^5 + y*z^5 - 3*z^6 + 2*x^4*y - x^3*y^2 - 2*x^2*y^3 + x*y^4 - 1/20*y^5 - 2*x^4*z - 3*x^3*y*z - 2*x^2*y^2*z - 2*x*y^3*z + y^4*z + 2*x^3*z^2 - 2*x^2*y*z^2 + x*y^2*z^2 + 3*y^3*z^2 + 3*x^2*z^3 + x*y*z^3 + y^2*z^3 + x*z^4 - y*z^4 + 2*x^3*y - 2*x^2*y^2 - x*y^3 - 4/3*x^3*z + 3*x*y^2*z + 3*y^3*z + 2*x^2*z^2 - x*y*z^2 + y^2*z^2 + 3*x*z^3 + 2*y*z^3 - 3*z^4 - 2*x*y^2 - 2*x*y*z + y^2*z - 3*x*z^2 - 2*y*z^2 + 2*z^3']
  ok   R3 L=Z, component W2 (P_060 = 0 = c): a point of the component (residual equations vanish)
      timing: member+triples 0.6 s, stabilization 0.3 s
  ok   R3 L=Z, component W2 (P_060 = 0 = c) anchor (A): fixed {'P_060': 0}, solved ['P_302']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 13)
      anchor generators: {'P': 'X^7 + 2*X*Y^2 + X*Y*Z - 2*X*Z^2 - 2*Z^3', 'G': 'Y^5 - 2*X*Y^2 + 2*X*Y*Z - 2*X*Z^2 - 2*Y*Z^2 - Z^3', 'H': 'X^3*Z + X*Y^2 + 2*X*Y*Z + 2*Y^2*Z + Y*Z^2 - Z^3'}
      anchor triple: ['-3*x^8 - x^7*y - 3*x^6*y^2 + 2*x^5*y^3 + x^4*y^4 - x^3*y^5 - 3*x^2*y^6 - 2*x*y^7 + 3*y^8 + 3*x^7*z + 2*x^4*y^3*z - x^3*y^4*z - 3*x^2*y^5*z - x^6*z^2 - x^5*y*z^2 - 2*x^4*y^2*z^2 + 3*x^3*y^3*z^2 + 2*x^2*y^4*z^2 + 3*x*y^5*z^2 - 2*y^6*z^2 - 3*x^5*z^3 - 2*x^4*y*z^3 + x^3*y^2*z^3 + x^2*y^3*z^3 - 3*x*y^4*z^3 - 2*y^5*z^3 + 3*x^4*z^4 + x^3*y*z^4 - 3*x^2*y^2*z^4 + 3*x*y^3*z^4 - 2*y^4*z^4 - x^3*z^5 + 2*x^2*y*z^5 - 3*x*y^2*z^5 + 2*y^3*z^5 + x^2*z^6 - 3*x*y*z^6 - 3*y^2*z^6 - 3*x*z^7 - 2*y*z^7 - z^8 - 37/5040*x^7 - 2*x^6*y - 2*x^5*y^2 + 3*x^4*y^3 + 2*x^3*y^4 - x^2*y^5 + 2*x*y^6 + y^7 - 3*x^6*z - 2*x^4*y^2*z + x^2*y^4*z + x*y^5*z + 3*y^6*z + 2*x^5*z^2 - 2*x^3*y^2*z^2 - 3*x^2*y^3*z^2 - 3*x*y^4*z^2 + y^5*z^2 - 3*x^4*z^3 + 2*x^3*y*z^3 + x^2*y^2*z^3 + 2*y^4*z^3 - x^3*z^4 + x^2*y*z^4 - x*y^2*z^4 - y^3*z^4 + 3*x^2*z^5 + 2*x*y*z^5 - 2*y^2*z^5 - y*z^6 + 2*x^5*y + 3*x^4*y^2 + x^3*y^3 + 3*x^2*y^4 - x*y^5 + 3*y^6 + x^5*z + 3*x^4*y*z + x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z + 2*y^5*z + 3*x^3*y*z^2 + 3*x^2*y^2*z^2 - 2*x*y^3*z^2 - y^4*z^2 - x^3*z^3 + 3*x*y^2*z^3 - y^3*z^3 - 2*x^2*z^4 + 2*x*y*z^4 + 3*y^2*z^4 - x*z^5 + 2*y*z^5 - 2*z^6 + 2*x^4*y - 2*x^3*y^2 + 2*x^2*y^3 - x*y^4 - 1/15*y^5 - 2*x^4*z - 3*x^3*y*z + 2*x^2*y^2*z - x*y^3*z + y^4*z - 2*x^2*y*z^2 + x*y^2*z^2 - 2*y^3*z^2 + x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 - y*z^4 - 3*z^5 - 7/3*x^3*z - 3*y^3*z - 3*x^2*z^2 - 3*y^2*z^2 + 2*x*z^3 + 2*y*z^3 + 3*z^4 + 2*x*y^2 + x*y*z - 2*y^2*z + 2*x*z^2 - y*z^2 - 3*z^3', '-2*x^8 + x^7*y + 2*x^6*y^2 + 3*x^4*y^4 + 2*x^2*y^6 - 2*x*y^7 - y^8 + 3*x^7*z + 3*x^6*y*z + 2*x^5*y^2*z + x^4*y^3*z + x^2*y^5*z + x^6*z^2 + 3*x^4*y^2*z^2 - 3*x^3*y^3*z^2 - 2*x^2*y^4*z^2 - 2*x*y^5*z^2 + y^6*z^2 + x^4*y*z^3 - 2*x^3*y^2*z^3 + x^2*y^3*z^3 + x*y^4*z^3 - 2*y^5*z^3 - x^4*z^4 + 2*x^3*y*z^4 + 2*y^4*z^4 + 2*x^3*z^5 + 2*x^2*y*z^5 + x*y^2*z^5 - y^3*z^5 - 3*x^2*z^6 + 2*x*y*z^6 + y^2*z^6 - 3*x*z^7 - y*z^7 + 19/5040*x^7 + 3*x^6*y - 3*x^5*y^2 - 2*x^3*y^4 - 3*x^2*y^5 - x*y^6 + y^7 - x^5*y*z - 3*x^4*y^2*z - 3*x^3*y^3*z + 3*x^2*y^4*z + 2*x*y^5*z + y^6*z + x^5*z^2 - 3*x^4*y*z^2 + 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 + 2*x*y^4*z^2 + y^5*z^2 + 3*x^4*z^3 - x^3*y*z^3 + x^2*y^2*z^3 + 2*x^3*z^4 + 2*x^2*y*z^4 + 2*x*y^2*z^4 + y^3*z^4 + x^2*z^5 + 2*x*y*z^5 - 3*y^2*z^5 - 3*x*z^6 - 2*y*z^6 + 2*z^7 - x^5*y - 2*x^4*y^2 + 2*x^3*y^3 + 3*x^2*y^4 - 3*x^4*y*z - 3*x^3*y^2*z + 2*x^2*y^3*z - x*y^4*z - 3*y^5*z - 3*x^4*z^2 - 3*x^3*y*z^2 + 2*x^2*y^2*z^2 + 2*x*y^3*z^2 + 2*y^4*z^2 - 2*x^3*z^3 + x^2*y*z^3 - x*y^2*z^3 + 3*y^3*z^3 + x^2*z^4 + x*y*z^4 + 2*y^2*z^4 - x*z^5 - 3*y*z^5 - z^6 - 3*x^4*y - 3*x^3*y^2 + x^2*y^3 + 2*x*y^4 + 4/15*y^5 + 3*x^4*z + x^3*y*z + 2*x^2*y^2*z - y^4*z - 2*x^3*z^2 + 3*x^2*y*z^2 + 3*x*y^2*z^2 - 3*y^3*z^2 + 2*x^2*z^3 - x*y*z^3 - 3*y^2*z^3 + 2*x*z^4 - 2*y*z^4 + z^5 - 2*x^3*y - 3*x^2*y^2 - 2*x*y^3 - 1/3*x^3*z - 2*x^2*y*z + x*y^2*z - 2*y^3*z + 3*x^2*z^2 + 3*x*y*z^2 - x*z^3 - 2*y*z^3 - 2*z^4 + x*y^2 - 3*x*y*z + 2*y^2*z + 2*x*z^2 + 2*y*z^2 + z^3', '-2*x^8 - x^7*y - x^6*y^2 + 2*x^5*y^3 - 2*x^4*y^4 - x^2*y^6 - y^8 + 3*x^7*z - x^6*y*z + x^5*y^2*z + 3*x^4*y^3*z + 2*x^3*y^4*z + 2*x^2*y^5*z - 3*x*y^6*z - 3*y^7*z + 2*x^6*z^2 + 2*x^5*y*z^2 - 3*x^4*y^2*z^2 + 3*x^3*y^3*z^2 - 2*x^2*y^4*z^2 - x*y^5*z^2 - y^6*z^2 - 3*x^5*z^3 - x^4*y*z^3 + 3*x^3*y^2*z^3 - 3*x^2*y^3*z^3 + x*y^4*z^3 + 2*y^5*z^3 + 3*x^4*z^4 - x^3*y*z^4 - 3*x^2*y^2*z^4 + y^4*z^4 - x^3*z^5 + 2*x^2*y*z^5 - x*y^2*z^5 + 2*x^2*z^6 + 3*y^2*z^6 + 3*x*z^7 + y*z^7 - z^8 + 1/144*x^7 - x^6*y + x^4*y^3 - 3*x^2*y^5 + 2*x*y^6 + 3*x^6*z + 2*x^4*y^2*z + 3*x^3*y^3*z + 3*x^2*y^4*z - 3*x*y^5*z + 2*x^5*z^2 + 3*x^4*y*z^2 - x^3*y^2*z^2 - 2*x*y^4*z^2 - 3*y^5*z^2 + 2*x^4*z^3 + 2*x^3*y*z^3 - x^2*y^2*z^3 + x*y^3*z^3 + 2*y^4*z^3 + 3*x^3*z^4 - x^2*y*z^4 + y^3*z^4 + 2*x^2*z^5 - 3*x*y*z^5 - 3*y^2*z^5 + 2*y*z^6 - z^7 + 3*x^5*y + x^4*y^2 - x^3*y^3 - 2*x^2*y^4 + 2*x*y^5 + 2*x^5*z - 2*x^4*y*z + 2*x^3*y^2*z - x^2*y^3*z - 3*x*y^4*z + y^5*z - 3*x^4*z^2 + x^3*y*z^2 - x*y^3*z^2 + x^3*z^3 + 3*x^2*y*z^3 + x*y^2*z^3 + 2*y^3*z^3 - x^2*z^4 + 3*x*y*z^4 + y^2*z^4 - x*z^5 + 2*y*z^5 - 2*x^2*y^3 - 3*x*y^4 + 13/60*y^5 + 3*x^4*z + 2*x^3*y*z + x^2*y^2*z + 3*x*y^3*z + 2*y^4*z + x^3*z^2 + x^2*y*z^2 + y^3*z^2 - x^2*z^3 - 2*x*y*z^3 + 2*y^2*z^3 + 3*x*z^4 + 3*y*z^4 - 2*z^5 - 2*x^3*y - 3*x*y^3 + 14/3*x^3*z + 2*x^2*y*z - 3*x*y^2*z + y^3*z - x^2*z^2 - 3*x*y*z^2 + 3*y^2*z^2 + 3*y*z^3 - 3*z^4 - x*y^2 - 3*x*y*z - 3*y^2*z + x*z^2 + 2*y*z^2 + 2*z^3']
  ok   R3 L=Z, component W3 (P_060 = 0, linear): a point of the component (residual equations vanish)
      timing: member+triples 0.4 s, stabilization 0.1 s
  ok   R3 L=Z, component W3 (P_060 = 0, linear) anchor (A): fixed {'P_060': 0}, solved ['P_510', 'H_120', 'H_021', 'H_012']; member closed with H and the prescribed graded data: True; a triple of I of local length 37 (ds), stabilization (37, 11)
      anchor generators: {'P': 'X^7 + 7*X^5*Y - X^5*Z + 35/3*X^3*Y^2 - 10/3*X^3*Y*Z - X^3*Z^2 + 35/9*X*Y^3 - 5/3*X*Y^2*Z - X*Y*Z^2 - 7/9*X*Z^3 + 13/21*Z^4 + X*Y^2 - X*Y*Z + 2*Y^2*Z + 2*X*Z^2 + Y*Z^2', 'G': 'Y^5 + 2*X*Y^2 + Y^2*Z + 2*X*Z^2 - 2*Y*Z^2', 'H': 'X^3*Z + X*Y*Z + X*Z^2 - Z^3'}
      anchor triple: ['-x^8 + 3*x^7*y - 3*x^5*y^3 - 2*x^4*y^4 - 2*x^3*y^5 + 2*x^2*y^6 - x*y^7 + 2*y^8 + x^6*y*z - x^4*y^3*z + 3*x^3*y^4*z - 3*x^2*y^5*z - x*y^6*z + 2*y^7*z + x^6*z^2 - x^5*y*z^2 + 3*x^4*y^2*z^2 - 2*x^3*y^3*z^2 - x^2*y^4*z^2 + 3*x*y^5*z^2 + 2*y^6*z^2 + 3*x^5*z^3 - 2*x^4*y*z^3 + 2*x^3*y^2*z^3 + 2*x^2*y^3*z^3 + x*y^4*z^3 - 2*y^5*z^3 - 2*x^4*z^4 - x^3*y*z^4 - 3*x^2*y^2*z^4 - 3*x*y^3*z^4 - 3*y^4*z^4 - 2*x^2*y*z^5 - 2*x*y^2*z^5 + y^3*z^5 + x^2*z^6 + x*y*z^6 - x*z^7 - 35743/105840*x^7 - 2*x^6*y + 3*x^4*y^3 + 3*x^3*y^4 + 3*x^2*y^5 + x*y^6 - 3*y^7 - x^6*z - x^5*y*z + 3*x^4*y^2*z - 3*x^3*y^3*z - x^2*y^4*z + 3*x*y^5*z - 2*y^6*z - 2*x^5*z^2 - 2*x^4*y*z^2 - 3*x^2*y^3*z^2 - x*y^4*z^2 - 2*y^5*z^2 + x^4*z^3 - 3*x^3*y*z^3 + x^2*y^2*z^3 + 3*x*y^3*z^3 + 2*y^4*z^3 + x^3*z^4 - x^2*y*z^4 - 3*x*y^2*z^4 + y^3*z^4 + x^2*z^5 + 2*x*y*z^5 - y^2*z^5 - 2*x*z^6 + y*z^6 + 2*z^7 + 31/840*x^6 + 2*x^5*y + 2*x^4*y^2 + 2*x^3*y^3 + 3*x^2*y^4 - 2*x*y^5 + y^6 + x^5*z + 3*x^4*y*z - 2*x^3*y^2*z + 3*x^2*y^3*z - y^5*z - x^4*z^2 + 2*x^3*y*z^2 + x^2*y^2*z^2 - 2*x*y^3*z^2 - x^3*z^3 - x^2*y*z^3 + 3*x*y^2*z^3 + 2*y^3*z^3 - 2*x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 - 3*x*z^5 + 2*y*z^5 - 2*z^6 - 19/210*x^5 + x^3*y^2 - 3*x^2*y^3 - 2*x*y^4 + 1/30*y^5 + 2*x^4*z - 2*x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + x^3*z^2 + 2*x^2*y*z^2 + y^3*z^2 + 2*x^2*z^3 + x*y*z^3 + y^2*z^3 + 3*y*z^4 - z^5 - x*y^3 + 1/6*x^3*z - 3*x^2*y*z - 3*x*y^2*z - 3*y^3*z + 3*y^2*z^2 + 2*x*z^3 + 2*y*z^3 + 2*z^4 + 3*x*y^2 - x*y*z + 2*y^2*z - 3*x*z^2 + 2*y*z^2 - z^3', '-3*x^7*y - x^6*y^2 - 2*x^4*y^4 + x^3*y^5 - 3*x^2*y^6 - 3*x*y^7 - y^8 + x^7*z + 3*x^6*y*z + 3*x^5*y^2*z - 3*x^4*y^3*z + x^3*y^4*z + 3*x^2*y^5*z + 3*y^7*z + 2*x^6*z^2 + 2*x^5*y*z^2 + x^4*y^2*z^2 - x*y^5*z^2 + 2*y^6*z^2 + x^5*z^3 - 3*x^3*y^2*z^3 - 2*x^2*y^3*z^3 + 3*x*y^4*z^3 - 2*y^5*z^3 + 2*x^4*z^4 - 2*x^3*y*z^4 - 3*x^2*y^2*z^4 + x*y^3*z^4 + y^4*z^4 - 3*x^3*z^5 + x^2*y*z^5 + 3*x*y^2*z^5 + 3*y^3*z^5 + x*y*z^6 + y^2*z^6 + x*z^7 - y*z^7 + 2311/35280*x^7 + 2*x^6*y - x^4*y^3 + x^3*y^4 - 2*x^2*y^5 - 2*y^7 - x^6*z + 3*x^5*y*z + x^4*y^2*z - x^3*y^3*z - 3*x^2*y^4*z + 3*x*y^5*z - y^6*z - x^4*y*z^2 + x^2*y^3*z^2 + 3*y^5*z^2 + 2*x^4*z^3 - 2*x^3*y*z^3 + x^2*y^2*z^3 - 2*x*y^3*z^3 - 3*x^2*y*z^4 - 3*x*y^2*z^4 - 2*y^3*z^4 - 2*y^2*z^5 - x*z^6 - 3*y*z^6 + 3*z^7 - 559/7560*x^6 + x^3*y^3 - 2*x^2*y^4 - 2*x*y^5 + y^6 + 2*x^5*z - 2*x^4*y*z - x^3*y^2*z + 2*x^2*y^3*z + x*y^4*z + y^5*z + x^4*z^2 - 3*x^3*y*z^2 - 2*x^2*y^2*z^2 - 2*x*y^3*z^2 - 2*y^4*z^2 + x^3*z^3 - 3*x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 - 3*x^2*z^4 - 2*x*y*z^4 - 3*y^2*z^4 - 3*x*z^5 + 3*y*z^5 - z^6 + 163/630*x^5 - x^2*y^3 + x*y^4 + 7/60*y^5 + 2*x^3*y*z - 2*x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + 3*x^3*z^2 - 2*x^2*y*z^2 + 3*x*y^2*z^2 + y^3*z^2 - x*y*z^3 - 3*y^2*z^3 - 3*x*z^4 + 3*y*z^4 + z^5 - x^3*y + 3*x^2*y^2 + 11/6*x^3*z + x^2*y*z + 3*x*y^2*z + y^3*z + 2*x^2*z^2 + 2*x*y*z^2 - 2*y^2*z^2 + 3*x*z^3 - 2*y*z^3 + z^4 - 2*x*y^2 - 3*x*y*z - 3*y^2*z + 2*x*z^2 + 2*y*z^2 + 2*z^3', '2*x^8 - x^7*y - 3*x^5*y^3 - 2*x^4*y^4 + 3*x^3*y^5 - x^2*y^6 + 3*x*y^7 - y^8 - 3*x^7*z - 2*x^6*y*z - 2*x^5*y^2*z - x^4*y^3*z + 2*x^3*y^4*z + x^2*y^5*z + 2*x*y^6*z + 2*y^7*z - 3*x^6*z^2 + 2*x^5*y*z^2 - 3*x^3*y^3*z^2 + 3*x^2*y^4*z^2 - 3*x*y^5*z^2 + x^5*z^3 + 2*x^4*y*z^3 - 2*x^2*y^3*z^3 + x*y^4*z^3 - 2*y^5*z^3 - 2*x^4*z^4 - 3*x^3*y*z^4 - 3*x*y^3*z^4 - 2*y^4*z^4 - 3*x^3*z^5 - 3*x^2*y*z^5 - x*y^2*z^5 + 3*y^3*z^5 + 2*x^2*z^6 + y^2*z^6 + 3*x*z^7 + 2*y*z^7 - 3*z^8 - 4903/11760*x^7 - x^6*y + x^5*y^2 + 3*x^4*y^3 + 3*x^3*y^4 + x^2*y^5 - 3*x*y^6 - 2*y^7 + 2*x^5*y*z - x^4*y^2*z + x^3*y^3*z - 3*x^2*y^4*z - 2*x*y^5*z - x^5*z^2 + x^4*y*z^2 - 3*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - y^5*z^2 - x^4*z^3 - x^3*y*z^3 + x^2*y^2*z^3 + x*y^3*z^3 - 2*y^4*z^3 + 3*x^3*z^4 + 3*x*y^2*z^4 + 3*y^3*z^4 - 3*x^2*z^5 - 3*x*y*z^5 - 3*y^2*z^5 - x*z^6 + 3*z^7 + 101/7560*x^6 + 3*x^5*y + x^4*y^2 - 3*x^3*y^3 - 2*x^2*y^4 + y^6 + 3*x^5*z - 3*x^4*y*z + x^3*y^2*z - x*y^4*z + y^5*z + x^4*z^2 - 3*x^3*y*z^2 + 3*x^2*y^2*z^2 - 2*x*y^3*z^2 + x^3*z^3 - x^2*y*z^3 + 2*x*y^2*z^3 - 3*y^3*z^3 - 3*x^2*z^4 + 3*x*y*z^4 + 3*y^2*z^4 - z^6 + 91/180*x^5 - x^2*y^3 + x*y^4 - 1/30*y^5 + 3*x^4*z + x^2*y^2*z + 3*x*y^3*z - 3*y^4*z + x^3*z^2 - 3*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 + 2*y^2*z^3 - y*z^4 - 3*x^3*y + 2*x^2*y^2 + 5/6*x^3*z + 3*x*y^2*z + y^3*z + 3*x*y*z^2 - 3*x*z^3 + 2*y*z^3 - 2*z^4 - 3*x*y*z - 2*y^2*z - x*z^2 - 3*y*z^2']
=== R2: B = [X] + V(m_Y^2); D_3 = <X^3,Y^3,XY^2,Y^2Z>, D_5 = <X^5,Y^5>, D_4 = <X^4,Y^4,Y^3L>, L in {X, Z}
--- R2 L=X
  ok   R2 L=X: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R2 L=X: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 57 eliminated with constant pivots; residual equations:
       (4) * G_022 * P_060
       (1/5) * (-3*P_060*G_220*G_031 - 10*P_060*G_121*H_210 + 30*P_060*G_201 + 20*P_140*H_201)
       (1/5) * (-3*P_060*G_121*G_031 - 10*P_060*G_121*H_111 + 60*P_060*G_102 + 40*P_140*H_102)
       (1/5) * (-3*P_060*G_031*G_022 - 10*P_060*G_121*H_012 + 90*P_060*G_003 + 60*P_140*H_003)
  ok   R2 L=X: on {P_060 != 0} the residual equations are triangular in ['G_022', 'G_201', 'G_102', 'G_003'] with diagonal (const)*P_060: a graph (irreducible)
  ok   R2 L=X: on {P_060 = 0}: each equation is (P_140) times a linear form; components {c = 0} and {linear forms ['4*H_201', '8*H_102', '12*H_003'] = 0}
  ok   R2 L=X, component W1 (P_060 != 0): a point of the component (residual equations vanish)
      timing: member+triples 0.4 s, stabilization 0.1 s
  ok   R2 L=X, component W1 (P_060 != 0) anchor (A): fixed {'P_060': 1}, solved ['G_022', 'G_201', 'G_102', 'G_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 11)
      anchor generators: {'P': 'X^7 + Y^6 - 3*X^2*Y^2 + 3*X*Y^2*Z - 6*Y^2*Z^2 - X^2*Y - 2*X^2*Z - 2*X*Y*Z + 2*X*Z^2 - Y*Z^2 + 2*Z^3', 'G': 'Y^5 - X^2*Y + X*Y*Z - 2*Y*Z^2', 'H': 'X*Y^3 - X^2*Y + X^2*Z - X*Y*Z - Y*Z^2 - 2*Z^3'}
      anchor triple: ['2*x^8 - 2*x^7*y - 2*x^6*y^2 + 2*x^5*y^3 - 3*x^4*y^4 - 3*x^3*y^5 - 3*x*y^7 + 3*y^8 + 2*x^6*y*z - 3*x^5*y^2*z - 2*x^3*y^4*z + x^2*y^5*z - x*y^6*z - 3*y^7*z - x^5*y*z^2 + 2*x^4*y^2*z^2 + 2*x^3*y^3*z^2 - x^2*y^4*z^2 + x*y^5*z^2 - y^6*z^2 - 3*x^5*z^3 - x^4*y*z^3 + 3*x^3*y^2*z^3 - 3*x^2*y^3*z^3 - 3*x*y^4*z^3 + 2*y^5*z^3 + 3*x^4*z^4 - 3*x^3*y*z^4 - x^2*y^2*z^4 + 2*x*y^3*z^4 - y^4*z^4 - 2*x^3*z^5 - x^2*y*z^5 + 2*x^2*z^6 - x*y*z^6 - y^2*z^6 - x*z^7 + 2*y*z^7 + 3*z^8 - 1/126*x^7 - x^6*y + x^5*y^2 - 2*x^3*y^4 - 2*x^2*y^5 + 2*x*y^6 - 3*y^7 + 3*x^6*z - 3*x^5*y*z + 2*x^4*y^2*z + x^3*y^3*z - x^2*y^4*z + 3*x*y^5*z + 3*y^6*z + 2*x^5*z^2 - 3*x^4*y*z^2 - 3*x^3*y^2*z^2 - 2*x^2*y^3*z^2 + 3*x*y^4*z^2 + 2*y^5*z^2 + 3*x^3*y*z^3 + x^2*y^2*z^3 + 3*x*y^3*z^3 - 3*x^3*z^4 - 2*x^2*y*z^4 + 2*x*y^2*z^4 - 3*y^3*z^4 + 2*x^2*z^5 - y^2*z^5 - 2*x*z^6 + 2*z^7 - x^5*y - x^4*y^2 - 3*x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 + 3*x^5*z + x^3*y^2*z - x^2*y^3*z + y^5*z - 2*x^4*z^2 + 2*x^3*y*z^2 - y^4*z^2 - 2*x^3*z^3 - x^2*y*z^3 + 2*x*y^2*z^3 - 2*y^3*z^3 + x^2*z^4 + 3*x*y*z^4 - 3*y^2*z^4 - 3*x*z^5 - 2*y*z^5 + 3*z^6 + 2*x^4*y - x^3*y^2 + 2*x^2*y^3 + 1/10*y^5 + x^2*y^2*z + 3*x*y^3*z - y^4*z - 3*x^3*z^2 - x^2*y*z^2 - 3*x*y^2*z^2 + y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 + 2*y*z^4 + z^5 - 3*x^3*y + 3*x^2*y^2 - 2/3*x*y^3 + 3*x^3*z + 2*x^2*y*z + 3*x*y^2*z + 2*y^3*z + 3*x^2*z^2 + 2*x*y*z^2 - 3*y^2*z^2 - x*z^3 + 2*z^4 - x^2*z + 3*y*z^2 - z^3', 'x^8 + 2*x^7*y + x^5*y^3 + 3*x^4*y^4 + 2*x^3*y^5 - x*y^7 - y^8 - 2*x^6*y*z - 3*x^5*y^2*z + 3*x^4*y^3*z + x^3*y^4*z + 3*x*y^6*z - 2*y^7*z + 3*x^6*z^2 + x^5*y*z^2 - 3*x^4*y^2*z^2 - x^3*y^3*z^2 - 2*x^2*y^4*z^2 - 2*x*y^5*z^2 - 3*y^6*z^2 - x^5*z^3 + x^4*y*z^3 + 2*x^3*y^2*z^3 - x*y^4*z^3 + 2*y^5*z^3 + 3*x^4*z^4 + x^3*y*z^4 + x^2*y^2*z^4 - 2*x*y^3*z^4 + 2*y^4*z^4 + 2*x^3*z^5 - x^2*y*z^5 + 3*x*y^2*z^5 + y^3*z^5 - x^2*z^6 - x*y*z^6 - 2*y^2*z^6 - 2*x*z^7 - 2*y*z^7 + z^8 - 1/315*x^7 - 3*x^6*y + 3*x^5*y^2 + 2*x^4*y^3 - 3*x^3*y^4 + x^2*y^5 - 2*x*y^6 + 3*y^7 + 2*x^6*z - 3*x^5*y*z - 3*x^4*y^2*z + x^3*y^3*z - 2*x^2*y^4*z + 2*y^6*z + 2*x^5*z^2 + 3*x^4*y*z^2 + 2*x^3*y^2*z^2 - 3*x*y^4*z^2 + y^5*z^2 + x^4*z^3 - x^2*y^2*z^3 - 3*x*y^3*z^3 - y^4*z^3 - x^2*y*z^4 - 3*x*y^2*z^4 - y^3*z^4 - 3*x^2*z^5 - 3*x*y*z^5 - 2*y^2*z^5 - 3*x*z^6 + 3*y*z^6 - 2*z^7 - 2*x^4*y^2 - 3*x^3*y^3 + x^2*y^4 - 3*x*y^5 - 3*x^4*y*z - 3*x^3*y^2*z - 2*x^2*y^3*z + y^5*z - 2*x^4*z^2 + x^2*y^2*z^2 - 3*y^4*z^2 - 2*x^2*y*z^3 + x*y^2*z^3 + 3*y^3*z^3 - 3*x^2*z^4 - 3*x*y*z^4 + 3*y^2*z^4 + 2*x*z^5 + 2*y*z^5 + x^4*y + x^3*y^2 + 2*x^2*y^3 + 3*x*y^4 - 19/120*y^5 - 3*x^4*z - 3*x^2*y^2*z + x*y^3*z + y^4*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*y^2*z^3 + 2*x*z^4 + 3*y*z^4 + 2*z^5 - 3*x^2*y^2 + 31/6*x*y^3 - 3*x^3*z - x^2*y*z - 3*x*y^2*z + 2*y^3*z + 3*x^2*z^2 - x*y*z^2 + 2*y^2*z^2 + x*z^3 + 2*y*z^3 + 2*z^4 - 3*x^2*y - 3*x^2*z + x*y*z - 3*x*z^2 - 3*y*z^2 + 3*z^3', '-x^7*y + x^5*y^3 + x^4*y^4 - 3*x^3*y^5 - x*y^7 + y^8 + x^7*z - 3*x^6*y*z + 2*x^5*y^2*z + x^4*y^3*z + 2*x^3*y^4*z - 2*x^2*y^5*z - x*y^6*z - y^7*z - 3*x^6*z^2 - 2*x^5*y*z^2 - 2*x^4*y^2*z^2 + x^2*y^4*z^2 - x*y^5*z^2 + 3*y^6*z^2 - 2*x^5*z^3 - 3*x^4*y*z^3 - 3*x^3*y^2*z^3 + x^2*y^3*z^3 + 3*x*y^4*z^3 - 2*y^5*z^3 - 3*x^4*z^4 + x^3*y*z^4 - 2*x^2*y^2*z^4 - x*y^3*z^4 + 3*y^4*z^4 - x^3*z^5 + 3*x^2*y*z^5 - 3*x*y^2*z^5 - 2*y^3*z^5 - 3*x*y*z^6 + 3*y^2*z^6 + 2*x*z^7 - y*z^7 - 3*z^8 - 101/360*x^7 + 3*x^6*y + 3*x^5*y^2 - 3*x^4*y^3 - x^3*y^4 - x^2*y^5 - 2*x*y^6 + 3*y^7 - 2*x^6*z - x^5*y*z + 2*x^4*y^2*z - 3*x^3*y^3*z + 3*x^2*y^4*z + 2*x*y^5*z - 3*y^6*z + x^5*z^2 + 3*x^3*y^2*z^2 + x^2*y^3*z^2 - y^5*z^2 + x^4*z^3 + 2*x^3*y*z^3 - 2*x^2*y^2*z^3 - y^4*z^3 + 2*x^3*z^4 - 2*x*y^2*z^4 + y^3*z^4 - 3*x*y*z^5 - 2*y^2*z^5 + 3*x*z^6 + 3*y*z^6 - 3*z^7 - x^5*y - 3*x^4*y^2 + 2*x^3*y^3 + x^2*y^4 + 3*x*y^5 + 2*y^6 - 3*x^4*y*z + x^2*y^3*z + 2*x*y^4*z - 3*y^5*z + 3*x^3*y*z^2 + 2*x^2*y^2*z^2 - 3*x*y^3*z^2 + 2*y^4*z^2 - 2*x^3*z^3 + x^2*y*z^3 - 2*x*y^2*z^3 + 2*y^3*z^3 - x^2*z^4 + 3*x*y*z^4 - 2*x*z^5 + 2*y*z^5 + z^6 + x^3*y^2 + 3*x^2*y^3 - 1/10*y^5 - x^3*y*z + 2*x^2*y^2*z - 3*x*y^3*z - 3*y^4*z + x^3*z^2 - 2*x^2*y*z^2 + 3*x*y^2*z^2 - y^3*z^2 - x^2*z^3 + y^2*z^3 - x*z^4 - x^3*y + 2*x^2*y^2 - 19/3*x*y^3 + 2*x^3*z + 3*x*y^2*z - x^2*z^2 - x*y*z^2 - y^2*z^2 - 2*x*z^3 - y*z^3 - 3*z^4 + x^2*y + 2*x*y*z - 2*x*z^2 - 3*y*z^2 - 3*z^3']
  ok   R2 L=X, component W2 (P_060 = 0 = P_140): a point of the component (residual equations vanish)
      timing: member+triples 0.4 s, stabilization 0.1 s
  ok   R2 L=X, component W2 (P_060 = 0 = P_140) anchor (A): fixed {'P_060': 0}, solved ['P_140']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 11)
      anchor generators: {'P': 'X^7 - 2*X^2*Y - X^2*Z - X*Y*Z + X*Z^2 - 2*Y*Z^2 + 2*Z^3', 'G': 'Y^5 - X^2*Y - 2*X^2*Z + X*Y*Z - 2*X*Z^2 - 2*Y*Z^2 - 2*Z^3', 'H': 'X*Y^3 + 2*X^2*Z + 2*X*Y*Z - X*Z^2 + 2*Y*Z^2'}
      anchor triple: ['x^7*y - 2*x^6*y^2 - 3*x^5*y^3 + 2*x^4*y^4 + x^3*y^5 - 3*x^2*y^6 - 2*x*y^7 - 2*y^8 - x^7*z - 3*x^6*y*z + 3*x^4*y^3*z - 3*x^3*y^4*z + x^2*y^5*z - 2*x*y^6*z + y^7*z - 3*x^5*y*z^2 + x^4*y^2*z^2 - 2*x^3*y^3*z^2 - 2*x^2*y^4*z^2 + 2*x*y^5*z^2 + 2*x^5*z^3 + 2*x^3*y^2*z^3 - 2*x^2*y^3*z^3 - 3*y^5*z^3 - x^4*z^4 - 3*x^3*y*z^4 - x^2*y^2*z^4 + x*y^3*z^4 - 2*y^4*z^4 + 3*x^3*z^5 + 2*x^2*y*z^5 - x*y^2*z^5 + 3*y^3*z^5 + x^2*z^6 - x*y*z^6 + 3*y^2*z^6 - 3*x*z^7 - y*z^7 + z^8 + 19/5040*x^7 + 2*x^6*y - 2*x^5*y^2 - 3*x^4*y^3 - 2*x^3*y^4 - 2*x^2*y^5 - 2*x*y^6 - x^6*z - 2*x^5*y*z - 2*x^4*y^2*z + 2*x^3*y^3*z - 3*x^2*y^4*z + 2*y^6*z + 2*x^5*z^2 - x^4*y*z^2 - x^3*y^2*z^2 - 3*x^2*y^3*z^2 + 2*x*y^4*z^2 + y^5*z^2 - x^3*y*z^3 - 3*x^2*y^2*z^3 + x*y^3*z^3 - y^4*z^3 + 3*x^2*y*z^4 + 2*y^3*z^4 - x^2*z^5 + x*y*z^5 - 3*y^2*z^5 - 2*x*z^6 - 2*y*z^6 + 2*z^7 - 3*x^5*y + 2*x^3*y^3 + 3*x^2*y^4 - 2*x*y^5 + y^6 + 2*x^5*z - x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z - x*y^4*z + 2*y^5*z + 2*x^4*z^2 + 2*x^3*y*z^2 + 2*x*y^3*z^2 + 2*x^3*z^3 + 3*x^2*y*z^3 - x*y^2*z^3 - y^3*z^3 + 3*x^2*z^4 + 3*x*y*z^4 - x*z^5 - 2*y*z^5 + x^4*y + 3*x^2*y^3 - 3*x*y^4 - 7/24*y^5 - 2*x^4*z - 3*x^3*y*z + 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 + 2*y^3*z^2 + x^2*z^3 - 3*y^2*z^3 - 3*x*z^4 - 2*y*z^4 - 2*z^5 - 2*x^3*y + 3*x^2*y^2 + 2*x*y^3 + 3*x^3*z + 2*x^2*y*z + x*y^2*z + 2*y^3*z + 3*x^2*z^2 + 2*x*y*z^2 + 2*y*z^3 + 2*z^4 - x^2*y + x*y*z + 3*x*z^2 - 2*y*z^2 - 3*z^3', '2*x^8 + 2*x^7*y + 2*x^5*y^3 + 3*x^4*y^4 - 2*x^3*y^5 - 3*x^2*y^6 - 2*x*y^7 - y^8 - 2*x^7*z - x^5*y^2*z + 3*x^4*y^3*z - 3*x^3*y^4*z + 2*x^2*y^5*z + 3*x*y^6*z + y^7*z - 2*x^6*z^2 + x^5*y*z^2 - 2*x^4*y^2*z^2 + 3*x^3*y^3*z^2 - x^2*y^4*z^2 + x*y^5*z^2 - y^6*z^2 + x^5*z^3 + 3*x^4*y*z^3 + 2*x^3*y^2*z^3 - x^2*y^3*z^3 - 3*y^5*z^3 - 2*x^3*y*z^4 + x^2*y*z^5 - 3*x*y^2*z^5 - 3*y^3*z^5 - 3*x^2*z^6 - 3*x*y*z^6 + y^2*z^6 + 3*x*z^7 - 3*y*z^7 - 1/720*x^7 - 2*x^6*y - 2*x^5*y^2 + x^4*y^3 + x^3*y^4 - 2*x^2*y^5 - x*y^6 - y^7 + x^6*z - 3*x^5*y*z + x^3*y^3*z - 2*x^2*y^4*z - x*y^5*z - 2*y^6*z - 2*x^5*z^2 - 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 - x*y^4*z^2 + 2*y^5*z^2 + 2*x^4*z^3 - x^3*y*z^3 + 3*x^2*y^2*z^3 + 3*x*y^3*z^3 - y^4*z^3 - 2*x^3*z^4 + 3*x*y^2*z^4 + y^3*z^4 + x^2*z^5 + x*y*z^5 + x*z^6 - 3*y*z^6 - 2*z^7 + x^5*y + x^4*y^2 - 2*x^3*y^3 - 2*x^2*y^4 - 2*x*y^5 - 3*y^6 - x^5*z + x^4*y*z - x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z + y^5*z - 2*x^4*z^2 + x^2*y^2*z^2 + 2*x*y^3*z^2 - 2*y^4*z^2 + 3*x^2*y*z^3 + 2*x*y^2*z^3 - y^3*z^3 + x^2*z^4 - 2*x*y*z^4 - y^2*z^4 + 2*x*z^5 - y*z^5 - 2*z^6 - 2*x^3*y^2 + 3*x*y^4 + 19/40*y^5 - x^4*z - 2*x^3*y*z - 3*x^2*y^2*z - x*y^3*z + 2*y^4*z - x^3*z^2 - 3*x^2*y*z^2 - 3*x*y^2*z^2 - 3*y^3*z^2 - x^2*z^3 + 2*x*y*z^3 - y^2*z^3 + x*z^4 - 3*z^5 - 3*x^3*y - 3*x^2*y^2 - 4*x*y^3 + x^3*z + x*y^2*z + 3*y^3*z + 2*x^2*z^2 + x*y*z^2 + 3*y^2*z^2 + 2*y*z^3 + 3*z^4 + 3*x^2*y + 3*x^2*z + x*y*z - x*z^2 + 2*y*z^2 + 3*z^3', '-2*x^8 - 3*x^7*y + 2*x^6*y^2 - 3*x^5*y^3 + 2*x^4*y^4 - x^3*y^5 + x^2*y^6 + 2*x*y^7 + y^8 - 2*x^7*z + x^5*y^2*z + x^4*y^3*z + 2*x^3*y^4*z - 2*x^2*y^5*z - x*y^6*z - x^6*z^2 - 3*x^5*y*z^2 + 3*x^4*y^2*z^2 + 3*x^3*y^3*z^2 + 2*x^2*y^4*z^2 - x*y^5*z^2 + 2*y^6*z^2 - x^5*z^3 + 3*x^3*y^2*z^3 + 2*x^2*y^3*z^3 - 2*y^5*z^3 - x^4*z^4 + 2*x^3*y*z^4 - 2*x^2*y^2*z^4 + x*y^3*z^4 + 3*y^4*z^4 + 3*x^3*z^5 - 2*x^2*y*z^5 + 2*x*y^2*z^5 - y^3*z^5 + 2*x*y*z^6 + 2*y^2*z^6 + x*z^7 + y*z^7 - 3*z^8 - 5/1008*x^7 - x^6*y + 2*x^5*y^2 - x^4*y^3 + x^3*y^4 + 2*x^2*y^5 + x*y^6 + 2*y^7 - 3*x^6*z - x^5*y*z - 2*x^4*y^2*z - 2*x^3*y^3*z + x^2*y^4*z - 3*x*y^5*z - 3*y^6*z + x^5*z^2 + x^4*y*z^2 - 2*x^2*y^3*z^2 - 2*y^5*z^2 - 2*x^4*z^3 + 3*x^3*y*z^3 + x^2*y^2*z^3 + 3*x*y^3*z^3 - 3*y^4*z^3 - 2*x^3*z^4 + x^2*y*z^4 + x*y^2*z^4 - 2*y^3*z^4 - x^2*z^5 + 3*x*y*z^5 - 3*y^2*z^5 + 3*x*z^6 + 2*y*z^6 - 3*x^4*y^2 - 2*x^3*y^3 - x*y^5 + 2*y^6 + 3*x^5*z - 3*x^4*y*z - x^3*y^2*z + 2*x^2*y^3*z - 2*x*y^4*z + 3*y^5*z - x^4*z^2 + x^3*y*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 - 2*y^4*z^2 - x^3*z^3 + 3*x^2*y*z^3 + x*y^2*z^3 + 2*y^3*z^3 + x^2*z^4 + 2*x*y*z^4 + 2*y^2*z^4 - x*z^5 - 3*y*z^5 + 3*z^6 - x^4*y - 2*x^3*y^2 + x^2*y^3 - 3*x*y^4 - 17/120*y^5 - 2*x^4*z + 2*x^2*y^2*z + 3*x*y^3*z + 3*y^4*z - 3*x^3*z^2 + x^2*y*z^2 + 2*x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 - x*y*z^3 + y^2*z^3 + 3*x*z^4 + 3*z^5 - x^2*y^2 + 7/3*x*y^3 + 2*x^3*z + x^2*y*z - 2*x*y^2*z + 3*y^3*z - x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 - x*z^3 + 3*z^4 - 3*x^2*y - 2*x^2*z + 3*x*y*z + 2*x*z^2 - 2*y*z^2']
  ok   R2 L=X, component W3 (P_060 = 0, linear): a point of the component (residual equations vanish)
      timing: member+triples 0.4 s, stabilization 0.1 s
  ok   R2 L=X, component W3 (P_060 = 0, linear) anchor (A): fixed {'P_060': 0}, solved ['H_201', 'H_102', 'H_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 11)
      anchor generators: {'P': 'X^7 - 2*X*Y^4 - 8*X^2*Y^2 + 8*X*Y^2*Z + X^2*Y + X^2*Z + 2*X*Y*Z - 2*X*Z^2 - Y*Z^2 + Z^3', 'G': 'Y^5 - X*Y*Z + X*Z^2 - Y*Z^2 - 2*Z^3', 'H': 'X*Y^3 + 2*X^2*Y - 2*X*Y*Z'}
      anchor triple: ['3*x^8 - x^7*y + 3*x^6*y^2 - 2*x^5*y^3 + x^4*y^4 - 2*x^3*y^5 + 2*x^2*y^6 + 2*x*y^7 - x^7*z + 3*x^6*y*z - 3*x^5*y^2*z - 3*x^4*y^3*z + x^3*y^4*z + x^2*y^5*z + 3*x*y^6*z - 2*y^7*z + 3*x^6*z^2 + 2*x^5*y*z^2 - x^4*y^2*z^2 + 3*x^3*y^3*z^2 - x^2*y^4*z^2 + x*y^5*z^2 - 3*y^6*z^2 + 3*x^5*z^3 - x^3*y^2*z^3 - 3*x^2*y^3*z^3 - 2*x*y^4*z^3 - 3*y^5*z^3 - 3*x^4*z^4 - 3*x^3*y*z^4 + x^2*y^2*z^4 + 2*x*y^3*z^4 + 2*x^3*z^5 + x^2*y*z^5 + 3*y^3*z^5 + 3*x^2*z^6 - 3*x*y*z^6 - 3*y^2*z^6 - x*z^7 + y*z^7 - 2*z^8 - 109/2520*x^7 - 2*x^6*y - 2*x^5*y^2 - 3*x^3*y^4 - 2*x^2*y^5 + 3*x*y^6 + y^7 + 3*x^6*z - x^5*y*z + x^4*y^2*z - x^3*y^3*z + 2*x^2*y^4*z - 3*x*y^5*z + x^4*y*z^2 - 2*x^3*y^2*z^2 - x*y^4*z^2 - 3*x^4*z^3 - x^3*y*z^3 - 3*x^2*y^2*z^3 - 2*x*y^3*z^3 + y^4*z^3 + 3*x^3*z^4 - 3*x^2*y*z^4 + 2*x*y^2*z^4 - 2*y^3*z^4 + 3*x^2*z^5 - 2*x*y*z^5 - 3*y^2*z^5 - y*z^6 + z^7 - 2*x^5*y - x^2*y^4 + x*y^5 + y^6 - x^5*z - x^4*y*z - 2*x^3*y^2*z - x^2*y^3*z - x*y^4*z + 2*y^5*z - x^4*z^2 + 3*x^2*y^2*z^2 + 2*y^4*z^2 + 2*x^3*z^3 - 3*x^2*y*z^3 + 2*x*y^2*z^3 - x^2*z^4 - x*y*z^4 - y^2*z^4 + x*z^5 - y*z^5 + z^6 + 2*x^4*y - 2*x^3*y^2 + 3*x^2*y^3 - 3*x*y^4 - 1/30*y^5 + x^4*z + 2*x^2*y^2*z - 3*x*y^3*z - 2*y^4*z - 3*x^3*z^2 + 3*x*y^2*z^2 - y^3*z^2 + 3*x^2*z^3 - 2*x*y*z^3 - y^2*z^3 - 3*x*z^4 - y*z^4 - z^5 - x^3*y - 2*x^2*y^2 + 4/3*x*y^3 - 2*x^3*z - x^2*y*z - 3*y^3*z + x^2*z^2 - x*y*z^2 + 3*y^2*z^2 - 2*x*z^3 - 3*y*z^3 - 3*z^4 - 3*x^2*y + 3*x^2*z - 2*x*y*z - 2*x*z^2 - 3*y*z^2', '-2*x^8 + 2*x^7*y + 3*x^6*y^2 + 2*x^5*y^3 - 2*x^4*y^4 - 3*x^3*y^5 - 2*x*y^7 + 2*y^8 + x^7*z + x^6*y*z + 3*x^5*y^2*z - 3*x^4*y^3*z + 3*x^3*y^4*z - 2*x^2*y^5*z + 2*x*y^6*z + x^6*z^2 + x^5*y*z^2 + x^4*y^2*z^2 - x^3*y^3*z^2 - 2*x^2*y^4*z^2 + x*y^5*z^2 + 2*y^6*z^2 - x^5*z^3 + x^4*y*z^3 - 2*x^3*y^2*z^3 + x^2*y^3*z^3 + 2*y^5*z^3 + 2*x^4*z^4 + x^3*y*z^4 - 3*x*y^3*z^4 + 3*x^2*y*z^5 + x*y^2*z^5 - y^3*z^5 + 3*x^2*z^6 - 3*x*y*z^6 + x*z^7 - 2*y*z^7 - 3*z^8 - 23/504*x^7 - 2*x^5*y^2 + 3*x^4*y^3 - 3*x^3*y^4 + x*y^6 - 2*y^7 + x^6*z + 2*x^5*y*z - x^4*y^2*z + x^3*y^3*z + 2*x^2*y^4*z + 2*y^6*z - x^5*z^2 + 2*x^4*y*z^2 - x^3*y^2*z^2 + x^2*y^3*z^2 + 3*x*y^4*z^2 + 3*y^5*z^2 + x^4*z^3 - 2*x^2*y^2*z^3 - x*y^3*z^3 - 2*y^4*z^3 - 3*x^3*z^4 + 3*x^2*y*z^4 + x*y^2*z^4 + 2*y^3*z^4 - 2*x^2*z^5 + x*y*z^5 + y^2*z^5 - x*z^6 + 3*y*z^6 - z^7 - 3*x^5*y - 3*x^4*y^2 + 2*x^3*y^3 - 3*x*y^5 + 2*y^6 - x^5*z - 3*x^4*y*z - 2*x*y^4*z + 2*y^5*z - 2*x^4*z^2 - 2*x^3*y*z^2 + 2*x^2*y^2*z^2 + x*y^3*z^2 - 3*x^2*y*z^3 + x*y^2*z^3 - y^3*z^3 - x^2*z^4 - 3*x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 - 2*y*z^5 - 2*z^6 + 2*x^3*y^2 + 2*x^2*y^3 - 2*x*y^4 + 11/40*y^5 + 2*x^2*y^2*z - x*y^3*z + 2*y^4*z - 2*x^2*y*z^2 - 3*x*y^2*z^2 + y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 + 3*y^2*z^3 - 2*x*z^4 - 3*y*z^4 + 3*z^5 - 2*x^3*y - 2*x^2*y^2 - x*y^3 + 3*x^3*z + x^2*y*z + 3*x*y^2*z + 2*y^3*z - 3*x^2*z^2 + x*y*z^2 - 3*y^2*z^2 + 3*x*z^3 + 2*y*z^3 - 3*z^4 + x^2*y - 2*x^2*z - x*y*z - x*z^2 - 2*y*z^2 + 3*z^3', '2*x^8 - 2*x^7*y - x^6*y^2 + 2*x^5*y^3 - 3*x^4*y^4 - 2*x^3*y^5 - 2*x^2*y^6 + 3*x*y^7 + x^7*z - x^5*y^2*z - x^4*y^3*z - x^3*y^4*z - 2*x^2*y^5*z - 2*x*y^6*z - y^7*z + 2*x^5*y*z^2 + 2*x^4*y^2*z^2 - 3*x^3*y^3*z^2 + 3*x^2*y^4*z^2 + 2*y^6*z^2 + 3*x^5*z^3 + 2*x^4*y*z^3 - 2*x^3*y^2*z^3 - 3*x^2*y^3*z^3 + 2*x*y^4*z^3 + y^5*z^3 - 2*x^4*z^4 - x^3*y*z^4 - x^2*y^2*z^4 - x*y^3*z^4 + 3*y^4*z^4 + x^3*z^5 + 3*x^2*y*z^5 + 2*x*y^2*z^5 - y^3*z^5 + 3*x^2*z^6 + x*y*z^6 + 2*y^2*z^6 + 3*x*z^7 + 3*y*z^7 - 2*z^8 - 13/504*x^7 + 2*x^6*y - x^5*y^2 - 2*x^4*y^3 + 3*x^3*y^4 - 3*x*y^6 + y^7 + 3*x^6*z + 3*x^5*y*z + x^4*y^2*z + 3*x^3*y^3*z - 3*x^2*y^4*z - 2*x*y^5*z - 3*y^6*z - x^5*z^2 + 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 - 3*x*y^4*z^2 + 2*y^5*z^2 - x^4*z^3 + x^3*y*z^3 + 3*y^4*z^3 + 2*x^3*z^4 + 3*x^2*y*z^4 - y^3*z^4 - 2*x^2*z^5 + 3*x*y*z^5 - 2*y^2*z^5 - x*z^6 + 3*y*z^6 + 3*z^7 - 2*x^5*y - 2*x^2*y^4 + 3*x*y^5 - 2*y^6 - 2*x^5*z - x^4*y*z - 2*x^3*y^2*z + 3*x^2*y^3*z + 3*x*y^4*z + 2*y^5*z + x^4*z^2 + 2*x^3*y*z^2 + x^2*y^2*z^2 - 3*y^4*z^2 + x^2*y*z^3 + 3*y^3*z^3 - 3*x*y*z^4 - 2*y^2*z^4 + 3*x*z^5 - y*z^5 + 3*z^6 - 3*x^4*y - x^3*y^2 + x^2*y^3 - 2*x*y^4 + 2/15*y^5 - 2*x^4*z - x^3*y*z - x*y^3*z + 3*y^4*z + 3*x^3*z^2 + 3*x^2*y*z^2 - 2*x*y^2*z^2 + x*y*z^3 - y^2*z^3 - 2*x*z^4 - 2*y*z^4 - 2*z^5 - 2*x^3*y - x^2*y^2 - 2*x*y^3 + 2*x^3*z + 3*x^2*y*z - x*y^2*z + 2*y^3*z - 3*y^2*z^2 + 2*y*z^3 + 2*z^4 + 3*x^2*y - x^2*z + x*z^2 - 3*y*z^2 + 2*z^3']
--- R2 L=Z
  ok   R2 L=Z: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R2 L=Z: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 57 eliminated with constant pivots; residual equations:
       (2) * G_121 * P_060
       (2/5) * (-10*P_060*G_022*H_210 - P_041*G_220 + 15*P_060*G_201 + 10*P_041*H_201)
       (2/5) * (-10*P_060*G_022*H_111 - P_041*G_121 + 30*P_060*G_102 + 20*P_041*H_102)
       (2/5) * (-10*P_060*G_022*H_012 - P_041*G_022 + 45*P_060*G_003 + 30*P_041*H_003)
  ok   R2 L=Z: on {P_060 != 0} the residual equations are triangular in ['G_121', 'G_201', 'G_102', 'G_003'] with diagonal (const)*P_060: a graph (irreducible)
  ok   R2 L=Z: on {P_060 = 0}: each equation is (P_041) times a linear form; components {c = 0} and {linear forms ['-2/5*G_220 + 4*H_201', '-2/5*G_121 + 8*H_102', '-2/5*G_022 + 12*H_003'] = 0}
  ok   R2 L=Z, component W1 (P_060 != 0): a point of the component (residual equations vanish)
      timing: member+triples 0.3 s, stabilization 0.1 s
  ok   R2 L=Z, component W1 (P_060 != 0) anchor (A): fixed {'P_060': 1}, solved ['G_121', 'G_201', 'G_102', 'G_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 11)
      anchor generators: {'P': 'X^7 + Y^6 + 6*X^2*Y^2 + 3*X*Y^2*Z + 3*Y^2*Z^2 - 2*X^2*Y - X*Y*Z - 2*X*Z^2 - Y*Z^2', 'G': 'Y^5 + 2*X^2*Y + X*Y*Z + Y*Z^2', 'H': 'Y^3*Z - 2*X^2*Y - 2*X^2*Z + X*Y*Z - X*Z^2 - Y*Z^2 - Z^3'}
      anchor triple: ['-2*x^8 - x^7*y - x^6*y^2 - 2*x^5*y^3 - 3*x^4*y^4 - x^3*y^5 - x^2*y^6 + 2*x*y^7 + y^8 - x^7*z - 2*x^5*y^2*z - 2*x^4*y^3*z + 2*x^3*y^4*z - x^2*y^5*z - 2*x*y^6*z + 2*y^7*z + x^5*y*z^2 + 2*x^4*y^2*z^2 + 3*x^3*y^3*z^2 - 2*x^2*y^4*z^2 + x*y^5*z^2 - x^5*z^3 + x^3*y^2*z^3 - 2*x^2*y^3*z^3 - 2*y^5*z^3 + 3*x^4*z^4 - 2*x^3*y*z^4 - x^2*y^2*z^4 - 3*x*y^3*z^4 + 3*y^4*z^4 + x^3*z^5 - 2*x^2*y*z^5 - 3*x^2*z^6 + x*y*z^6 + y^2*z^6 + 3*x*z^7 + 3*y*z^7 - 3*z^8 - 1321/5040*x^7 + 3*x^5*y^2 + 3*x^3*y^4 + 3*x^2*y^5 - 2*y^7 - 3*x^5*y*z + x^4*y^2*z - x^3*y^3*z - 2*x^2*y^4*z + x*y^5*z + 2*y^6*z + 3*x^4*y*z^2 + 3*x^3*y^2*z^2 + 3*x^2*y^3*z^2 + x*y^4*z^2 + y^5*z^2 - x^4*z^3 - 3*x^3*y*z^3 + x^2*y^2*z^3 + 2*x*y^3*z^3 + 2*y^4*z^3 - 2*x^3*z^4 + x^2*y*z^4 + 3*x*y^2*z^4 - 3*y^3*z^4 - 2*x^2*z^5 + x*y*z^5 - y^2*z^5 + 2*x*z^6 - 2*y*z^6 + 2*z^7 + x^5*y - x^4*y^2 - 3*x^3*y^3 + 2*x^2*y^4 - 2*x*y^5 + 2*y^6 + x^5*z + x^4*y*z - 3*x^3*y^2*z + 3*x^2*y^3*z - 3*x*y^4*z + 3*x^4*z^2 - 3*x^3*y*z^2 + x^2*y^2*z^2 + 3*x*y^3*z^2 - y^4*z^2 + 2*x^3*z^3 + x^2*y*z^3 - 2*x*y^2*z^3 - y^3*z^3 - 2*x^2*z^4 - 3*x*y*z^4 + 3*y^2*z^4 - x*z^5 + 3*y*z^5 + 2*z^6 + 3*x^4*y - x^2*y^3 - 3*x*y^4 + 1/120*y^5 - x^4*z + x^3*y*z - 3*x*y^3*z - 3*y^4*z + x^3*z^2 + x^2*y*z^2 + x*y^2*z^2 - 3*x^2*z^3 - x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 + y*z^4 - z^5 + 3*x^3*y - 3*x^2*y^2 - 2*x*y^3 - 3*x^3*z - x^2*y*z - 2*x*y^2*z + 17/6*y^3*z + 3*x^2*z^2 - x*y*z^2 - 2*y^2*z^2 + x*z^3 - y*z^3 - 2*z^4 - x^2*y + 3*x*y*z + 3*x*z^2 + 3*z^3', '-3*x^8 - x^6*y^2 - x^5*y^3 + 3*x^4*y^4 + x^2*y^6 + 2*y^8 + 3*x^6*y*z - 2*x^4*y^3*z + x^3*y^4*z - 3*x^2*y^5*z + 2*x*y^6*z - 2*y^7*z + 2*x^6*z^2 - x^5*y*z^2 - x^4*y^2*z^2 - 2*x^3*y^3*z^2 + 3*x*y^5*z^2 + 2*y^6*z^2 - 2*x^5*z^3 - 3*x^4*y*z^3 + 2*x^3*y^2*z^3 - 2*x^2*y^3*z^3 + x*y^4*z^3 - 2*y^5*z^3 - x^4*z^4 + 2*y^4*z^4 + x^3*z^5 - 3*x^2*y*z^5 + 2*x*y^2*z^5 - 2*y^3*z^5 + x^2*z^6 - 2*x*y*z^6 - 2*x*z^7 - 3*y*z^7 - 2*z^8 - 433/1008*x^7 + x^5*y^2 + x^4*y^3 - x^3*y^4 + 3*x^2*y^5 + 2*x*y^6 - 2*y^7 + 2*x^6*z - 3*x^5*y*z - 3*x^4*y^2*z + 2*x^3*y^3*z + 2*x^2*y^4*z + x*y^5*z + y^6*z + x^5*z^2 + x^4*y*z^2 - x^3*y^2*z^2 - 2*x^2*y^3*z^2 - x*y^4*z^2 + 2*y^5*z^2 + x^4*z^3 + x^2*y^2*z^3 - x*y^3*z^3 + y^4*z^3 + 3*x^3*z^4 + x^2*y*z^4 - 2*x*y^2*z^4 - 2*y^3*z^4 - x^2*z^5 + x*y*z^5 - 3*y^2*z^5 - x*z^6 + x^5*y - x^4*y^2 - 3*x^3*y^3 - 3*x^2*y^4 - x*y^5 + 3*y^6 + 3*x^5*z - x^4*y*z + x^3*y^2*z + x^2*y^3*z + 2*x*y^4*z - y^5*z - x^4*z^2 - 3*x^3*y*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 - 2*x*y^2*z^3 + 3*y^3*z^3 - 3*x^2*z^4 - x*y*z^4 - y^2*z^4 + 2*y*z^5 - 2*x^4*y + x^3*y^2 - x^2*y^3 + x*y^4 + 1/40*y^5 + x^4*z + 2*x^3*y*z + x^2*y^2*z - x*y^3*z - 2*y^4*z - x^3*z^2 + 2*x^2*y*z^2 - 2*x^2*z^3 - x*y*z^3 + 3*y^2*z^3 - 2*x*z^4 + y*z^4 + 3*z^5 + 2*x^3*y + x*y^3 + x^3*z + x^2*y*z - x*y^2*z - 3/2*y^3*z + 3*x^2*z^2 - x*y*z^2 + 2*x*z^3 - 3*y*z^3 - 3*z^4 - x^2*y - 3*x^2*z + x*y*z - 2*x*z^2 + 2*z^3', '-2*x^8 - 2*x^7*y + 2*x^6*y^2 + x^5*y^3 - 3*x^4*y^4 - 3*x^3*y^5 + x^2*y^6 + 2*x*y^7 + 2*y^8 - x^7*z + x^6*y*z + x^5*y^2*z - x^3*y^4*z - x^2*y^5*z + 3*x*y^6*z + y^7*z + 3*x^6*z^2 - x^5*y*z^2 - 2*x^3*y^3*z^2 - x*y^5*z^2 + 3*y^6*z^2 - x^5*z^3 - x^4*y*z^3 - x^3*y^2*z^3 + 2*x^2*y^3*z^3 - x*y^4*z^3 + y^5*z^3 + x^4*z^4 + 2*x^3*y*z^4 - 3*x^2*y^2*z^4 + 3*x*y^3*z^4 - 2*y^4*z^4 - x^2*y*z^5 + 2*x*y^2*z^5 + y^3*z^5 + 3*x^2*z^6 + 2*x*y*z^6 + 2*y^2*z^6 + x*z^7 - 3*z^8 - 767/5040*x^7 + x^6*y - 2*x^5*y^2 - 2*x^4*y^3 + 3*x^3*y^4 - 2*x^2*y^5 - 2*y^7 - 2*x^6*z + 2*x^5*y*z - x^4*y^2*z - 3*x^2*y^4*z - 2*x*y^5*z + 2*y^6*z - 2*x^5*z^2 + 2*x^4*y*z^2 - 2*x^3*y^2*z^2 + x^2*y^3*z^2 - 3*x*y^4*z^2 - y^5*z^2 + 2*x^4*z^3 + 3*x^2*y^2*z^3 + 3*x*y^3*z^3 - y^4*z^3 + 2*x^3*z^4 + 3*y^3*z^4 + 2*x^2*z^5 - x*y*z^5 + y^2*z^5 + x*z^6 - 2*y*z^6 - z^7 + x^5*y + x^4*y^2 - 3*x^3*y^3 + x^2*y^4 - x*y^5 + y^6 + 2*x^5*z + 3*x^4*y*z + 3*x^3*y^2*z - 3*x*y^4*z - 3*y^5*z + 3*x^4*z^2 + 3*x*y^3*z^2 - x^3*z^3 + x^2*y*z^3 - 2*x*y^2*z^3 + 3*y^3*z^3 - x^2*z^4 - 3*x*y*z^4 + y^2*z^4 - 2*x*z^5 + 2*y*z^5 - 3*x^4*y - x^3*y^2 - x^2*y^3 - 2*x*y^4 + 1/24*y^5 + 3*x^4*z - 3*x^3*y*z - 3*x^2*y^2*z - x*y^3*z + 2*y^4*z + 3*x^3*z^2 - x^2*y*z^2 + x*y^2*z^2 - y^3*z^2 - 2*x^2*z^3 - x*y*z^3 + 2*y^2*z^3 + 2*y*z^4 - 2*z^5 + 2*x^2*y^2 - 3*x*y^3 - 2*x^2*y*z + 3*x*y^2*z - 23/6*y^3*z - 2*x^2*z^2 - 3*y^2*z^2 + 2*x*z^3 - 2*y*z^3 - 3*z^4 + x^2*y - 3*x^2*z - 3*x*y*z - 3*x*z^2 - 3*y*z^2 - z^3']
  ok   R2 L=Z, component W2 (P_060 = 0 = P_041): a point of the component (residual equations vanish)
      timing: member+triples 0.3 s, stabilization 0.1 s
  ok   R2 L=Z, component W2 (P_060 = 0 = P_041) anchor (A): fixed {'P_060': 0}, solved ['P_041']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 11)
      anchor generators: {'P': 'X^7 - 2*X^2*Y - X^2*Z - X*Y*Z + 2*X*Z^2 - Z^3', 'G': 'Y^5 + X^2*Y + 2*X^2*Z - X*Y*Z + 2*X*Z^2 + 2*Y*Z^2 - Z^3', 'H': 'Y^3*Z - 2*X^2*Y - 2*X*Y*Z + 2*Z^3'}
      anchor triple: ['2*x^8 + 3*x^7*y - 3*x^6*y^2 + 2*x^5*y^3 + x^4*y^4 - x^3*y^5 + 3*x^2*y^6 + x*y^7 - 3*y^8 + x^7*z - 3*x^6*y*z + 3*x^5*y^2*z + 3*x^4*y^3*z + x^3*y^4*z + x^2*y^5*z + 2*x*y^6*z + 2*y^7*z + 3*x^6*z^2 + x^5*y*z^2 - 2*x^4*y^2*z^2 - 2*x^3*y^3*z^2 - x^2*y^4*z^2 - 2*x*y^5*z^2 - y^6*z^2 + 3*x^5*z^3 + x^4*y*z^3 - 3*x^3*y^2*z^3 + 3*x*y^4*z^3 + 2*y^5*z^3 + x^3*y*z^4 + 3*x^2*y^2*z^4 + 3*x*y^3*z^4 + y^4*z^4 - 3*x^3*z^5 + x^2*y*z^5 + x*y^2*z^5 - 2*x^2*z^6 + 3*x*y*z^6 - x*z^7 - 2*y*z^7 + z^8 - 1/504*x^7 - 3*x^6*y - 2*x^5*y^2 - 2*x^4*y^3 + 3*x^3*y^4 - x^2*y^5 - 3*x*y^6 + 2*y^7 - 2*x^6*z - 3*x^5*y*z + 2*x^3*y^3*z - 3*x^2*y^4*z - x*y^5*z - y^6*z + 2*x^5*z^2 + 2*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - 2*y^5*z^2 + 2*x^4*z^3 - 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 2*y^4*z^3 + x^3*z^4 - y^3*z^4 + 2*x^2*z^5 + 3*x*y*z^5 - 3*y^2*z^5 + 3*x*z^6 - y*z^6 + 3*z^7 - x^5*y + 2*x^4*y^2 - x^3*y^3 - 3*x*y^5 + y^6 + 2*x^5*z - 2*x^4*y*z + x^3*y^2*z + 2*x^2*y^3*z + x*y^4*z + x^4*z^2 - x^2*y^2*z^2 - 3*x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 + x*y^2*z^3 - 3*y^3*z^3 - x*y*z^4 - y^2*z^4 + x*z^5 + 3*y*z^5 - 3*z^6 - 2*x^4*y + 3*x^2*y^3 - 2*x*y^4 + 1/12*y^5 + 3*x^4*z + x^3*y*z - 2*x^2*y^2*z - x*y^3*z + 3*y^4*z + 2*x^2*y*z^2 - 2*x*y^2*z^2 + 2*y^3*z^2 + 2*x^2*z^3 + 2*x*y*z^3 + 3*y^2*z^3 + 3*x*z^4 + y*z^4 - z^5 - 3*x^3*y - 2*x^2*y^2 - x*y^3 + x^3*z - x^2*y*z - x*y^2*z + 2/3*y^3*z - 3*x^2*z^2 - x*y*z^2 + 2*x*z^3 - 3*y*z^3 - 3*z^4 - x^2*y - x^2*z - 2*x*y*z - x*z^2 - 2*y*z^2 - z^3', 'x^8 + x^7*y - x^5*y^3 + 2*x^4*y^4 + 2*x^3*y^5 - x^2*y^6 + 2*x*y^7 + 3*y^8 + 3*x^6*y*z - 2*x^4*y^3*z + x^3*y^4*z + 3*x^2*y^5*z + 3*x*y^6*z + 2*y^7*z - 3*x^6*z^2 - x^5*y*z^2 + 2*x^2*y^4*z^2 - 2*x*y^5*z^2 + 3*y^6*z^2 + 2*x^5*z^3 - 2*x^3*y^2*z^3 + 3*x^2*y^3*z^3 + x*y^4*z^3 - 3*y^5*z^3 - 2*x^4*z^4 + 2*x^3*y*z^4 + 2*x*y^3*z^4 - y^4*z^4 - 3*x^2*y*z^5 + x*y^2*z^5 + y^3*z^5 - 3*x^2*z^6 - 3*x*y*z^6 - 2*y^2*z^6 + 3*y*z^7 - 3*z^8 - 13/5040*x^7 + 2*x^6*y + 2*x^5*y^2 + 2*x^4*y^3 - 3*x^3*y^4 - 2*x^2*y^5 + 2*x*y^6 + 3*y^7 + 2*x^6*z - 2*x^5*y*z + x^4*y^2*z + x^3*y^3*z - x^2*y^4*z + 3*x*y^5*z + y^6*z - 3*x^5*z^2 + 2*x^4*y*z^2 + 3*x^2*y^3*z^2 - x*y^4*z^2 + 3*y^5*z^2 - x^3*y*z^3 + 3*x^2*y^2*z^3 - 2*x*y^3*z^3 - y^4*z^3 + x^3*z^4 + 2*x*y^2*z^4 - 2*y^3*z^4 + 2*x*y*z^5 - 3*y^2*z^5 + x*z^6 + y*z^6 - z^7 - x^4*y^2 + x^3*y^3 + 3*x^2*y^4 + 3*y^6 - 2*x^5*z + 2*x^4*y*z + 2*x^3*y^2*z + 3*x^2*y^3*z - 3*y^5*z + 2*x^4*z^2 - 2*x^3*y*z^2 - x^2*y^2*z^2 + 2*x*y^3*z^2 + 2*y^4*z^2 + 3*x^3*z^3 - x^2*y*z^3 + x*y^2*z^3 + 2*y^3*z^3 + x^2*z^4 - 2*x*y*z^4 + 2*y*z^5 - 2*z^6 - 2*x^4*y + 2*x^3*y^2 - 11/120*y^5 + 3*x^3*y*z + x^2*y^2*z - x*y^3*z - y^4*z - 3*x^3*z^2 + 3*x*y^2*z^2 + 3*y^3*z^2 + 3*x^2*z^3 - 2*x*y*z^3 + y^2*z^3 - 2*x*z^4 - 2*y*z^4 - z^5 - x^3*y - 2*x*y^3 + 3*x^3*z + 3*x^2*y*z + 2*x*y^2*z + 3*y^3*z + x^2*z^2 + 2*x*y*z^2 + y^2*z^2 + 3*y*z^3 + z^4 + x^2*z - 3*x*y*z - 2*y*z^2 - 2*z^3', '2*x^8 - x^7*y - 2*x^6*y^2 + x^5*y^3 - 3*x^4*y^4 - 2*x^3*y^5 - 3*x^2*y^6 + 2*x*y^7 - 2*x^7*z - 3*x^6*y*z + 2*x^5*y^2*z + 3*x^4*y^3*z - x^3*y^4*z - 3*x^2*y^5*z + 2*x*y^6*z + 2*y^7*z + x^6*z^2 - 3*x^5*y*z^2 + 2*x^4*y^2*z^2 - x^3*y^3*z^2 + x^2*y^4*z^2 - 3*x*y^5*z^2 - 2*x^5*z^3 - x^4*y*z^3 + 2*x^3*y^2*z^3 + 3*x^2*y^3*z^3 - x*y^4*z^3 + 2*x^4*z^4 - 3*x^3*y*z^4 + 2*x*y^3*z^4 + 3*x^3*z^5 + 3*x*y^2*z^5 + 2*y^3*z^5 + 3*x*y*z^6 + 3*x*z^7 + 2*y*z^7 - 2*z^8 - 1/5040*x^7 - 3*x^6*y + 3*x^5*y^2 - x^4*y^3 - 2*x^3*y^4 - x^2*y^5 + y^7 - x^6*z + x^5*y*z - x^4*y^2*z + 3*x^2*y^4*z - 3*x*y^5*z - 2*x^5*z^2 - 3*x^3*y^2*z^2 + 3*x^2*y^3*z^2 + x*y^4*z^2 - y^5*z^2 - 2*x^4*z^3 + 3*x^3*y*z^3 + x^2*y^2*z^3 + x^3*z^4 + x^2*y*z^4 - y^3*z^4 - 2*x^2*z^5 + 2*x*y*z^5 + 3*y^2*z^5 + x*z^6 + 2*y*z^6 + z^7 + 2*x^5*y + 3*x^4*y^2 + x^2*y^4 + 2*x*y^5 + 2*y^6 + 2*x^5*z + 2*x^3*y^2*z - x^2*y^3*z + x*y^4*z + 3*y^5*z + x^4*z^2 + 2*x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*y^4*z^2 + 2*x^3*z^3 - x*y^2*z^3 - y^3*z^3 + x^2*z^4 + y^2*z^4 + 2*x*z^5 + y*z^5 - z^6 + 3*x^4*y - 2*x^3*y^2 - 2*x*y^4 + 41/120*y^5 + 2*x^4*z - 3*x^3*y*z + 3*x^2*y^2*z - 2*x*y^3*z + 3*y^4*z - y^3*z^2 + x*y*z^3 + 2*y^2*z^3 - x*z^4 + y*z^4 + z^5 - 2*x^3*y - 3*x^2*y^2 + 3*x*y^3 - 2*x^3*z - 3*x^2*y*z + 3*x*y^2*z - 23/3*y^3*z + 3*x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 - x*z^3 + 2*z^4 - 2*x^2*y - 3*x^2*z - x*y*z + x*z^2 - 3*y*z^2 + 3*z^3']
  ok   R2 L=Z, component W3 (P_060 = 0, linear): a point of the component (residual equations vanish)
      timing: member+triples 0.3 s, stabilization 0.1 s
  ok   R2 L=Z, component W3 (P_060 = 0, linear) anchor (A): fixed {'P_060': 0}, solved ['G_220', 'G_121', 'G_022']; member closed with H and the prescribed graded data: True; a triple of I of local length 34 (ds), stabilization (34, 10)
      anchor generators: {'P': 'X^7 + 2*Y^4*Z - 4*X^2*Y^2 - 8*X^2*Y*Z + 4*X*Y^2*Z + 16*X*Y*Z^2 + X^2*Y - X^2*Z + 2*X*Y*Z - 2*X*Z^2', 'G': 'Y^5 - 10*X^2*Y^2 + 40*X*Y^2*Z + 2*X^2*Z - 2*X*Y*Z + Y*Z^2 - 2*Z^3', 'H': 'Y^3*Z - X^2*Y - X^2*Z + X*Y*Z + 2*X*Z^2'}
      anchor triple: ['2*x^8 + x^7*y - 3*x^5*y^3 + x^4*y^4 + 3*x^3*y^5 - 3*x^2*y^6 + 2*x*y^7 - 2*y^8 - x^7*z + 2*x^6*y*z + 3*x^5*y^2*z - 3*x^4*y^3*z + 2*x^3*y^4*z - 3*x^2*y^5*z - 2*x*y^6*z - 3*x^6*z^2 - 2*x^5*y*z^2 - 3*x^4*y^2*z^2 - 3*x^3*y^3*z^2 - 2*x^2*y^4*z^2 - 2*x*y^5*z^2 + x^5*z^3 + x^4*y*z^3 + 2*x^3*y^2*z^3 + 3*x^2*y^3*z^3 + 2*x*y^4*z^3 + y^5*z^3 + 2*x^4*z^4 + 3*x^2*y^2*z^4 - 2*y^4*z^4 - 2*x^3*z^5 - 2*x^2*y*z^5 + x*y^2*z^5 + 3*y^3*z^5 - x*y*z^6 - 3*y^2*z^6 - 3*x*z^7 + y*z^7 - 2*z^8 - 89/2520*x^7 - 3*x^6*y - x^5*y^2 - 2*x^4*y^3 + 2*x^3*y^4 - x^2*y^5 - x*y^6 - 3*y^7 - 2*x^6*z + 3*x^5*y*z - x^4*y^2*z - x^3*y^3*z - x*y^5*z + 3*y^6*z - 2*x^5*z^2 - 3*x^4*y*z^2 + 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 - x*y^4*z^2 + y^5*z^2 - 2*x^3*y*z^3 - 2*x^2*y^2*z^3 - x*y^3*z^3 - 3*y^4*z^3 + 2*x^3*z^4 + 2*x^2*y*z^4 - 2*x*y^2*z^4 + 2*y^3*z^4 - 2*x^2*z^5 + x*y*z^5 + y^2*z^5 + 2*x*z^6 + y*z^6 - 2*z^7 - 1/105*x^6 - 2*x^5*y - 3*x^4*y^2 + 2*x^3*y^3 + 2*x^2*y^4 - x*y^5 - 3*y^6 + 2*x^5*z + 3*x^4*y*z + 2*x^3*y^2*z - 2*x*y^4*z + 3*y^5*z + 3*x^4*z^2 - 2*x*y^3*z^2 - x^3*z^3 + 2*x^2*y*z^3 - x*y^2*z^3 + 3*x^2*z^4 - 2*x*y*z^4 + 3*y^2*z^4 - x*z^5 + 3*y*z^5 + 3*x^4*y - x^3*y^2 + x^2*y^3 + 3*x*y^4 - 29/20*y^5 + 3*x^4*z - 2*x^3*y*z + 3*x*y^3*z + y^4*z - 2*x^3*z^2 - x*y^2*z^2 + y^3*z^2 - x*y*z^3 + y^2*z^3 - y*z^4 + 3*z^5 - 2*x^3*y - 2*x^2*y^2 - 3*x*y^3 - 5/3*y^4 + 2*x^3*z - x^2*y*z + x*y^2*z - 13/6*y^3*z + x^2*z^2 + 3*x*y*z^2 - y^2*z^2 - y*z^3 - z^4 - 3*x^2*y + 3*x^2*z + x*y*z + 3*x*z^2 + 2*y*z^2', '3*x^8 - 3*x^7*y - 3*x^6*y^2 - x^5*y^3 + 3*x^4*y^4 + 3*x^3*y^5 - x*y^7 + 3*x^7*z - x^6*y*z - 3*x^4*y^3*z - 3*x^2*y^5*z + 3*x*y^6*z - 3*y^7*z + 2*x^6*z^2 + x^5*y*z^2 - 3*x^4*y^2*z^2 + 2*x^3*y^3*z^2 + x^2*y^4*z^2 + 3*x*y^5*z^2 + 2*y^6*z^2 + 2*x^4*y*z^3 - 2*x^3*y^2*z^3 + 3*x^2*y^3*z^3 + x*y^4*z^3 + y^5*z^3 - 2*x^4*z^4 + 2*x^3*y*z^4 - 3*x^2*y^2*z^4 + 3*x*y^3*z^4 + 2*y^4*z^4 - x^3*z^5 - 3*x^2*y*z^5 + x*y^2*z^5 + 2*y^3*z^5 - 2*x^2*z^6 - 3*x*y*z^6 - y^2*z^6 + 3*x*z^7 - 3*y*z^7 - 3*z^8 - 43/1260*x^7 + x^6*y - x^5*y^2 - 3*x^4*y^3 - 3*x*y^6 - 3*y^7 - 3*x^6*z + 2*x^5*y*z + 3*x^4*y^2*z - 2*x^3*y^3*z - 3*x^2*y^4*z + x*y^5*z - 2*y^6*z - 3*x^5*z^2 + 2*x^4*y*z^2 - 2*x^3*y^2*z^2 + 3*x*y^4*z^2 + 3*y^5*z^2 - 2*x^4*z^3 + x^3*y*z^3 - x^2*y^2*z^3 - 2*x*y^3*z^3 + 3*y^4*z^3 - 2*x^3*z^4 + 2*x^2*y*z^4 + y^3*z^4 + 2*x^2*z^5 - 3*x*y*z^5 + y^2*z^5 + 2*x*z^6 + y*z^6 + 2*z^7 - 1/105*x^6 + x^5*y + 2*x^4*y^2 - 2*x^3*y^3 + x^2*y^4 - x*y^5 + y^6 - x^5*z - 3*x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z - x^4*z^2 - x^2*y^2*z^2 - 3*x*y^3*z^2 - 3*x^3*z^3 + 2*x^2*y*z^3 + y^3*z^3 + 3*x*y*z^4 - y^2*z^4 - x*z^5 - 2*z^6 - 2*x^3*y^2 - 3*x^2*y^3 - 3*x*y^4 - 23/15*y^5 - 3*x^4*z - x^3*y*z + 3*x^2*y^2*z - 3*x*y^3*z + 2*y^4*z - x^3*z^2 + 2*x^2*y*z^2 - 3*y^3*z^2 - x*y*z^3 + 2*y^2*z^3 + 3*x*z^4 - y*z^4 - 3*z^5 + x^3*y + x*y^3 - 2*y^4 - 3*x^3*z + x^2*y*z + 2*x*y^2*z - 3/2*y^3*z + 2*x^2*z^2 + 2*x*y*z^2 - y^2*z^2 + x*z^3 - 2*y*z^3 + 3*z^4 - 3*x^2*z + 3*x*y*z + 3*y*z^2 - 3*z^3', '-3*x^8 + 2*x^7*y + 3*x^6*y^2 - 2*x^5*y^3 - x^4*y^4 + 2*x^2*y^6 - 3*x*y^7 + 3*y^8 - 3*x^7*z + 3*x^6*y*z - 2*x^5*y^2*z - 2*x^4*y^3*z - x^3*y^4*z - x^2*y^5*z + x*y^6*z - 3*y^7*z + x^3*y^3*z^2 - 3*x^2*y^4*z^2 - 2*x^5*z^3 + 2*x^3*y^2*z^3 - 3*x*y^4*z^3 - 3*y^5*z^3 - 3*x^3*y*z^4 - x^2*y^2*z^4 - 3*x*y^3*z^4 - 2*y^4*z^4 + 3*x^3*z^5 - x^2*y*z^5 + 3*x*y^2*z^5 + y^3*z^5 + x^2*z^6 + 2*x*z^7 + 3*y*z^7 + z^8 + 53/2520*x^7 + 2*x^5*y^2 + 2*x^4*y^3 - 3*x^3*y^4 + x^2*y^5 - x*y^6 - 2*y^7 + 2*x^5*y*z - 3*x^4*y^2*z + 2*x^3*y^3*z - 3*x*y^5*z - 2*y^6*z - x^5*z^2 - x^4*y*z^2 + 2*x^3*y^2*z^2 - 3*x^2*y^3*z^2 + 3*x^4*z^3 - 3*x^3*y*z^3 + 3*x^2*y^2*z^3 - 3*x*y^3*z^3 + 2*y^4*z^3 + 2*x^3*z^4 - 3*x^2*y*z^4 + 2*x*y^2*z^4 - 3*x^2*z^5 + 3*x*y*z^5 - 2*y^2*z^5 - x*z^6 + y*z^6 + z^7 - 1/45*x^6 + x^5*y + x^4*y^2 - 2*x^3*y^3 - 3*x*y^5 + 2*y^6 - x^5*z - x^4*y*z - x^3*y^2*z - x^2*y^3*z + x*y^4*z - y^5*z + 3*x^4*z^2 - 3*x^3*y*z^2 - 3*x*y^3*z^2 + y^4*z^2 + x^3*z^3 + x^2*y*z^3 - 3*y^3*z^3 - x^2*z^4 + 3*x*y*z^4 - 3*x*z^5 + 3*y*z^5 + z^6 + x^4*y - 3*x^3*y^2 - 2*x^2*y^3 - 2*x*y^4 + 3/20*y^5 + 2*x^3*y*z - 2*x^2*y^2*z - 2*x*y^3*z - x^3*z^2 + 2*x*y^2*z^2 - y^3*z^2 - 2*x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 + x*z^4 + y*z^4 + 3*z^5 + 2*x^3*y + 3*x*y^3 + 5/3*y^4 + 2*x^3*z - 5/6*y^3*z + 2*x^2*z^2 - 3*x*y*z^2 - y^2*z^2 - 2*x*z^3 - y*z^3 - x^2*y - x^2*z - 3*x*y*z + x*z^2 + 2*y*z^2 + 2*z^3']
time 10.0 s
anchor lengths: {'R3 L=Y': [40, 39, 37], 'R3 L=Z': [40, 39, 37], 'R2 L=X': [39, 39, 39], 'R2 L=Z': [39, 39, 34]}
ALL CHECKS PASSED
