=== R5: B = V(y^2, z^2) (local ideal (u^2,w^2) at [X]); D_3 = <X^3,X^2Y,X^2Z,XYZ>, D_4 = X^3 T_1, D_5 = <X^5, X^4 l>, l in {Y, Y+Z}
  ok   R5: nu_3(V(y^2,z^2)) = <X^3, X^2Y, X^2Z, XYZ>
--- R5 l=Y
  ok   R5 l=Y: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R5 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:
       (-15/4) * G_130 * (2*P_501 - 7*G_211)
       (105) * G_130 * G_202
       (1/252) * (-210*P_501*G_220*G_130 + 105*P_510*G_211*G_130 + 120*P_501^2*H_030 - 40*P_510*P_501*H_021 - 63*P_311*G_130 + 4410*G_130*G_021 - 504*P_302*H_030 + 84*P_311*H_021)
       (1/84) * (-105*P_501*G_211*G_130 + 210*P_510*G_202*G_130 + 40*P_501^2*H_021 - 40*P_510*P_501*H_012 + 4410*G_130*G_012 - 168*P_302*H_021 + 84*P_311*H_012)
       (1/42) * (-105*P_501*G_202*G_130 + 20*P_501^2*H_012 - 60*P_510*P_501*H_003 + 6615*G_130*G_003 - 84*P_302*H_012 + 126*P_311*H_003)
       (-15/14) * G_130 * (2*P_501 - 7*G_211)
  ok   R5 l=Y: on {G_130 != 0} the residual equations are triangular in ['G_211', 'G_202', 'G_021', 'G_012', 'G_003'] with diagonal (const)*G_130: a graph (irreducible)
  ok   R5 l=Y: on {G_130 = 0}: equations M(beta, gamma) H = 0 with beta = 5*P_501^2 - 21*P_302, gamma = -10*P_510*P_501 + 21*P_311, rows [[10/21*P_501^2 - 2*P_302, -10/63*P_510*P_501 + 1/3*P_311, 0, 0], [0, 10/21*P_501^2 - 2*P_302, -10/21*P_510*P_501 + P_311, 0], [0, 0, 10/21*P_501^2 - 2*P_302, -10/7*P_510*P_501 + 3*P_311]]; M has rank 3 exactly on (beta, gamma) != (0, 0) (its 3x3 minors, with B = beta and G = gamma, are ['(1/9261) * G^3', '(2/3087) * B * G^2', '(4/3087) * G * B^2', '(8/9261) * B^3'] and generate an ideal containing beta^3 and gamma^3); components {beta = gamma = 0} and the closure of the kernel line bundle over {(beta,gamma) != 0}
  ok   R5 l=Y, component W1 (G_130 != 0): a point of the component (residual equations vanish)
      timing: member+triples 0.6 s, stabilization 0.1 s
  ok   R5 l=Y, component W1 (G_130 != 0) anchor (A): fixed {'G_130': 1}, solved ['G_211', 'G_202', 'G_021', 'G_012', 'G_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 36 (ds), stabilization (36, 11)
      anchor generators: {'P': 'X^7 + 105/4*X^4*Y^2 + 105/8*X*Y^4 + 35/2*X*Y^3 - 105/8*Y^4 + 105/2*X*Y*Z^2 + X*Y^2 - Y^3 + 2*Y^2*Z + X*Z^2 + Y*Z^2 - Z^3', 'G': 'X^4*Y + X*Y^3 + X*Y^2 - Y^3 + X*Z^2', 'H': 'X^3*Z + X*Y^2 + Y^2*Z + 2*Y*Z^2 - Z^3'}
      anchor triple: ['3*x^8 + 2*x^7*y - x^6*y^2 + x^5*y^3 - 2*x^4*y^4 + 2*x^3*y^5 + y^8 - 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^2*y^5*z - x*y^6*z - 3*x^6*z^2 - x^5*y*z^2 - 2*x^4*y^2*z^2 - x^3*y^3*z^2 - 3*x^2*y^4*z^2 - 3*y^6*z^2 + 2*x^5*z^3 + x^4*y*z^3 + x^3*y^2*z^3 + 3*x^2*y^3*z^3 - x*y^4*z^3 + 2*y^5*z^3 - x^4*z^4 - 2*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 + 2*x*y^2*z^5 - x^2*z^6 + 2*y^2*z^6 + 2*x*z^7 + 2*y*z^7 - 3*z^8 + 527/5040*x^7 + 3*x^4*y^3 - 2*x^3*y^4 + x^2*y^5 - x*y^6 + y^7 - 2*x^6*z + 3*x^5*y*z - 2*x^3*y^3*z + 2*x^2*y^4*z - x*y^5*z + 3*x^5*z^2 - x^3*y^2*z^2 + 3*x^2*y^3*z^2 - x*y^4*z^2 + 2*y^5*z^2 + 2*x^4*z^3 - x^2*y^2*z^3 + 3*y^4*z^3 + 3*x^2*y*z^4 - 2*x*y^2*z^4 + y^3*z^4 - 3*x^2*z^5 + x*y*z^5 - 2*x*z^6 + y*z^6 + z^7 + 43/48*x^6 - 2*x^5*y - x^4*y^2 - x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 - 2*y^6 + x^5*z - 3*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 - 2*x*y^3*z^2 - y^4*z^2 + 3*x^3*z^3 - 2*x^2*y*z^3 - 2*x*y^2*z^3 - 3*x^2*z^4 + 3*x*y*z^4 + x*z^5 - 3*y*z^5 - 3*z^6 + 1/2*x^5 + 1/12*x^4*y - 3*x^3*y^2 - 2*x^2*y^3 - y^5 - 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 - 2*x^2*z^3 - 3*x*y*z^3 + x*z^4 - 3*y*z^4 + 2*z^5 - 1/2*x^4 - 1/4*x^3*y - 2*x^2*y^2 - x*y^3 - 3*y^4 + 1/3*x^3*z - 3*x^2*y*z + 3*x*y^2*z + 3*y^3*z - 2*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 - 3*x*z^3 + y*z^3 + 3*z^4 + 2*x*y^2 + y^3 + y^2*z + 3*x*z^2 + y*z^2 + 2*z^3', 'x^7*y + 2*x^6*y^2 + x^4*y^4 + 3*x^3*y^5 + 2*x^2*y^6 - 3*x*y^7 - 2*y^8 + 2*x^7*z + 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 - 3*x*y^6*z - x^6*z^2 - 2*x^5*y*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 + 3*x^4*y*z^3 + 3*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 + x^3*y*z^4 + 2*x^2*y^2*z^4 + 3*x*y^3*z^4 - 2*y^4*z^4 + 2*x^3*z^5 + 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 + y^2*z^6 + 3*x*z^7 + 3*y*z^7 + 229/504*x^7 + 2*x^6*y + 3*x^5*y^2 - x^4*y^3 + 3*x^3*y^4 + x^2*y^5 + 3*x*y^6 + y^7 - 3*x^6*z - 2*x^3*y^3*z - 3*x^2*y^4*z - 3*x*y^5*z - y^6*z - 2*x^5*z^2 - x^4*y*z^2 + 2*x^2*y^3*z^2 + x*y^4*z^2 + 2*y^5*z^2 + 3*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 + x^3*z^4 - y^3*z^4 + 2*x^2*z^5 + 2*x*y*z^5 + 3*y^2*z^5 - 2*x*z^6 - 3*z^7 + 7/48*x^6 - x^5*y - x^4*y^2 + 2*x^3*y^3 + 3*x^2*y^4 - 2*x*y^5 - y^6 - 2*x^3*y^2*z + 3*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 - x^3*z^3 - x*y^2*z^3 - 2*y^3*z^3 - x^2*z^4 + 2*y^2*z^4 + 3*x*z^5 + 2*z^6 - 1/2*x^5 + 5/12*x^4*y - x^3*y^2 - x^2*y^3 - 2*x*y^4 + 2*y^5 + 3*x^4*z + 2*x^3*y*z - x^2*y^2*z + 3*x*y^3*z + y^4*z + 3*x^3*z^2 - x^2*y*z^2 + 3*y^3*z^2 - 2*x^2*z^3 + x*y*z^3 - 2*y^2*z^3 + 2*y*z^4 + 3*z^5 - 1/2*x^4 + 1/4*x^3*y + 2*x^2*y^2 - 3*x*y^3 + y^4 - 14/3*x^3*z + 2*x^2*y*z + 2*x*y^2*z - 3*y^3*z + 2*x^2*z^2 + 2*x*y*z^2 - 2*y^2*z^2 - x*z^3 + 2*z^4 + 2*x*y^2 - y^3 - 3*y^2*z - x*z^2 + 3*y*z^2 - 3*z^3', '-3*x^8 - x^7*y - 3*x^6*y^2 + x^5*y^3 - 2*x^4*y^4 + x^3*y^5 + x*y^7 + 3*x^7*z - 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 - 3*x*y^6*z + 3*y^7*z - x^6*z^2 + 3*x^5*y*z^2 - x^4*y^2*z^2 + x^2*y^4*z^2 + 2*x*y^5*z^2 + 2*y^6*z^2 + 3*x^5*z^3 - 3*x^4*y*z^3 - 2*x^3*y^2*z^3 + 2*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 + x*y^3*z^4 - 3*y^4*z^4 - 2*x^3*z^5 - x^2*y*z^5 - y^3*z^5 + x^2*z^6 - 2*x*y*z^6 + x*z^7 + y*z^7 - 3*z^8 - 2209/5040*x^7 + x^6*y - 2*x^5*y^2 + 2*x^4*y^3 + 3*x^2*y^5 - 3*x*y^6 + 2*y^7 - x^6*z - 2*x^5*y*z - x^3*y^3*z + 2*x^2*y^4*z + 3*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 - 3*x*y^4*z^2 + y^5*z^2 + x^4*z^3 - 2*x^3*y*z^3 + 2*x^2*y^2*z^3 + x*y^3*z^3 + 3*x^3*z^4 + x^2*y*z^4 + x*y^2*z^4 - 3*y^3*z^4 - 3*x^2*z^5 - 2*x*y*z^5 - y^2*z^5 + 3*x*z^6 + 3*z^7 - 5/6*x^6 - 3*x^5*y + 2*x^4*y^2 - 3*x^3*y^3 - x*y^5 - 3*y^6 - x^4*y*z - 3*x^3*y^2*z + 3*x^2*y^3*z + 3*x*y^4*z - y^5*z - x^4*z^2 + 3*x^3*y*z^2 + 3*x^2*y^2*z^2 + x*y^3*z^2 - y^4*z^2 - 3*x^3*z^3 - 3*x^2*y*z^3 - 2*x*y^2*z^3 - 2*x^2*z^4 + x*y*z^4 + 3*y^2*z^4 + 2*y*z^5 - 3*z^6 - 1/4*x^5 + 13/12*x^4*y + 3*x^3*y^2 - 2*x^2*y^3 + 2*x*y^4 + 3*y^5 + 3*x^4*z + 3*x^3*y*z - 2*x^2*y^2*z - 2*x*y^3*z + 3*x^3*z^2 - 3*x^2*y*z^2 + 3*x*y^2*z^2 + y^3*z^2 + 3*x^2*z^3 - x*y*z^3 - 2*y^2*z^3 - 2*x*z^4 - y*z^4 + 2*z^5 - 1/4*x^3*y + x^2*y^2 - 3*x*y^3 + y^4 - 2*x^3*z + 2*x^2*y*z + y^3*z - x^2*z^2 - 3*x*y*z^2 - 3*y^2*z^2 - 2*x*z^3 + z^4 + y^3 - x*z^2 - 2*z^3']
  ok   R5 l=Y, component W2 (G_130 = 0, beta = gamma = 0): a point of the component (residual equations vanish)
      timing: member+triples 0.8 s, stabilization 0.8 s
  ok   R5 l=Y, component W2 (G_130 = 0, beta = gamma = 0) anchor (A): fixed {'G_130': 0}, solved ['P_302', 'P_311']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 14)
      anchor generators: {'P': 'X^7 - Y^3 - 2*X*Z^2 - Z^3', 'G': 'X^4*Y + 2*Y^2*Z - 2*X*Z^2 - Y*Z^2 + 2*Z^3', 'H': 'X^3*Z + X*Y^2 + Y^3 - Y^2*Z + X*Z^2 + Y*Z^2 - Z^3'}
      anchor triple: ['-x^8 - x^7*y - 2*x^5*y^3 + 3*x^4*y^4 - 2*x^3*y^5 + 3*x*y^7 - 2*y^8 + x^7*z + 2*x^5*y^2*z - x^4*y^3*z - 2*x^3*y^4*z + 3*x^2*y^5*z - x*y^6*z - 2*x^5*y*z^2 - 3*x^3*y^3*z^2 + x*y^5*z^2 + 2*y^6*z^2 + 3*x^5*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 - 3*x^2*y^2*z^4 - 3*x*y^3*z^4 - 3*y^4*z^4 - 3*x^3*z^5 + 2*x^2*y*z^5 - 3*x*y^2*z^5 + y^3*z^5 + 3*x^2*z^6 - x*y*z^6 - 2*x*z^7 - y*z^7 - 3*z^8 + 1/2520*x^7 - x^6*y + 2*x^5*y^2 - x^4*y^3 + 3*x^3*y^4 - 2*x^2*y^5 + 3*x*y^6 - 2*y^7 - 2*x^6*z + 2*x^5*y*z - x^3*y^3*z - x*y^5*z + 3*y^6*z - x^5*z^2 + 3*x^4*y*z^2 - x^3*y^2*z^2 - 2*x^2*y^3*z^2 + 2*x*y^4*z^2 + 2*y^5*z^2 - x^4*z^3 + x^3*y*z^3 + x^2*y^2*z^3 - 3*x*y^3*z^3 - 3*y^4*z^3 + 3*x^3*z^4 + 2*x*y^2*z^4 + y^3*z^4 + 3*x^2*z^5 + x*y*z^5 - 2*y^2*z^5 + 3*x*z^6 - 2*y*z^6 - z^7 + 3*x^5*y - 2*x^3*y^3 - x^2*y^4 + 2*x*y^5 - 3*y^6 - 3*x^5*z + 2*x*y^4*z + 2*y^5*z - 2*x^4*z^2 - 2*x^3*y*z^2 + x^2*y^2*z^2 + x*y^3*z^2 - 2*y^4*z^2 + 2*x^3*z^3 + 2*x^2*y*z^3 + y^3*z^3 + 3*x^2*z^4 - y^2*z^4 + 3*x*z^5 - y*z^5 + 2/3*x^4*y + 3*x^3*y^2 - x^2*y^3 - 2*x*y^4 + x^4*z + 3*x^3*y*z + 3*x*y^3*z - 2*y^4*z - 2*x^3*z^2 - 2*x^2*y*z^2 - 2*x*y^2*z^2 + y^3*z^2 + 2*x^2*z^3 - 2*x*y*z^3 + 3*y^2*z^3 + x*z^4 + y*z^4 + z^5 - 3*x^2*y^2 - 3*x*y^3 + y^4 - 5*x^3*z + 2*x^2*y*z + x*y^2*z - 3*y^3*z - 3*x^2*z^2 - 2*y^2*z^2 + x*z^3 + y*z^3 - z^4 + x*y^2 + 3*y^3 + 2*y^2*z - x*z^2 + 2*y*z^2 - 2*z^3', '-3*x^8 + x^7*y - x^6*y^2 - x^4*y^4 - 3*x^3*y^5 + 3*x^2*y^6 - 3*x*y^7 - y^8 - 3*x^7*z - x^6*y*z - x^5*y^2*z + x^4*y^3*z + 3*x^3*y^4*z + x^2*y^5*z + 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 - 3*x^2*y^4*z^2 + 3*x*y^5*z^2 - y^6*z^2 + x^5*z^3 - 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 - 2*y^5*z^3 + x^4*z^4 + 3*x^3*y*z^4 + 2*x^2*y^2*z^4 - x*y^3*z^4 + 2*y^4*z^4 - 2*x^3*z^5 - 3*x^2*y*z^5 - 3*x*y^2*z^5 - 3*y^3*z^5 + 3*x^2*z^6 + 2*x*y*z^6 - 2*y^2*z^6 + x*z^7 + 3*y*z^7 + 3*z^8 - x^6*y + x^5*y^2 - 2*x^4*y^3 + 2*x^2*y^5 - x*y^6 - 2*y^7 - 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*x*y^5*z + y^6*z + 2*x^5*z^2 - x^4*y*z^2 - 2*x^3*y^2*z^2 + x^2*y^3*z^2 + x*y^4*z^2 - x^4*z^3 - x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*x*y^3*z^3 + y^4*z^3 + x^3*z^4 + 2*x^2*y*z^4 + y^3*z^4 + 3*x^2*z^5 - 3*x*z^6 - 3*y*z^6 - 2*z^7 + 2*x^5*y - x^4*y^2 + 3*x^3*y^3 + x*y^5 - y^6 + 2*x^5*z - 3*x^4*y*z + x^3*y^2*z - x^2*y^3*z - x*y^4*z + y^5*z - x^4*z^2 + x^2*y^2*z^2 + y^4*z^2 + 3*x^3*z^3 + 3*x^2*y*z^3 - 3*x*y^2*z^3 - 2*y^3*z^3 + x*y*z^4 - 3*y^2*z^4 - x*z^5 + 2*y*z^5 - 2*z^6 + x^4*y - 3*x^3*y^2 - 2*x^2*y^3 + 2*x*y^4 - y^5 + 2*x^4*z + 2*x^3*y*z - x^2*y^2*z + 3*x*y^3*z - y^4*z + 3*x^3*z^2 - 3*x^2*y*z^2 + 3*x*y^2*z^2 + 3*y^3*z^2 + 3*x*y*z^3 + y^2*z^3 + 3*x*z^4 - y*z^4 + 3*z^5 - x^2*y^2 + 2*x*y^3 + 3*y^4 - 2/3*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 + 2*x*z^3 + 2*y*z^3 - 2*z^4 + 2*x*y^2 - 2*y^3 - 3*y^2*z + 3*x*z^2', '-3*x^8 - 2*x^7*y + 3*x^6*y^2 - x^5*y^3 - x^4*y^4 - 2*x^3*y^5 + 2*x^2*y^6 - 2*y^8 + 2*x^7*z - 3*x^6*y*z - 3*x^5*y^2*z - 3*x^4*y^3*z + 3*x^3*y^4*z + x*y^6*z - 2*y^7*z + x^6*z^2 - x^5*y*z^2 + 2*x^4*y^2*z^2 - 3*x^2*y^4*z^2 + 2*x*y^5*z^2 - 2*y^6*z^2 - x^5*z^3 + 3*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 - 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 - x*y^2*z^5 - 2*y^3*z^5 - 3*x^2*z^6 - x*y*z^6 + x*z^7 + 3*y*z^7 - 2*z^8 - 1/420*x^7 + x^6*y - x^5*y^2 - 2*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^4*y^2*z - 2*x^3*y^3*z + x^2*y^4*z + 2*x*y^5*z + 3*y^6*z + 3*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 + 2*x^4*z^3 + x^2*y^2*z^3 + 2*y^4*z^3 - 2*x^3*z^4 - x^2*y*z^4 - x*y^2*z^4 + y^3*z^4 + 3*x^2*z^5 + 3*x*y*z^5 - 2*y^2*z^5 + 2*y*z^6 - 2*z^7 + 2*x^5*y + 2*x^4*y^2 + 3*x^3*y^3 + x^2*y^4 - x*y^5 + 2*y^6 - 3*x^5*z + x^4*y*z - x^3*y^2*z + 3*x^2*y^3*z + x*y^4*z + 3*y^5*z - 2*x^4*z^2 - x^3*y*z^2 - 2*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 - y^3*z^3 - 2*x^2*z^4 - y^2*z^4 + x*z^5 - y*z^5 + 2*z^6 - 1/12*x^4*y - x*y^4 + 2*y^5 + x^4*z - x^3*y*z - x^2*y^2*z + 3*y^4*z + 3*x^2*y*z^2 + 2*x*y^2*z^2 - 3*y^3*z^2 + 3*x^2*z^3 + x*y*z^3 + y^2*z^3 + y*z^4 - 3*z^5 + x^2*y^2 + 3*x*y^3 - y^4 + 3*x^3*z + 3*x^2*y*z + 2*y^3*z - x^2*z^2 + 3*y^2*z^2 - 3*x*z^3 - 2*y*z^3 - 2*z^4 - x*y^2 - 2*y^3 - y^2*z - 3*y*z^2']
  ok   R5 l=Y, component W3 (G_130 = 0, H in the kernel): a point of the component (residual equations vanish)
      timing: member+triples 0.3 s, stabilization 0.1 s
  ok   R5 l=Y, component W3 (G_130 = 0, H in the kernel) anchor (A): fixed {'G_130': 0}, solved ['H_021', 'H_012', 'H_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 35 (ds), stabilization (35, 10)
      anchor generators: {'P': 'X^7 + 2*X^5*Y + 2*X^5*Z - X^3*Y^2 - 2/21*X*Y^3 - 10/21*Y^4 - 2/7*X*Y^2*Z - 40/21*Y^3*Z - 20/7*Y^2*Z^2 - 40/21*Y*Z^3 - 10/21*Z^4 - X*Y^2 - 2*Y^3 + 2*Y^2*Z - 2*X*Z^2 + 2*Z^3', 'G': 'X^4*Y - X*Y^2 - 2*Y^3 - 2*Y^2*Z - Y*Z^2 - 2*Z^3', 'H': 'X^3*Z + Y^3 + 3*Y^2*Z + 3*Y*Z^2 + Z^3'}
      anchor triple: ['-x^8 + x^6*y^2 - 2*x^5*y^3 + 2*x^4*y^4 + 3*x^3*y^5 + x^2*y^6 - 3*x*y^7 + 3*y^8 + x^6*y*z - 2*x^5*y^2*z - 3*x^4*y^3*z + 2*x^3*y^4*z - 3*x^2*y^5*z + 3*y^7*z - 3*x^6*z^2 - 2*x^5*y*z^2 - 3*x^4*y^2*z^2 - x^3*y^3*z^2 + x^2*y^4*z^2 - 3*x*y^5*z^2 + 3*x^5*z^3 + x^4*y*z^3 - x^2*y^3*z^3 - y^5*z^3 + 2*x^4*z^4 + x^2*y^2*z^4 + 3*x*y^3*z^4 + 3*y^4*z^4 - 3*x^3*z^5 - 3*x^2*y*z^5 - 2*x*y^2*z^5 + 2*x^2*z^6 + 3*x*y*z^6 + 2*y^2*z^6 - x*z^7 + 3*y*z^7 + 3*z^8 + 799/17640*x^7 + 2*x^5*y^2 - x^4*y^3 - x^3*y^4 + 3*x^2*y^5 - 3*x*y^6 - 2*y^7 + 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 - 3*x*y^5*z + 2*y^6*z - 2*x^5*z^2 - 3*x^4*y*z^2 + 2*x^3*y^2*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 - x*y^3*z^3 - x^3*z^4 + x^2*y*z^4 + x*y^2*z^4 - y^3*z^4 - 2*x^2*z^5 + x*y*z^5 + 3*x*z^6 + 2*y*z^6 + 3*z^7 - 179/1764*x^6 + 2*x^5*y + 2*x^4*y^2 + 3*x^3*y^3 - x^2*y^4 + 3*y^6 - 3*x^5*z - 3*x^3*y^2*z - 2*x^2*y^3*z + 2*x*y^4*z - 2*y^5*z + x^4*z^2 - x^3*y*z^2 - x^2*y^2*z^2 - 3*x*y^3*z^2 - 3*y^4*z^2 - 2*x^2*y*z^3 + 2*x*y^2*z^3 + y^3*z^3 - x^2*z^4 - 2*y^2*z^4 - x*z^5 - z^6 - 19/420*x^5 + 13/12*x^4*y + 2*x^2*y^3 + 3*x*y^4 + y^5 + x^4*z + 3*x^3*y*z - x^2*y^2*z + x*y^3*z - 3*y^4*z + 2*x^3*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 + y^2*z^3 + 2*x*z^4 - 3*z^5 - x^2*y^2 - x*y^3 - 3*y^4 + x^3*z + x*y^2*z + 2*y^3*z + 3*x^2*z^2 - 2*x*y*z^2 + y^2*z^2 + 3*x*z^3 - y*z^3 - 3*z^4 + x*y^2 + 3*y^3 - 2*y^2*z - 3*x*z^2 - 2*y*z^2', 'x^8 - 3*x^7*y + x^6*y^2 + 3*x^5*y^3 + x^4*y^4 + x^3*y^5 + x*y^7 + 3*y^8 + 3*x^7*z + x^6*y*z + 2*x^5*y^2*z + 2*x^4*y^3*z - 3*x^3*y^4*z - 3*x^2*y^5*z - 2*x*y^6*z - 2*y^7*z + x^6*z^2 + x^5*y*z^2 - 3*x^4*y^2*z^2 - 3*x^3*y^3*z^2 + x^2*y^4*z^2 + y^6*z^2 + x^5*z^3 - x^3*y^2*z^3 - x^2*y^3*z^3 - 2*x*y^4*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 - 3*y^4*z^4 - 2*x^3*z^5 - x^2*y*z^5 - 2*x*y^2*z^5 - 3*y^3*z^5 + 3*x^2*z^6 + 3*x*y*z^6 - 2*y^2*z^6 + 3*x*z^7 - 3*y*z^7 + 3*z^8 - 655/3528*x^7 + x^6*y - x^5*y^2 + x^4*y^3 - 2*x^3*y^4 + 3*x^2*y^5 - x*y^6 - 2*y^7 + 3*x^5*y*z + 3*x^4*y^2*z + x^3*y^3*z - x^2*y^4*z - x*y^5*z - y^6*z - 3*x^5*z^2 + x^4*y*z^2 + 3*x^3*y^2*z^2 - 3*x^2*y^3*z^2 + x*y^4*z^2 - 3*y^5*z^2 + 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + y^4*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 + 3*x*y*z^5 + x*z^6 + y*z^6 + z^7 - 937/4410*x^6 + 3*x^5*y + 2*x^4*y^2 + x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 + x^5*z + x^4*y*z + 3*x^3*y^2*z + 3*x^2*y^3*z - 2*x*y^4*z + 2*x^3*y*z^2 + 2*x^2*y^2*z^2 - 3*x*y^3*z^2 + 3*y^4*z^2 - x^3*z^3 - x^2*y*z^3 - y^3*z^3 - x^2*z^4 + 3*x*y*z^4 - 3*x*z^5 + 3*y*z^5 + 3*z^6 + 79/420*x^5 + 17/12*x^4*y + x^3*y^2 - 2*x*y^4 - y^5 + 3*x^4*z - 2*x^3*y*z - x^2*y^2*z + x*y^3*z - 3*y^4*z + 3*x^3*z^2 - 2*x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 - 3*x*y*z^3 - y^2*z^3 + 3*y*z^4 - 2*z^5 - x^2*y^2 - 3*x*y^3 + 3*y^4 - 4*x^3*z + 3*x^2*y*z - 2*x*y^2*z - y^3*z - x*y*z^2 - 3*y^2*z^2 - 3*x*z^3 - 2*y*z^3 + z^4 - x*y^2 + 3*y^3 - y^2*z + 2*y*z^2', '-2*x^8 + x^7*y - x^6*y^2 + x^5*y^3 - 2*x^4*y^4 - 3*x^3*y^5 + 3*x^2*y^6 - 2*y^8 + x^7*z - x^4*y^3*z + 2*x^3*y^4*z + 3*x^2*y^5*z - x*y^6*z - y^7*z - x^6*z^2 - 3*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 - 2*x^2*y^3*z^3 + 2*x*y^4*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 + 3*x*y*z^6 - 2*y^2*z^6 - 2*x*z^7 + 2*y*z^7 - z^8 + 1723/17640*x^7 - x^6*y + 3*x^5*y^2 - 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^4*y^2*z + 2*x^3*y^3*z + 2*x^2*y^4*z + 3*y^6*z - x^5*z^2 + 3*x^4*y*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 - 3*x*y^3*z^3 + 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 + 3*x*y*z^5 + y^2*z^5 - 3*x*z^6 + y*z^6 - 2*z^7 + 751/4410*x^6 - x^4*y^2 - 3*x^3*y^3 - 3*x^2*y^4 - x*y^5 + y^6 - 2*x^5*z - x^4*y*z + x^3*y^2*z + 3*x*y^4*z + y^5*z - 3*x^4*z^2 - 3*x^3*y*z^2 - x*y^3*z^2 + x^3*z^3 - 3*x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 + x^2*z^4 - 2*x*y*z^4 + 2*y^2*z^4 - 3*x*z^5 + 3*y*z^5 - z^6 - 39/140*x^5 - 19/12*x^4*y + 3*x^3*y^2 - 2*x^2*y^3 - 3*x*y^4 + 2*y^5 - 2*x^4*z + 3*x^3*y*z - 3*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 - 3*x*y^2*z^2 - 3*y^3*z^2 - x^2*z^3 - 3*x*y*z^3 + 3*y^2*z^3 + y*z^4 - z^5 - 2*x*y^3 - 2*y^4 + 6*x^3*z - 2*x*y^2*z + 2*y^3*z + 3*x^2*z^2 + 2*x*y*z^2 + 2*y^2*z^2 + 2*x*z^3 - y*z^3 - 2*z^4 + 3*x*y^2 - 2*y^3 - y^2*z - 2*x*z^2 - 2*y*z^2 - z^3']
--- R5 l=Y+Z
  ok   R5 l=Y+Z: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R5 l=Y+Z: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 57 eliminated with constant pivots; residual equations:
       (-15/4) * (-2*P_510 + 2*P_501 + 14*G_220 - 7*G_211) * G_103
       (-15/2) * (-2*P_510 + 2*P_501 + 7*G_211 - 14*G_202) * G_103
       (1/252) * (-210*P_501*G_220*G_103 + 105*P_510*G_211*G_103 - 120*P_510*P_501*H_030 + 120*P_501^2*H_030 + 40*P_510^2*H_021 - 40*P_510*P_501*H_021 + 126*P_320*G_103 - 63*P_311*G_103 - 13230*G_103*G_030 + 4410*G_103*G_021 + 252*P_311*H_030 - 504*P_302*H_030 - 168*P_320*H_021 + 84*P_311*H_021)
       (1/84) * (-105*P_501*G_211*G_103 + 210*P_510*G_202*G_103 - 40*P_510*P_501*H_021 + 40*P_501^2*H_021 + 40*P_510^2*H_012 - 40*P_510*P_501*H_012 + 126*P_320*G_103 - 63*P_311*G_103 - 4410*G_103*G_021 + 4410*G_103*G_012 + 84*P_311*H_021 - 168*P_302*H_021 - 168*P_320*H_012 + 84*P_311*H_012)
       (1/84) * (-30*P_510^2*G_103 + 30*P_510*P_501*G_103 + 210*P_510*G_202*G_103 - 210*P_501*G_202*G_103 - 40*P_510*P_501*H_012 + 40*P_501^2*H_012 + 120*P_510^2*H_003 - 120*P_510*P_501*H_003 + 126*P_320*G_103 - 63*P_311*G_103 - 4410*G_103*G_012 + 13230*G_103*G_003 + 84*P_311*H_012 - 168*P_302*H_012 - 504*P_320*H_003 + 252*P_311*H_003)
       (-15/14) * (-2*P_510 + 2*P_501 + 14*G_220 - 7*G_211) * G_103
  ok   R5 l=Y+Z: on {G_103 != 0} the residual equations are triangular in ['G_211', 'G_202', 'G_030', 'G_012', 'G_003'] with diagonal (const)*G_103: a graph (irreducible)
  ok   R5 l=Y+Z: on {G_103 = 0}: equations M(beta, gamma) H = 0 with beta = -10*P_510*P_501 + 10*P_501^2 + 21*P_311 - 42*P_302, gamma = 10*P_510^2 - 10*P_510*P_501 - 42*P_320 + 21*P_311, rows [[-10/21*P_510*P_501 + 10/21*P_501^2 + P_311 - 2*P_302, 10/63*P_510^2 - 10/63*P_510*P_501 - 2/3*P_320 + 1/3*P_311, 0, 0], [0, -10/21*P_510*P_501 + 10/21*P_501^2 + P_311 - 2*P_302, 10/21*P_510^2 - 10/21*P_510*P_501 - 2*P_320 + P_311, 0], [0, 0, -10/21*P_510*P_501 + 10/21*P_501^2 + P_311 - 2*P_302, 10/7*P_510^2 - 10/7*P_510*P_501 - 6*P_320 + 3*P_311]]; M has rank 3 exactly on (beta, gamma) != (0, 0) (its 3x3 minors, with B = beta and G = gamma, are ['(1/3087) * B * G^2', '(1/3087) * G * B^2', '(1/9261) * B^3', '(1/9261) * G^3'] and generate an ideal containing beta^3 and gamma^3); components {beta = gamma = 0} and the closure of the kernel line bundle over {(beta,gamma) != 0}
  ok   R5 l=Y+Z, component W1 (G_103 != 0): a point of the component (residual equations vanish)
      timing: member+triples 0.3 s, stabilization 0.1 s
  ok   R5 l=Y+Z, component W1 (G_103 != 0) anchor (A): fixed {'G_103': 1}, solved ['G_211', 'G_202', 'G_030', 'G_012', 'G_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 35 (ds), stabilization (35, 10)
      anchor generators: {'P': 'X^7 + 105/4*X^4*Y^2 + 105/2*X^4*Y*Z + 105/4*X^4*Z^2 + 105/8*X*Y^4 + 105/2*X*Y^3*Z + 315/4*X*Y^2*Z^2 + 105/2*X*Y*Z^3 + 105/8*X*Z^4 + 35*X*Y^3 - 35/4*Y^4 + 105*X*Y^2*Z - 35*Y^3*Z - 105/2*X*Y*Z^2 - 105/2*Y^2*Z^2 - 35/2*X*Z^3 - 35*Y*Z^3 - 35/4*Z^4 + 2*Y^3 - Y^2*Z - Y*Z^2 + Z^3', 'G': 'X^4*Y + X^4*Z + X*Y^3 + 3*X*Y^2*Z + 3*X*Y*Z^2 + X*Z^3 + 2*X*Y^2 - 2/3*Y^3 - 2*Y^2*Z - X*Z^2 - 2*Y*Z^2 - 2/3*Z^3', 'H': 'X^3*Z + 2*Y^3 + Y^2*Z - 2*X*Z^2 + Y*Z^2 - Z^3'}
      anchor triple: ['x^8 - 3*x^7*y + x^6*y^2 + 3*x^5*y^3 + x^4*y^4 + x^3*y^5 - 2*x^2*y^6 + x*y^7 - 3*y^8 + 2*x^7*z + 2*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 - 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^2*y^4*z^2 - x*y^5*z^2 + 2*y^6*z^2 - 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 + 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 + x^2*z^6 - x*y*z^6 - y^2*z^6 + x*z^7 + y*z^7 - z^8 + 179/252*x^7 + 3*x^6*y - x^5*y^2 + 3*x^4*y^3 + 3*x^3*y^4 - 2*x^2*y^5 + x*y^6 - 3*x^6*z + 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 - 2*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - 2*x*y^4*z^2 - 2*y^5*z^2 - 2*x^4*z^3 + x^3*y*z^3 + 2*x*y^3*z^3 - 2*x^2*y*z^4 - 3*x*y^2*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 - 3*z^7 + 7/16*x^6 + x^4*y^2 + 2*x^3*y^3 + 2*x^2*y^4 + 2*x*y^5 + 3*y^6 + 2*x^5*z - 2*x^4*y*z + 3*x^3*y^2*z - x^2*y^3*z + 3*x*y^4*z - 2*y^5*z - 2*x^4*z^2 - 3*x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*y^4*z^2 + 2*x^3*z^3 - 2*x^2*y*z^3 + 2*x*y^2*z^3 - 3*y^3*z^3 + 3*x^2*z^4 + x*y*z^4 - 2*y^2*z^4 - 3*x*z^5 - 3*y*z^5 - 3*z^6 - 1/2*x^5 - 1/4*x^4*y - 2*x^3*y^2 + x^2*y^3 - x*y^4 + 2*y^5 - x^4*z - 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^2*y*z^2 + 2*x*y^2*z^2 - 2*y^3*z^2 + 2*x^2*z^3 + 2*y^2*z^3 - x*z^4 - y*z^4 - 2*z^5 + 7/6*x^3*y + 2*x*y^3 - 2*y^4 + 1/3*x^3*z - x^2*y*z - 3*x*y^2*z + 3*y^3*z + 3*x^2*z^2 - 3*x*y*z^2 + 2*x*z^3 - 3*y*z^3 - z^4 + 3*x*y^2 - y^3 - y^2*z - 3*x*z^2 - 3*y*z^2 - z^3', '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 + 2*x^2*y^6 + 2*y^8 - x^7*z - 2*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 + 2*x^6*z^2 + 2*x^5*y*z^2 + 2*x^4*y^2*z^2 - x^2*y^4*z^2 + 2*y^6*z^2 - 3*x^5*z^3 + x^4*y*z^3 + x^3*y^2*z^3 - 3*x^2*y^3*z^3 + y^5*z^3 - x^4*z^4 - 2*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 - y^3*z^5 + 3*x^2*z^6 - x*y*z^6 - y^2*z^6 + x*z^7 + 2*y*z^7 + z^8 + 277/5040*x^7 + 3*x^6*y + 2*x^5*y^2 + x^3*y^4 - 2*x^2*y^5 - x*y^6 + x^6*z - x^5*y*z - 2*x^4*y^2*z + 2*x^3*y^3*z + 3*x*y^5*z - y^6*z - 3*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 + y^5*z^2 - 3*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 + x*y^2*z^4 + y^3*z^4 + 3*x^2*z^5 + 2*x*y*z^5 + 2*y^2*z^5 - 3*y*z^6 - 3*z^7 + 29/48*x^6 - x^5*y + 3*x^4*y^2 + 3*x^3*y^3 + 3*x^2*y^4 + 2*x*y^5 - 3*y^6 + 2*x^5*z + x^3*y^2*z - 3*x*y^4*z + 3*y^5*z - 2*x^3*y*z^2 + y^4*z^2 + x^2*y*z^3 + x*y^2*z^3 + y^3*z^3 - 3*x^2*z^4 + x*y*z^4 + y^2*z^4 + 2*x*z^5 + 2*y*z^5 + 3*z^6 - 1/4*x^5 - 13/6*x^4*y - 2*x^3*y^2 - 3*x*y^4 - y^5 + 2*x^4*z - x^3*y*z - 3*x^2*y^2*z + 3*x*y^3*z - 3*x^3*z^2 - 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 - 3*x*z^4 - 2*y*z^4 - z^5 + 31/6*x^3*y + x^2*y^2 + y^4 - 17/3*x^3*z - 2*x^2*y*z + 3*y^3*z + 2*x^2*z^2 + 3*x*y*z^2 + 3*y^2*z^2 - x*z^3 + 2*y*z^3 + 2*z^4 + 3*y^3 + y^2*z - 2*y*z^2', '-2*x^8 + 3*x^7*y - 2*x^6*y^2 - x^5*y^3 + 2*x^2*y^6 + 3*x*y^7 - 3*y^8 + 2*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 - 3*x^2*y^5*z + 2*x^6*z^2 + x^5*y*z^2 + 2*x^3*y^3*z^2 - 2*x^2*y^4*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 + 2*x*y^4*z^3 + 3*y^5*z^3 + 3*x^4*z^4 + 3*x^3*y*z^4 + 3*x^2*y^2*z^4 + x*y^3*z^4 - y^4*z^4 - 2*x^3*z^5 - 3*x^2*y*z^5 + x*y^2*z^5 - y^3*z^5 + 2*x^2*z^6 + 2*y*z^7 + z^8 + 13/280*x^7 + x^6*y - 3*x^5*y^2 + x^2*y^5 + x*y^6 - 3*y^7 - 3*x^6*z - 2*x^5*y*z - 3*x^3*y^3*z + x^2*y^4*z - 2*x*y^5*z + y^6*z - x^5*z^2 - 3*x^4*y*z^2 + 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 + 2*x*y^4*z^2 - y^5*z^2 + x^4*z^3 - x^3*y*z^3 - x^2*y^2*z^3 - 2*x*y^3*z^3 - y^4*z^3 - 2*x^3*z^4 + 3*x^2*y*z^4 + 3*x^2*z^5 - y^2*z^5 + 2*y*z^6 - 35/48*x^6 - 2*x^5*y - 3*x^4*y^2 + 2*x^3*y^3 + x^2*y^4 + 3*x*y^5 + 3*y^6 + 3*x^5*z + x^4*y*z - 2*x^3*y^2*z + 2*x^2*y^3*z - 3*x*y^4*z + x^4*z^2 - x^3*y*z^2 + x^2*y^2*z^2 - y^4*z^2 - 3*x^3*z^3 + 3*x^2*y*z^3 - 2*x*y^2*z^3 + 2*y^3*z^3 - 2*x*y*z^4 + 3*y^2*z^4 - x*z^5 + 2*z^6 + 5/4*x^5 - 4*x^4*y - 2*x^3*y^2 + 3*x*y^4 - 2*y^5 + 2*x^4*z + 3*x^3*y*z + 2*x^2*y^2*z + y^4*z + 2*x^3*z^2 + x*y^2*z^2 - 3*y^3*z^2 - 2*x^2*z^3 - x*y*z^3 - y^2*z^3 + 2*x*z^4 - 2*y*z^4 - z^5 + 5/4*x^4 - 19/4*x^3*y - x*y^3 + y^4 + 6*x^3*z - 3*x^2*y*z + 3*x*y^2*z + 3*y^3*z - 2*x^2*z^2 + x*y*z^2 - y^2*z^2 + 2*x*z^3 - 3*y*z^3 + 3*z^4 - 2*x*y^2 - 3*y^3 - 2*y^2*z - 3*x*z^2 - y*z^2 + z^3']
  ok   R5 l=Y+Z, component W2 (G_103 = 0, beta = gamma = 0): a point of the component (residual equations vanish)
      timing: member+triples 0.7 s, stabilization 0.5 s
  ok   R5 l=Y+Z, component W2 (G_103 = 0, beta = gamma = 0) anchor (A): fixed {'G_103': 0}, solved ['P_302', 'P_320']; member closed with H and the prescribed graded data: True; a triple of I of local length 39 (ds), stabilization (39, 14)
      anchor generators: {'P': 'X^7 + X*Y^2 - Y^3 - Y^2*Z - X*Z^2 + 2*Z^3', 'G': 'X^4*Y + X^4*Z + 2*X*Y^2 + Y^3 - 2*Y^2*Z - X*Z^2 + 2*Y*Z^2 + Z^3', 'H': 'X^3*Z - X*Y^2 - 2*Y^3 + 2*Y^2*Z - 2*X*Z^2 - Y*Z^2 - 2*Z^3'}
      anchor triple: ['3*x^8 - x^7*y - 3*x^6*y^2 + 3*x^5*y^3 + 2*x^4*y^4 - 2*x^3*y^5 + 3*x^2*y^6 - 3*y^8 + x^6*y*z + 3*x^5*y^2*z + x^4*y^3*z - 2*x^3*y^4*z - 3*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 + 3*x^3*y^3*z^2 + 2*x^2*y^4*z^2 - 3*x*y^5*z^2 - y^6*z^2 + x^5*z^3 - x^4*y*z^3 - x^3*y^2*z^3 - 3*x^2*y^3*z^3 - 3*y^5*z^3 - 2*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 - 2*y^3*z^5 - 2*x*y*z^6 + 3*y^2*z^6 + x*z^7 + 3*y*z^7 - 3*z^8 - 1/252*x^7 + 3*x^6*y - 2*x^5*y^2 + 2*x^4*y^3 - 2*x^3*y^4 - x^2*y^5 + y^7 + 2*x^6*z - 3*x^5*y*z - 3*x^4*y^2*z - 3*x^2*y^4*z + 2*x*y^5*z - 3*y^6*z - 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*x^4*z^3 - 3*x^3*y*z^3 + x^2*y^2*z^3 + 3*x*y^3*z^3 - y^4*z^3 - 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 + 2*x*y*z^5 - y^2*z^5 - x*z^6 - 3*y*z^6 - x^5*y - x^4*y^2 - x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 - y^6 - 2*x^5*z - x^4*y*z + 3*x^3*y^2*z - 2*x^2*y^3*z - 3*x*y^4*z + 3*y^5*z - 2*x^4*z^2 + x^3*y*z^2 + 3*x^2*y^2*z^2 - 3*x*y^3*z^2 + 3*y^4*z^2 + 2*x^3*z^3 + 2*x^2*y*z^3 + 2*x*y^2*z^3 - 3*y^3*z^3 + x^2*z^4 - 2*x*y*z^4 - 3*x*z^5 - 2*y*z^5 + 2*z^6 + 1/3*x^4*y - 2*x^3*y^2 + 2*x*y^4 + 2*y^5 + x^4*z - x^3*y*z - 3*x*y^3*z + 3*y^4*z - 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 + 3*y^2*z^3 + 3*x*z^4 + y*z^4 + 3*z^5 + 14/3*x^3*y - x^2*y^2 + 3*x*y^3 - 14/3*x^3*z + x*y^2*z - 2*y^3*z - 2*x^2*z^2 - 2*x*y*z^2 + y^2*z^2 + x*z^3 - 2*z^4 - x*y^2 - 3*y^3 + 2*y^2*z + 2*x*z^2 - y*z^2 + z^3', '-3*x^8 + 2*x^6*y^2 - x^5*y^3 + 2*x^4*y^4 + x^3*y^5 - x^2*y^6 - 2*x*y^7 - 3*y^8 - 3*x^7*z + 3*x^6*y*z + 2*x^5*y^2*z + 3*x^4*y^3*z - 3*x^3*y^4*z + x^2*y^5*z - x*y^6*z - 3*y^7*z - x^6*z^2 + 2*x^5*y*z^2 + 2*x^4*y^2*z^2 - x^2*y^4*z^2 + 2*x*y^5*z^2 - 3*y^6*z^2 - x^5*z^3 - 3*x^4*y*z^3 + 3*x^3*y^2*z^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 - 3*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 + 3*y^3*z^5 - 3*x^2*z^6 + 2*y^2*z^6 - x*z^7 + y*z^7 - 3*z^8 + 1/1260*x^7 + 2*x^6*y + 2*x^5*y^2 - x^4*y^3 - 2*x^3*y^4 + 3*x*y^6 - 3*y^7 + 2*x^6*z + 3*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 - 2*y^6*z - 2*x^5*z^2 + 2*x^4*y*z^2 - 3*x^3*y^2*z^2 - 3*x^2*y^3*z^2 + 3*x*y^4*z^2 + 2*y^5*z^2 - 2*x^4*z^3 + 3*x^3*y*z^3 + x*y^3*z^3 - 3*y^3*z^4 + x^2*z^5 + 3*y^2*z^5 + x*z^6 + y*z^6 - z^7 - 3*x^5*y - 3*x^4*y^2 - 2*x^3*y^3 + x^2*y^4 + 3*x*y^5 - y^6 - x^5*z + 2*x^4*y*z + 2*x^3*y^2*z + 3*x^2*y^3*z - 2*x*y^4*z + 2*y^5*z - 3*x^4*z^2 + x^2*y^2*z^2 - 3*x*y^3*z^2 + y^4*z^2 + 2*x^2*y*z^3 + y^3*z^3 + 2*x^2*z^4 + 2*y^2*z^4 - 2*x*z^5 - y*z^5 - 3*z^6 + 43/12*x^4*y + x^2*y^3 + 2*x*y^4 - 2*y^5 - 3*x^4*z + 3*x^3*y*z + 3*x^2*y^2*z - 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 + x^2*z^3 - 2*x*y*z^3 + 2*y^2*z^3 - 2*x*z^4 + y*z^4 - z^5 - 5/3*x^3*y + x^2*y^2 - 3*x*y^3 - 3*y^4 + 5/3*x^3*z + 2*x^2*y*z - 3*x*y^2*z + y^3*z - x^2*z^2 - x*y*z^2 + 3*y^2*z^2 - 3*x*z^3 - 2*y*z^3 + z^4 - y^2*z + 3*x*z^2 - 3*y*z^2', 'x^8 + x^7*y - 3*x^6*y^2 - x^5*y^3 + 2*x^4*y^4 - 3*x^3*y^5 + x^2*y^6 + 2*x*y^7 + y^8 - x^7*z + 3*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 + x^6*z^2 + 3*x^5*y*z^2 + x^4*y^2*z^2 - 2*x^3*y^3*z^2 + 3*x^2*y^4*z^2 + 2*x^5*z^3 - x^4*y*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 - x^3*y*z^4 - 3*x^2*y^2*z^4 + 2*x*y^3*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 + 2*x*y*z^6 - 2*y^2*z^6 - x*z^7 - y*z^7 - 3*z^8 - 1/210*x^7 + 2*x^6*y - x^5*y^2 - x^4*y^3 - 3*x^3*y^4 + 2*x*y^6 + 3*y^7 - 3*x^6*z - x^5*y*z - 2*x^4*y^2*z + 3*x^3*y^3*z + 2*x^2*y^4*z - x*y^5*z - y^6*z - 2*x^4*y*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^3*y*z^3 + 3*x^2*y^2*z^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 + x^2*z^5 + 3*x*y*z^5 + 2*y^2*z^5 - x*z^6 - y*z^6 + z^7 + x^5*y + 3*x^4*y^2 + x^2*y^4 - 3*x*y^5 - y^6 + x^5*z + x^4*y*z - 2*x^3*y^2*z - 3*x^2*y^3*z + 3*x*y^4*z + 3*y^5*z - 2*x^2*y^2*z^2 - x*y^3*z^2 + 3*x^3*z^3 - 2*y^3*z^3 + 3*x*y*z^4 - 2*y^2*z^4 - 3*x*z^5 + 2*y*z^5 - z^6 - 23/12*x^4*y + x^2*y^3 + 2*x*y^4 - 2*y^5 + x^4*z + 2*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 - 2*x*y^2*z^2 + 3*x^2*z^3 - 3*x*y*z^3 + 2*x*z^4 + y*z^4 - 3*z^5 - 12*x^3*y + 3*x^2*y^2 - 2*x*y^3 - 2*y^4 + 12*x^3*z - 3*x^2*y*z - 3*x*y^2*z - 3*y^3*z + 2*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 - x*z^3 + 3*y*z^3 + z^4 - x*y^2 + 2*y^3 - 3*y^2*z + 2*x*z^2 - 3*y*z^2 + 3*z^3']
  ok   R5 l=Y+Z, component W3 (G_103 = 0, H in the kernel): a point of the component (residual equations vanish)
      timing: member+triples 0.4 s, stabilization 0.1 s
  ok   R5 l=Y+Z, component W3 (G_103 = 0, H in the kernel) anchor (A): fixed {'G_103': 0}, solved ['H_021', 'H_012', 'H_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 35 (ds), stabilization (35, 11)
      anchor generators: {'P': 'X^7 + X^5*Y - 2*X^5*Z + X^3*Y*Z - 2*X^3*Z^2 - 17/21*X*Y^3 + 17/14*Y^4 + 55/7*X*Y^2*Z - 110/7*Y^3*Z + 32/7*X*Y*Z^2 + 9075/119*Y^2*Z^2 - 106/21*X*Z^3 - 332750/2023*Y*Z^3 + 9150625/68782*Z^4 - X*Y^2 + Y^3 + 2*Y^2*Z - 2*X*Z^2 - Y*Z^2 - 2*Z^3', 'G': 'X^4*Y + X^4*Z - 2*Y*Z^2 + Z^3', 'H': 'X^3*Z - X*Y^2 + 2*Y^3 - 330/17*Y^2*Z + 2*X*Z^2 + 18150/289*Y*Z^2 - 332750/4913*Z^3'}
      anchor triple: ['2*x^8 + x^6*y^2 + 3*x^5*y^3 + 3*x^4*y^4 + 2*x^3*y^5 + x^2*y^6 - x*y^7 + 3*y^8 + 2*x^7*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 + 3*y^7*z - x^6*z^2 + 3*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 + 3*x*y^5*z^2 + 3*y^6*z^2 + 2*x^5*z^3 - 2*x^3*y^2*z^3 + 2*x^2*y^3*z^3 + 3*x*y^4*z^3 + 2*x^4*z^4 + x^3*y*z^4 - 2*x^2*y^2*z^4 + 3*x*y^3*z^4 - x^2*y*z^5 - 3*y^3*z^5 + x^2*z^6 + 2*x*y*z^6 + y^2*z^6 + 2*x*z^7 + 2*y*z^7 - 3*z^8 - 72545231/43332660*x^7 + 3*x^5*y^2 - x^4*y^3 - 3*x^2*y^5 - 2*x*y^6 - 3*y^7 + 3*x^5*y*z - x^4*y^2*z + 2*x^3*y^3*z - 2*x^2*y^4*z - 2*x*y^5*z + 3*y^6*z - 3*x^3*y^2*z^2 - x^2*y^3*z^2 - 3*x*y^4*z^2 - 3*y^5*z^2 + 2*x^4*z^3 + 3*x^3*y*z^3 + 3*x^2*y^2*z^3 + x*y^3*z^3 - 3*y^4*z^3 + x^3*z^4 + 2*x^2*y*z^4 - x*y^2*z^4 - 3*y^3*z^4 + 2*x^2*z^5 + x*y*z^5 - y^2*z^5 - x*z^6 - y*z^6 + z^7 + 97/882*x^6 + 3*x^4*y^2 - 2*x^3*y^3 - 2*x^2*y^4 + 2*x*y^5 - y^6 + 3*x^5*z + 2*x^4*y*z + x^3*y^2*z + 2*x^2*y^3*z - 3*x*y^4*z - 3*y^5*z + 2*x^4*z^2 - 2*x^3*y*z^2 + 3*x^2*y^2*z^2 - x*y^3*z^2 + 3*y^4*z^2 + x^3*z^3 - 3*x^2*y*z^3 + 2*x*y^2*z^3 - 2*y^3*z^3 + 3*x^2*z^4 + 2*x*y*z^4 + y^2*z^4 + 2*x*z^5 + 3*y*z^5 + z^6 + 5549717/343910*x^5 - 23/12*x^4*y + 3*x^3*y^2 + 2*x^2*y^3 + 3*y^5 + x^4*z - 2*x^2*y^2*z - x*y^3*z - y^4*z - 2*x^2*y*z^2 - 3*x*y^2*z^2 + 2*x^2*z^3 + 3*x*y*z^3 - 3*y^2*z^3 + 3*x*z^4 + y*z^4 + 3*z^5 - 3327865/14739*x^3*y + x^2*y^2 + 3*y^4 + 3327865/14739*x^3*z - 3*x^2*y*z + 2*y^3*z - x^2*z^2 - 3*x*y*z^2 - y^2*z^2 - 2*x*z^3 + 3*z^4 - 3*x*y^2 - 2*y^3 + 2*x*z^2 - y*z^2 + 3*z^3', '-2*x^8 + x^7*y + 3*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 + 2*x^7*z - 3*x^6*y*z + x^5*y^2*z + x^4*y^3*z - 3*x^3*y^4*z - 3*x*y^6*z + 2*x^6*z^2 - 3*x^5*y*z^2 - 3*x^4*y^2*z^2 - 3*x^3*y^3*z^2 + x^2*y^4*z^2 - 2*x*y^5*z^2 - 3*x^4*y*z^3 + x^3*y^2*z^3 - x^2*y^3*z^3 - 3*x*y^4*z^3 - y^5*z^3 - 3*x^4*z^4 + 2*x^3*y*z^4 + x^2*y^2*z^4 + 2*y^4*z^4 + 2*x^3*z^5 + 2*x^2*y*z^5 + 2*x*y^2*z^5 + 3*x^2*z^6 + 3*x*y*z^6 - 3*x*z^7 - 2*y*z^7 - z^8 - 10036189/14444220*x^7 + x^4*y^3 + 2*x^3*y^4 - x*y^6 + x^5*y*z + 3*x^4*y^2*z + 2*x*y^5*z + y^6*z + 3*x^5*z^2 + x^4*y*z^2 + x^3*y^2*z^2 - x*y^4*z^2 + y^5*z^2 + 3*x^4*z^3 - 2*x^3*y*z^3 + 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 + 3*x^2*z^5 + x*y*z^5 - 2*y^2*z^5 + 3*x*z^6 - 2*y*z^6 + 2*z^7 - 1249/17640*x^6 + 3*x^5*y - x^4*y^2 - 3*x^3*y^3 + 2*x^2*y^4 - 3*x*y^5 + 2*y^6 - 2*x^5*z + 2*x^4*y*z + x^3*y^2*z + 3*x^2*y^3*z + 2*x*y^4*z + x^4*z^2 - 3*x^2*y^2*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 + x*z^5 + y*z^5 - z^6 + 2387794/515865*x^5 + 11/12*x^4*y + x^2*y^3 + 3*x*y^4 - x^4*z - 2*x^3*y*z + 3*x^2*y^2*z - 2*x*y^3*z + 3*y^4*z - 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 + 3*y^2*z^3 - 2*z^5 - 318045/4913*x^3*y + 3*x^2*y^2 + 2*x*y^3 - 3*y^4 + 318045/4913*x^3*z - 3*x^2*y*z + x*y^2*z - 2*y^3*z + 3*x*y*z^2 + y^2*z^2 - x*z^3 + y*z^3 + z^4 - x*y^2 - 3*y^3 + 2*y^2*z + x*z^2 + y*z^2 + z^3', '-2*x^8 + 2*x^7*y + 3*x^6*y^2 - x^5*y^3 - 3*x^4*y^4 - 2*x^3*y^5 + 3*x^2*y^6 - 3*x*y^7 - 2*y^8 + 2*x^7*z - x^6*y*z - 3*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 - 3*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 + y^6*z^2 + 2*x^5*z^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 + x^4*z^4 - 2*x^2*y^2*z^4 + 3*x*y^3*z^4 - 3*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 - 3*x*y*z^6 - y^2*z^6 + x*z^7 - 3*y*z^7 + 13562231/12380760*x^7 + x^6*y - 2*x^5*y^2 + x^3*y^4 - x^2*y^5 - 2*y^7 + 2*x^6*z - 3*x^5*y*z - 2*x^4*y^2*z + x^3*y^3*z + 3*x^2*y^4*z - 2*x*y^5*z - 3*y^6*z + x^4*y*z^2 + 3*x*y^4*z^2 - 3*y^5*z^2 + x^4*z^3 - 2*x^3*y*z^3 - 3*x^2*y^2*z^3 + x*y^3*z^3 + 2*x^3*z^4 - x^2*y*z^4 - 2*x*y^2*z^4 + y^3*z^4 - x^2*z^5 - 2*y^2*z^5 - 2*x*z^6 - 3*y*z^6 + 3*z^7 + 3071/17640*x^6 + x^5*y - x^4*y^2 - x^3*y^3 - 2*x^2*y^4 - 3*x^5*z - 3*x^4*y*z + 3*x^3*y^2*z - 3*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*y^4*z^2 + x^3*z^3 + 2*x^2*y*z^3 + y^3*z^3 + 2*x*y*z^4 - 3*y^2*z^4 + 3*x*z^5 + y*z^5 - 2*z^6 - 2926439/171955*x^5 - 25/12*x^4*y - 3*x^3*y^2 + x^2*y^3 + 3*x*y^4 - 3*y^5 + 3*x^4*z + 3*x^3*y*z - 2*x^2*y^2*z + 2*x*y^3*z - y^4*z - 3*x^3*z^2 + 3*x*y^2*z^2 - 3*y^3*z^2 - 2*x^2*z^3 + 3*y^2*z^3 + x*z^4 + 2*y*z^4 + z^5 + 3513692/14739*x^3*y - 3*x^2*y^2 + 3*y^4 - 3513692/14739*x^3*z - x*y^2*z - 2*y^3*z - x^2*z^2 - x*y*z^2 + 3*y^2*z^2 + x*z^3 - 2*y*z^3 - 3*z^4 - 2*y^2*z + 2*x*z^2 + y*z^2 - 3*z^3']
=== R1: B curvilinear of length 4 at [X] on the conic [1:t:t^2] or inflectional [1:t:t^3]; D_3 = nu_3(B), D_4 = nu_4(B_3), D_5 = nu_5(B_2)
  ok   R1 conic: D_3 = <E_0..E_3>, D_4 = <E_0,E_1,E_2> (Q = 3/2*X^2*Y^2 + X^3*Z), D_5 = <E_0,E_1>, jets of [1:t:t^2]
--- R1 conic
  ok   R1 conic: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R1 conic: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 58 eliminated with constant pivots; residual equations:
       (8) * G_040 * P_420
       (24) * G_040 * P_420
       (-1/630) * (8*P_420^2*G_220 + 10*P_510*P_420*G_211 + 140*P_420*G_220*G_211 - 30*P_510*P_420*G_130 - 420*P_420*G_220*G_130 - 40*P_510*P_420*H_102 - 280*P_420*G_220*H_102 - 48*P_420^2*H_030 + 1260*P_420*G_130*H_030 + 40*P_510*P_420*H_021 + 280*P_420*G_220*H_021 - 105*P_230*G_211 + 315*P_230*G_130 + 420*P_420*G_102 - 420*P_420*G_021 + 420*P_230*H_102 - 420*P_230*H_021)
       (-1/210) * (4*P_420^2*G_211 + 35*P_420*G_211^2 - 105*P_420*G_211*G_130 - 240*P_510*P_420*G_040 - 840*P_420*G_220*G_040 - 16*P_420^2*H_021 + 420*P_420*G_130*H_021 + 40*P_510*P_420*H_012 + 280*P_420*G_220*H_012 + 1260*P_230*G_040 - 420*P_420*G_012 - 420*P_230*H_012)
       (-2/105) * (12*P_420^2*G_040 + 105*P_420*G_211*G_040 - 315*P_420*G_130*G_040 - 4*P_420^2*H_012 + 105*P_420*G_130*H_012 + 30*P_510*P_420*H_003 + 210*P_420*G_220*H_003 - 315*P_420*G_003 - 315*P_230*H_003)
  ok   R1 conic: on {P_420 != 0} the residual equations are triangular in ['G_040', 'G_102', 'G_012', 'G_003'] with diagonal (const)*P_420: a graph (irreducible)
  ok   R1 conic: on {P_420 = 0}: each equation is (P_230) times a linear form; components {c = 0} and {linear forms ['1/6*G_211 - 1/2*G_130 - 2/3*H_102 + 2/3*H_021', '-6*G_040 + 2*H_012', '6*H_003'] = 0}
  ok   R1 conic, component W1 (P_420 != 0): a point of the component (residual equations vanish)
      timing: member+triples 0.3 s, stabilization 0.1 s
  ok   R1 conic, component W1 (P_420 != 0) anchor (A): fixed {'P_420': 1}, solved ['G_040', 'G_102', 'G_012', 'G_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 35 (ds), stabilization (35, 10)
      anchor generators: {'P': 'X^7 + X^4*Y^2 + 2/5*X^5*Z - 4*X^2*Y*Z - 6*X*Y^2*Z + 2/3*Y^3*Z - 323/105*X^2*Z^2 + 54/35*X*Y*Z^2 - 4/105*Y^2*Z^2 + 8/315*X*Z^3 + 16/315*Y*Z^3 - 2/105*Z^4 - 2*X*Y^2 + 2*Y^3 + 2*X*Z^2', 'G': 'X^4*Y + 2*X*Y^2 + Y^3 + Y^2*Z + 27/35*X*Z^2 - 4/105*Y*Z^2 + 8/315*Z^3', 'H': '3/2*X^2*Y^2 + X^3*Z - 2*X*Y^2 - 2*Y^3 + Y^2*Z - X*Z^2 - 2*Y*Z^2 + Z^3'}
      anchor triple: ['2*x^8 + 2*x^7*y + 3*x^6*y^2 + 2*x^5*y^3 + 2*x^4*y^4 - 2*x^3*y^5 + 3*x^2*y^6 + x*y^7 - 3*y^8 + x^7*z + 2*x^6*y*z - 3*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 + 2*x^6*z^2 - 3*x^4*y^2*z^2 - 2*x^3*y^3*z^2 - 2*x*y^5*z^2 + 2*y^6*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 - x*y^4*z^3 - y^5*z^3 + 2*x^4*z^4 - 3*x^2*y^2*z^4 - 2*x*y^3*z^4 - 3*x^3*z^5 - x^2*y*z^5 - 3*x*y^2*z^5 - y^3*z^5 + 3*x^2*z^6 + 3*x*y*z^6 + y^2*z^6 - 2*z^8 - 1189/66150*x^7 - 2*x^6*y + 3*x^5*y^2 - 3*x^4*y^3 + 2*x^3*y^4 - 2*x^2*y^5 - x*y^6 + 2*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 - x*y^5*z + 2*y^6*z + x^5*z^2 - x^3*y^2*z^2 - x^2*y^3*z^2 - 2*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 + x*y^3*z^3 - 2*y^4*z^3 - 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 + 3*x*z^6 + y*z^6 - 3*z^7 + 1049/33075*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^5*z + 3*x^2*y^3*z + 2*y^5*z - 2*x^4*z^2 - x^3*y*z^2 - 3*x^2*y^2*z^2 + y^4*z^2 - 3*x^3*z^3 + 2*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 - 8/315*x^5 - 473/1260*x^4*y + x*y^4 + 2*y^5 - 3*x^4*z - 3*x^3*y*z - x^2*y^2*z + 3*x*y^3*z + 3*x^3*z^2 - x^2*y*z^2 - x*y^2*z^2 - 3*y^3*z^2 + 2*x*y*z^3 - y^2*z^3 + 2*x*z^4 - y*z^4 + 11/3*x^2*y^2 - 3*x*y^3 + 2*y^4 - x^3*z + 2*x^2*y*z + x*y^2*z - y^3*z + x^2*z^2 - 3*x*y*z^2 + x*z^3 + 2*x*y^2 - 2*x^2*z - y^2*z + 2*x*z^2 - y*z^2 - z^3', 'x^8 + x^7*y + x^6*y^2 + 3*x^5*y^3 + x^4*y^4 + x^3*y^5 - 2*x^2*y^6 + 3*x*y^7 - 2*y^8 - 2*x^7*z - 2*x^6*y*z + 2*x^4*y^3*z - 3*x^2*y^5*z - x*y^6*z + y^7*z + 3*x^6*z^2 + 3*x^5*y*z^2 + 3*x^4*y^2*z^2 + 2*x^3*y^3*z^2 + y^6*z^2 - x^5*z^3 + 2*x^3*y^2*z^3 - 2*x^2*y^3*z^3 - 3*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 - 3*x*y^3*z^4 - 3*y^4*z^4 + x^2*y*z^5 + 3*x*y^2*z^5 - 2*x^2*z^6 - 2*x*y*z^6 - 3*x*z^7 + y*z^7 - z^8 + 3/98*x^7 - 3*x^5*y^2 - x^4*y^3 - x^3*y^4 - 2*x^2*y^5 + 2*x*y^6 - 3*y^7 + 3*x^6*z - x^5*y*z + 2*x^4*y^2*z + 3*x^3*y^3*z - 2*x^2*y^4*z - 2*y^6*z - x^4*y*z^2 - 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 + 3*x*y^4*z^2 - y^5*z^2 - x^3*y*z^3 + 2*x*y^3*z^3 - 2*y^4*z^3 - x^3*z^4 - 2*x^2*y*z^4 + x*y^2*z^4 - y^3*z^4 - 3*x^2*z^5 + 3*y^2*z^5 - 2*x*z^6 + 2*y*z^6 + z^7 + 527/13230*x^6 - 2*x^5*y - 3*x^4*y^2 + 2*x^3*y^3 + 2*x*y^5 + 3*y^6 + 2*x^4*y*z - 2*x^3*y^2*z + 3*y^5*z + 3*x^4*z^2 - 3*x^3*y*z^2 - x^2*y^2*z^2 - 3*x*y^3*z^2 + 2*x^3*z^3 + 3*x^2*y*z^3 - x*y^2*z^3 - 2*y^3*z^3 + 3*x^2*z^4 + 2*x*y*z^4 + 2*y^2*z^4 + y*z^5 + z^6 + 2/63*x^5 + 103/126*x^4*y - x^3*y^2 + x*y^4 + 2*y^5 - 3*x^4*z - 3*x^2*y^2*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 + 2*x*y*z^3 - 2*x*z^4 + 2*y*z^4 - 1/3*x^2*y^2 - 2*y^4 - 3*x^3*z + 2*x^2*y*z - 2*x*y^2*z + 3*y^3*z - x^2*z^2 + x*y*z^2 + 3*y^2*z^2 - 3*x*z^3 - y*z^3 + z^4 - 3*y^3 + 3*x*y*z + y^2*z - 2*x*z^2 + y*z^2 - 3*z^3', '3*x^8 - 2*x^7*y - x^6*y^2 - 2*x^5*y^3 + 3*x^4*y^4 + x^3*y^5 + 3*x*y^7 - 2*y^8 + x^7*z - 2*x^5*y^2*z + 3*x^4*y^3*z + 3*x^3*y^4*z + 2*x*y^6*z - y^7*z + 2*x^6*z^2 - 3*x^5*y*z^2 - 3*x^3*y^3*z^2 - x^2*y^4*z^2 + 3*y^6*z^2 + 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 - x^2*y^2*z^4 + 2*x*y^3*z^4 - 3*y^4*z^4 + 3*x^3*z^5 - 3*x^2*y*z^5 + y^3*z^5 - 2*x^2*z^6 - 3*x*y*z^6 - 2*y^2*z^6 - 2*x*z^7 + 2*y*z^7 - 3/4900*x^7 + 2*x^6*y - x^5*y^2 - 2*x^4*y^3 - 3*x^2*y^5 - x*y^6 - y^7 + 3*x^6*z + 2*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 + x^4*y*z^2 - 2*x^2*y^3*z^2 + 3*x*y^4*z^2 - 2*y^5*z^2 + 2*x^3*y*z^3 - 3*x^2*y^2*z^3 + 2*x*y^3*z^3 + y^4*z^3 + 2*x^2*y*z^4 - 3*x*y^2*z^4 + 2*y^3*z^4 - 3*x^2*z^5 - 3*x*y*z^5 - 2*y^2*z^5 + 2*x*z^6 - 2*y*z^6 + 3*z^7 - 19/6300*x^6 - 2*x^5*y - 3*x^4*y^2 - x^3*y^3 - 2*x^2*y^4 + x*y^5 + 2*y^6 + 2*x^5*z - x^4*y*z - 3*x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z - 2*x^4*z^2 + 2*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 - y^3*z^3 + 2*x^2*z^4 + x*y*z^4 + y^2*z^4 + 2*x*z^5 + 2*y*z^5 - 2*z^6 - 1/63*x^5 - 779/1260*x^4*y - x^3*y^2 + 3*x^2*y^3 - x*y^4 + x^4*z - x^3*y*z + x^2*y^2*z + 2*x*y^3*z + 3*y^4*z + x^3*z^2 - 2*x^2*y*z^2 + x*y^2*z^2 - 3*y^3*z^2 - x^2*z^3 - x*y*z^3 + 3*y^2*z^3 - 2*x*z^4 - 2*y*z^4 + 2*z^5 + 11/3*x^2*y^2 + x*y^3 - 2*x^3*z - x^2*y*z + 2*x*y^2*z + y^3*z - 2*x^2*z^2 + x*y*z^2 + 2*y^2*z^2 - y*z^3 - x*y^2 + 3*y^3 + x^2*z - 3*x*y*z + y^2*z - x*z^2 - 3*y*z^2 + z^3']
  ok   R1 conic, component W2 (P_420 = 0 = P_230): a point of the component (residual equations vanish)
      timing: member+triples 0.6 s, stabilization 0.3 s
  ok   R1 conic, component W2 (P_420 = 0 = P_230) anchor (A): fixed {'P_420': 0}, solved ['P_230']; member closed with H and the prescribed graded data: True; a triple of I of local length 38 (ds), stabilization (38, 13)
      anchor generators: {'P': 'X^7 + X*Y^2 - Y^3 + 2*Y^2*Z + Y*Z^2 - Z^3', 'G': 'X^4*Y - 2*X*Y^2 + 2*Y^3 + Y^2*Z + 2*X*Z^2 - 2*Y*Z^2', 'H': '3/2*X^2*Y^2 + X^3*Z + 2*Y^2*Z + 2*X*Z^2 - 2*Z^3'}
      anchor triple: ['-x^8 - x^7*y + x^6*y^2 - 3*x^5*y^3 + x^4*y^4 - x^3*y^5 + 2*x*y^7 + y^8 + 2*x^7*z - 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 - 3*x*y^6*z - 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 + 3*x*y^5*z^2 - 2*y^6*z^2 - 3*x^4*y*z^3 + x^3*y^2*z^3 - 3*x^2*y^3*z^3 + 2*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 - x*y^3*z^4 - 2*y^4*z^4 - 3*x^3*z^5 + 2*x^2*y*z^5 + 2*x*y^2*z^5 - 2*y^3*z^5 + x*y*z^6 + y^2*z^6 - 3*x*z^7 + y*z^7 + z^8 + 2/315*x^7 - x^5*y^2 + 2*x^4*y^3 + 3*x^3*y^4 + 3*x^2*y^5 + y^7 - 3*x^6*z + x^5*y*z + x^4*y^2*z + 2*x^2*y^4*z - 3*x*y^5*z + y^6*z + 3*x^5*z^2 + 3*x^4*y*z^2 + 2*x^3*y^2*z^2 + 2*x^2*y^3*z^2 + 3*x*y^4*z^2 + 2*x^4*z^3 - 2*x^3*y*z^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 - 3*x*y*z^5 - 2*y^2*z^5 - z^7 + x^4*y^2 - 3*x^3*y^3 - x^2*y^4 - x*y^5 + 3*y^6 - 3*x^5*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 - x*y^3*z^2 + 3*x^3*z^3 + 3*x^2*y*z^3 - 2*y^3*z^3 + 3*x^2*z^4 + y^2*z^4 + 2*x*z^5 + z^6 - x^4*y + 3*x^3*y^2 + 2*x^2*y^3 - 2*x*y^4 - y^5 - 3*x^4*z - 3*x^3*y*z - 3*x^2*y^2*z - x*y^3*z + 3*y^4*z - y^3*z^2 - x^2*z^3 - 2*x*y*z^3 - y^2*z^3 + 3*x*z^4 + 3*y*z^4 + z^5 + 8/3*x^2*y^2 + x*y^3 + y^4 + 2*x^3*z - 3*x^2*y*z + x*y^2*z + 2*y^3*z + 3*x^2*z^2 - x*y*z^2 + 2*x*z^3 + y*z^3 - 2*z^4 + 3*x*y^2 + 3*y^3 - 3*x^2*z - 3*x*y*z - 2*y^2*z + x*z^2 + 2*z^3', 'x^8 - x^7*y - 2*x^6*y^2 - x^5*y^3 + 3*x^3*y^5 + 2*x^2*y^6 + 2*x*y^7 - y^8 + 2*x^7*z + 3*x^6*y*z + x^4*y^3*z + x^3*y^4*z - x^2*y^5*z - x*y^6*z - y^7*z - 3*x^6*z^2 + 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 + 2*x*y^5*z^2 - 3*y^6*z^2 - x^5*z^3 - x^4*y*z^3 + 3*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 + 2*x^3*y*z^4 - 2*x^2*y^2*z^4 + x*y^3*z^4 - y^4*z^4 - 3*x^3*z^5 - 3*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 - y^2*z^6 - x*z^7 + 2*y*z^7 + 1/840*x^7 - 3*x^6*y + 2*x^5*y^2 + x^4*y^3 - x^2*y^5 + 2*x*y^6 - 3*y^7 + 3*x^6*z - 2*x^5*y*z + 2*x^4*y^2*z - 2*x^2*y^4*z + 3*x*y^5*z + y^6*z + 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 + x^4*z^3 - 2*y^4*z^3 + x^3*z^4 + x^2*y*z^4 - x*y^2*z^4 - 3*y^3*z^4 - 3*x*y*z^5 + x*z^6 - 2*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 - 2*x^5*z + 3*x^4*y*z + 3*x^3*y^2*z - 2*x^2*y^3*z + 2*x*y^4*z - 2*y^5*z - 3*x^4*z^2 - 3*x^3*y*z^2 + 2*x^2*y^2*z^2 + x*y^3*z^2 + 2*x^3*z^3 + x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 + 2*x^2*z^4 + x*y*z^4 - y^2*z^4 + 3*x*z^5 - y*z^5 + 3*z^6 + 2/3*x^4*y + 2*x^3*y^2 - x^2*y^3 - 3*x*y^4 + 3*x^4*z - 2*x^3*y*z + 3*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 - y^3*z^2 - 2*x^2*z^3 - x*y*z^3 + 2*y^2*z^3 + 3*x*z^4 - 3*y*z^4 - z^5 + 8/3*x^2*y^2 - 2*x*y^3 - 3*y^4 + 3*x^2*y*z + x*y^2*z + 3*y^3*z + 3*x^2*z^2 - y^2*z^2 + 2*x*z^3 - 2*y*z^3 - y^3 + x*y*z - 2*y^2*z - 2*x*z^2 - 2*y*z^2', '-x^8 + 2*x^6*y^2 + 3*x^5*y^3 + 3*x^4*y^4 - 2*x^3*y^5 - x^2*y^6 - 2*y^8 - x^7*z + 3*x^6*y*z + x^5*y^2*z + 2*x^4*y^3*z + 2*x^3*y^4*z + x^2*y^5*z - x*y^6*z + y^7*z - x^6*z^2 - 2*x^5*y*z^2 - x^4*y^2*z^2 - 3*x^3*y^3*z^2 - 3*x^2*y^4*z^2 + y^6*z^2 + 3*x^5*z^3 - x^2*y^3*z^3 - 3*x*y^4*z^3 - x^4*z^4 - x^2*y^2*z^4 - x*y^3*z^4 + y^4*z^4 - 2*x^3*z^5 - 3*x*y^2*z^5 + 2*y^3*z^5 - x*y*z^6 + 2*y^2*z^6 - 2*z^8 - 1/1260*x^7 + 3*x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 - x^2*y^5 + 3*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 + 3*x^2*y^4*z + 3*x*y^5*z + x^5*z^2 - 2*x^3*y^2*z^2 - 3*x^2*y^3*z^2 + x*y^4*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 - x^3*z^4 + 2*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 + x*z^6 - 3*y*z^6 + 3*z^7 + 3*x^5*y - x^4*y^2 + x^3*y^3 - 3*x*y^5 + 3*y^6 - 2*x^5*z - 3*x^4*y*z - x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z + x^4*z^2 - 2*x^3*y*z^2 - 2*x^2*y^2*z^2 - x*y^3*z^2 + 2*y^4*z^2 + 2*x^3*z^3 + 2*x^2*y*z^3 + x*y^2*z^3 + 2*y^3*z^3 + 2*x^2*z^4 - 2*x*y*z^4 + y^2*z^4 + 2*x*z^5 + 2*y*z^5 + z^6 - 5/6*x^4*y - x^3*y^2 + 3*x^2*y^3 + y^5 - 2*x^4*z + 3*x^3*y*z + x^2*y^2*z - 3*x*y^3*z + y^4*z - 3*x^3*z^2 + 3*x^2*y*z^2 - 2*x*y^2*z^2 + 3*y^3*z^2 - 3*x^2*z^3 - 3*x*y*z^3 + y^2*z^3 - 3*x*z^4 - y*z^4 - z^5 - 20/3*x^2*y^2 + 2*x*y^3 + y^4 + 2*x^3*z - 2*x*y^2*z + 2*y^3*z + 2*y^2*z^2 - 2*x*z^3 + y^3 - x*y*z + x*z^2 - y*z^2 - 2*z^3']
  ok   R1 conic, component W3 (P_420 = 0, linear): a point of the component (residual equations vanish)
      timing: member+triples 0.5 s, stabilization 0.2 s
  ok   R1 conic, component W3 (P_420 = 0, linear) anchor (A): fixed {'P_420': 0}, solved ['G_211', 'H_012', 'H_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 40 (ds), stabilization (40, 12)
      anchor generators: {'P': 'X^7 - 42*X^5*Z + X^2*Y^3 + 2*X^3*Y*Z + 420*X^3*Z^2 + 4*X^2*Y*Z + 4/3*Y^3*Z - 2*X*Y*Z^2 - 840*X*Z^3 - X*Y^2 - Y^3 + Y^2*Z + X*Z^2 - 2*Z^3', 'G': 'X^4*Y - 12*X^2*Y*Z + X*Y^2 + 2*Y^3 - X*Z^2 + Y*Z^2 + Z^3', 'H': '3/2*X^2*Y^2 + X^3*Z - 2*X*Y^2 + 2*Y^2*Z - X*Z^2'}
      anchor triple: ['3*x^7*y - 2*x^6*y^2 + 3*x^5*y^3 - 3*x^4*y^4 - x^3*y^5 + x^2*y^6 - 2*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 - 3*x^3*y^4*z + 3*x^2*y^5*z + 2*x*y^6*z - 3*x^6*z^2 - 3*x^5*y*z^2 - 2*x^3*y^3*z^2 - 2*x^2*y^4*z^2 - x^5*z^3 - 2*x^4*y*z^3 - x^3*y^2*z^3 + x^2*y^3*z^3 - 2*x*y^4*z^3 - x^4*z^4 + 3*x^2*y^2*z^4 + 3*x*y^3*z^4 - y^4*z^4 - 2*x^3*z^5 + 3*x^2*y*z^5 - 3*x*y^2*z^5 + y^3*z^5 + 3*x^2*z^6 + 3*y^2*z^6 - 3*x*z^7 - z^8 - 509/504*x^7 - 2*x^6*y + 2*x^5*y^2 + x^4*y^3 + x^3*y^4 - 3*x^2*y^5 + x*y^6 + 3*y^7 - 2*x^6*z - 2*x^5*y*z + x^3*y^3*z + 2*x^2*y^4*z + 2*x*y^5*z + 2*y^6*z - x^4*y*z^2 - 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 + 2*y^5*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 + 2*x^2*y*z^4 + 3*x*y^2*z^4 - 2*y^3*z^4 - 2*x^2*z^5 - 2*x*y*z^5 + x*z^6 - y*z^6 - z^7 - 8*x^6 - 3*x^5*y - x^4*y^2 - x^3*y^3 - 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*x*y^4*z + 2*x^4*z^2 + 2*x^3*y*z^2 - 3*x^2*y^2*z^2 + x*y^3*z^2 - 2*y^4*z^2 + 3*x^2*y*z^3 - x*y^2*z^3 + 2*y^3*z^3 + 3*x^2*z^4 + 2*x*y*z^4 - y^2*z^4 + 3*x*z^5 + 2*y*z^5 + 3*z^6 + 3*x^5 + 17/6*x^4*y + 3*x^3*y^2 - x^2*y^3 + 2*y^5 - 3*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 - 3*x*y^2*z^2 + y^3*z^2 + 2*x^2*z^3 + x*y*z^3 - 3*y^2*z^3 + x*z^4 + 2*y*z^4 - 2*z^5 + 3*x^3*y - 3*x^2*y^2 - 3*x*y^3 + x^3*z + x^2*y*z + 2*x*y^2*z + y^3*z + 3*x^2*z^2 - x*y*z^2 - y^2*z^2 - 3*x*z^3 - 3*y*z^3 + 3*z^4 - 3*y^3 + 3*x*y*z + 2*y^2*z - 2*x*z^2 - 2*z^3', '-3*x^8 - 2*x^7*y + 2*x^5*y^3 + x^4*y^4 + 3*x^3*y^5 + x*y^7 - 3*y^8 - x^7*z + 2*x^6*y*z + 3*x^5*y^2*z - 3*x^3*y^4*z + 3*x^2*y^5*z + 3*x*y^6*z + 3*x^5*y*z^2 + 3*x^4*y^2*z^2 + x^3*y^3*z^2 + x*y^5*z^2 + y^6*z^2 + 3*x^5*z^3 + 2*x^4*y*z^3 - x^3*y^2*z^3 + 3*x^2*y^3*z^3 + x*y^4*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 - 2*x^2*y*z^5 + x*y^2*z^5 + 3*y^3*z^5 + 2*x^2*z^6 - 3*x*y*z^6 - 2*y^2*z^6 - 2*x*z^7 - 3*y*z^7 - z^8 + 10091/2520*x^7 + 3*x^6*y + 2*x^5*y^2 - x^3*y^4 + x*y^6 - 3*y^7 - 3*x^6*z - x^5*y*z - 2*x^4*y^2*z + x^3*y^3*z - 2*x^2*y^4*z + 2*y^6*z - 3*x^5*z^2 + 2*x^4*y*z^2 + 3*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 - 3*x^2*y^2*z^3 + x*y^3*z^3 + 3*y^4*z^3 + 2*x^3*z^4 + x^2*y*z^4 + 3*x*y^2*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 - 6317/1260*x^6 - x^5*y - 3*x^3*y^3 + 2*x^2*y^4 + 3*x*y^5 - 2*y^6 + x^5*z - x^4*y*z - 2*x^2*y^3*z - x*y^4*z - 3*y^5*z - x^4*z^2 + x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*x*y^3*z^2 - 2*x^3*z^3 - 2*x^2*y*z^3 + 3*x*y^2*z^3 + 2*y^3*z^3 + x^2*z^4 + x*y*z^4 + y^2*z^4 - 3*y*z^5 + 2*z^6 - x^5 + 7/3*x^4*y + 2*x^3*y^2 - 3*x^2*y^3 - x*y^4 - 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^2*y*z^2 + 3*x*y^2*z^2 - 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 - 3*z^5 - x^3*y + x^2*y^2 + 3*x*y^3 - y^4 - x^3*z + 3*x^2*y*z - 2*x*y^2*z + 3*y^3*z + 3*x^2*z^2 - 2*x*y*z^2 - 2*y^2*z^2 + 3*x*z^3 - y*z^3 - z^4 + y^3 - x*y*z - y*z^2 + z^3', '3*x^8 + 2*x^7*y + 3*x^6*y^2 + 3*x^5*y^3 + 3*x^4*y^4 + 2*x^3*y^5 - x*y^7 + 2*y^8 + 3*x^6*y*z - 3*x^5*y^2*z + x^4*y^3*z - 2*x^2*y^5*z - 2*x*y^6*z + y^7*z + 2*x^6*z^2 - x^5*y*z^2 - 3*x^4*y^2*z^2 - 3*x^3*y^3*z^2 - x^2*y^4*z^2 + x^5*z^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*x^4*z^4 + 2*x^3*y*z^4 - 3*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 - x*y*z^6 - 2*y^2*z^6 + 3*x*z^7 + 3*y*z^7 - z^8 - 1/315*x^7 + x^6*y + 3*x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + x^2*y^5 + x*y^6 - 3*y^7 + x^6*z + 2*x^5*y*z - x^4*y^2*z + 3*x^3*y^3*z - x^2*y^4*z + 3*x*y^5*z - y^6*z + 2*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 + 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 - 3*x^3*z^4 + 2*x^2*y*z^4 + 2*y^3*z^4 - 2*x^2*z^5 + x*y*z^5 + 2*y^2*z^5 - x*z^6 + y*z^6 + z^7 - 1261/210*x^6 + x^5*y + 2*x^4*y^2 - x^3*y^3 - 2*x^2*y^4 - 3*y^6 + 3*x^5*z + 3*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 + 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 + x^2*y*z^3 - 2*y^3*z^3 - 3*x^2*z^4 - 3*y^2*z^4 + 2*x*z^5 - 2*y*z^5 - 3*z^6 + 4*x^5 + 31/12*x^4*y + 2*x^3*y^2 + 3*x^2*y^3 - 3*x*y^4 - y^5 - 3*x^4*z - 3*x^3*y*z - 3*x^2*y^2*z + x*y^3*z - 3*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 - x*y*z^3 - 3*y^2*z^3 + x*z^4 - 3*z^5 + 3*x^4 - x^3*y - 14/3*x^2*y^2 - 2*y^4 + 3*x^3*z + 2*x^2*y*z + x*y^2*z - 3*y^3*z + 2*x*y*z^2 + 3*y^2*z^2 - x*z^3 + 2*y*z^3 - 3*x*y^2 + y^3 + 3*x^2*z - x*y*z - y^2*z - x*z^2 - 2*y*z^2 - 3*z^3']
  ok   R1 inflectional: D_3 = <E_0..E_3>, D_4 = <E_0,E_1,E_2> (Q = X^2*Y^2), D_5 = <E_0,E_1>, jets of [1:t:t^3]
--- R1 inflectional
  ok   R1 inflectional: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R1 inflectional: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 58 eliminated with constant pivots; residual equations:
       (2/7) * (-7*P_420*G_301*G_211 + 42*P_420*G_301*G_040 - 42*P_420*G_040*H_111 - 2*P_510*P_420*H_102 + 14*P_420*G_102 + 21*P_230*H_102)
       (1/42) * (-7*P_420*G_211^2 + 84*P_420*G_211*G_040 - 504*P_420*G_040*H_021 - 12*P_510*P_420*H_012 + 84*P_420*G_012 + 126*P_230*H_012)
       (3/7) * (-28*P_420*G_040*H_012 - 2*P_510*P_420*H_003 + 14*P_420*G_003 + 21*P_230*H_003)
  ok   R1 inflectional: on {P_420 != 0} the residual equations are triangular in ['G_102', 'G_012', 'G_003'] with diagonal (const)*P_420: a graph (irreducible)
  ok   R1 inflectional: on {P_420 = 0}: each equation is (P_230) times a linear form; components {c = 0} and {linear forms ['6*H_102', '3*H_012', '9*H_003'] = 0}
  ok   R1 inflectional, component W1 (P_420 != 0): a point of the component (residual equations vanish)
      timing: member+triples 0.3 s, stabilization 0.1 s
  ok   R1 inflectional, component W1 (P_420 != 0) anchor (A): fixed {'P_420': 1}, solved ['G_102', 'G_012', 'G_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 35 (ds), stabilization (35, 10)
      anchor generators: {'P': 'X^7 + X^4*Y^2 + 6*X^2*Y*Z + X*Y^2*Z + 4/3*Y^3*Z + 2*X^2*Z^2 - 2*Y^3 + Y*Z^2 + Z^3', 'G': 'X^4*Y - Y^3 + X*Y*Z + 2*Y^2*Z', 'H': 'X^2*Y^2 - 2*X*Y*Z - Y^2*Z - X*Z^2 - Z^3'}
      anchor triple: ['3*x^7*y - x^6*y^2 + 3*x^5*y^3 + x^4*y^4 + x^3*y^5 - 2*x^2*y^6 + 3*x*y^7 - y^8 + 2*x^7*z + x^6*y*z - 3*x^5*y^2*z + x^4*y^3*z - x^2*y^5*z + 2*x*y^6*z + y^7*z + 3*x^6*z^2 - 3*x^4*y^2*z^2 - 2*x^3*y^3*z^2 - 3*x^2*y^4*z^2 - 3*x*y^5*z^2 - 2*x^4*y*z^3 + x^3*y^2*z^3 + 3*x^2*y^3*z^3 + x^4*z^4 - 2*x^3*y*z^4 - 2*x^2*y^2*z^4 + 2*y^4*z^4 + x^2*y*z^5 - 2*x*y^2*z^5 - y^3*z^5 - x^2*z^6 + 2*x*y*z^6 + 3*y^2*z^6 + x*z^7 + y*z^7 + z^8 - 11/420*x^7 - 2*x^6*y + 3*x^5*y^2 + x^4*y^3 + x^3*y^4 + x*y^6 + y^7 - 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 - 3*x*y^5*z - y^6*z + 3*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 + y^5*z^2 - 2*x^3*y*z^3 + x^2*y^2*z^3 - x*y^3*z^3 - y^4*z^3 - x^3*z^4 + 3*x^2*y*z^4 + x*y^2*z^4 - y^3*z^4 + 3*x^2*z^5 - x*y*z^5 - y^2*z^5 - x*z^6 - y*z^6 - 41/2520*x^6 + 3*x^5*y + 2*x^4*y^2 + x^3*y^3 + 3*x^2*y^4 + y^6 - x^5*z - 2*x^4*y*z - x^3*y^2*z - 2*x*y^4*z - 2*y^5*z + 2*x^4*z^2 + x^2*y^2*z^2 + x*y^3*z^2 - 2*y^4*z^2 + 3*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 - x*y*z^4 + 3*y^2*z^4 + 3*x*z^5 - 3*y*z^5 - z^6 - 1/42*x^5 - 1/8*x^4*y + 2*x^3*y^2 - 3*x^2*y^3 - x*y^4 - 3*y^5 - 3*x^4*z + x^3*y*z - 2*x*y^3*z - 3*x^3*z^2 - 2*x^2*y*z^2 - 2*x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 + 3*x*y*z^3 - 2*y^2*z^3 - 2*x*z^4 - 2*z^5 + 5/2*x^2*y^2 - x*y^3 + 3*x^3*z + 3*x^2*y*z - x*y^2*z + 3*y^3*z - 2*x^2*z^2 + 3*x*y*z^2 + 2*y^2*z^2 - 3*x*z^3 + 2*y*z^3 + 2*z^4 + y^3 - x^2*z - 3*x*y*z + 3*y^2*z + 2*x*z^2 + z^3', 'x^8 - 2*x^7*y - 3*x^6*y^2 + 2*x^5*y^3 + 3*x^3*y^5 - 3*x^2*y^6 - x*y^7 - 2*y^8 - x^7*z - 3*x^6*y*z + x^5*y^2*z + 3*x^4*y^3*z - x^3*y^4*z - 3*x^2*y^5*z + x*y^6*z - y^7*z + 3*x^6*z^2 + 3*x^5*y*z^2 - 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*y^6*z^2 + 2*x^5*z^3 - 3*x^2*y^3*z^3 + x*y^4*z^3 - 3*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 - 3*x*y^2*z^5 + y^3*z^5 + 3*x^2*z^6 - y^2*z^6 - 3*x*z^7 + 3*y*z^7 - 3*z^8 - 17/504*x^7 + 3*x^6*y + 3*x^5*y^2 - x^4*y^3 + 2*x^2*y^5 - y^7 - 3*x^6*z - 2*x^5*y*z - 2*x^3*y^3*z - 3*x^2*y^4*z + x*y^5*z - 2*y^6*z + x^5*z^2 - 3*x^4*y*z^2 - 2*x^3*y^2*z^2 + x^2*y^3*z^2 + 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 - x*y^3*z^3 - y^4*z^3 - x^3*z^4 - 2*x^2*y*z^4 + x*y^2*z^4 - 2*y^3*z^4 + x*y*z^5 + 3*y^2*z^5 - x*z^6 - y*z^6 + z^7 + 1/56*x^6 + x^5*y + 3*x^4*y^2 + 2*x^2*y^4 + 3*x*y^5 - x^5*z + 2*x^4*y*z + 2*x^3*y^2*z + x^2*y^3*z - 3*x*y^4*z - 3*y^5*z - x^4*z^2 - x^2*y^2*z^2 + 3*x*y^3*z^2 - 2*y^4*z^2 + x^3*z^3 + 3*x^2*y*z^3 + 2*x*y^2*z^3 - 3*y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 - 3*y^2*z^4 + 2*x*z^5 - 3*y*z^5 + z^6 + 1/70*x^5 - 19/24*x^4*y - 3*x^3*y^2 + 2*x^2*y^3 - x*y^4 + y^5 + 2*x^4*z + x^3*y*z + x^2*y^2*z - 3*x*y^3*z + 3*y^4*z + 2*x^3*z^2 - 2*x^2*y*z^2 - 2*x*y^2*z^2 + 2*x^2*z^3 - x*y*z^3 - y^2*z^3 - 2*x*z^4 - z^5 - 3/2*x^2*y^2 - x*y^3 - x^2*y*z - 2*x*y^2*z + 3*y^3*z + 2*x^2*z^2 - 2*x*y*z^2 - 3*y^2*z^2 + 2*z^4 - 2*y^3 + 2*x^2*z + 3*x*y*z + y^2*z + 2*x*z^2 - 2*y*z^2 - 3*z^3', '3*x^8 + 3*x^6*y^2 + x^5*y^3 + 3*x^4*y^4 + 2*x^3*y^5 - x^2*y^6 - 2*x*y^7 + 3*y^8 + 2*x^7*z + 3*x^6*y*z - 2*x^5*y^2*z - 3*x^4*y^3*z - 3*x^3*y^4*z - x^2*y^5*z - x*y^6*z + y^7*z + 2*x^6*z^2 + 3*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 + x*y^5*z^2 - 2*y^6*z^2 - 3*x^5*z^3 + 2*x^4*y*z^3 - 3*x^3*y^2*z^3 - 3*x^2*y^3*z^3 + x*y^4*z^3 - y^5*z^3 - x^4*z^4 + x^3*y*z^4 + x^2*y^2*z^4 - 2*x*y^3*z^4 + 3*y^4*z^4 + 2*x^2*y*z^5 + 2*y^3*z^5 - x^2*z^6 - 2*x*y*z^6 + 3*y^2*z^6 + x*z^7 - 2*y*z^7 - z^8 + 23/2520*x^7 + 2*x^6*y + 3*x^5*y^2 - 2*x^4*y^3 + 2*x^3*y^4 + 3*x*y^6 + 3*y^7 + x^6*z + x^5*y*z - 2*x^4*y^2*z - x^3*y^3*z + 2*x^2*y^4*z + 3*x*y^5*z + y^6*z + 2*x^5*z^2 - x^4*y*z^2 - 3*x^3*y^2*z^2 + x^2*y^3*z^2 + x*y^4*z^2 + 3*y^5*z^2 - 2*x^4*z^3 + 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 - 3*x*y^2*z^4 + 3*y^3*z^4 - 3*x^2*z^5 + 3*y^2*z^5 + 3*y*z^6 + 2*z^7 - 79/2520*x^6 - 3*x^5*y - x^4*y^2 + 3*x^3*y^3 + 2*x^2*y^4 + x*y^5 - 3*y^6 + 3*x^5*z - 2*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 + 2*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 + x*y^2*z^3 + 2*y^3*z^3 + 3*x^2*z^4 - 3*x*y*z^4 - 2*y^2*z^4 - x*z^5 + y*z^5 + z^6 + 4/105*x^5 - 1/3*x^4*y + 3*x^3*y^2 - 3*x^2*y^3 + 2*x*y^4 - 2*x^4*z - 3*x^3*y*z - 3*x*y^3*z - 3*y^4*z + 2*x^3*z^2 + 3*y^3*z^2 + x^2*z^3 + 3*x*y*z^3 + 3*y^2*z^3 - 3*x*z^4 - 2*y*z^4 - 2*z^5 - 4*x^2*y^2 - 3*x*y^3 - 2*y^4 + 2*x^3*z - 3*x*y^2*z + y^3*z - 3*x*y*z^2 + 3*y^2*z^2 - 2*x*z^3 - 3*y*z^3 + 2*z^4 - 2*y^3 + 2*x^2*z - y^2*z + 2*x*z^2 - 3*y*z^2 - 3*z^3']
  ok   R1 inflectional, component W2 (P_420 = 0 = P_230): a point of the component (residual equations vanish)
      timing: member+triples 0.6 s, stabilization 0.4 s
  ok   R1 inflectional, component W2 (P_420 = 0 = P_230) anchor (A): fixed {'P_420': 0}, solved ['P_230']; member closed with H and the prescribed graded data: True; a triple of I of local length 38 (ds), stabilization (38, 13)
      anchor generators: {'P': 'X^7 - 2*Y^3 + 2*X*Y*Z - 2*Y^2*Z + X*Z^2 + 2*Y*Z^2', 'G': 'X^4*Y - 2*Y^3 + 2*X*Z^2 - 2*Y*Z^2', 'H': 'X^2*Y^2 - 2*Y^3 + X*Y*Z - 2*Y^2*Z + X*Z^2 + 2*Y*Z^2'}
      anchor triple: ['x^8 + 3*x^6*y^2 + 3*x^5*y^3 - x^4*y^4 - 3*x^3*y^5 + x^2*y^6 - 2*x*y^7 + 3*y^8 + x^6*y*z + 2*x^4*y^3*z - 2*x^3*y^4*z - x^2*y^5*z - y^7*z + 3*x^6*z^2 - 3*x^5*y*z^2 - 3*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 - 2*x^4*y*z^3 - x^3*y^2*z^3 - 3*x^2*y^3*z^3 + y^5*z^3 - 2*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 + 3*x^2*y*z^5 - 2*x*y^2*z^5 - x*y*z^6 + 3*y^2*z^6 - 3*x*z^7 + z^8 + 1/90*x^7 - 3*x^6*y - 2*x^5*y^2 - 3*x^3*y^4 - x^2*y^5 - 3*x*y^6 - 3*y^7 + 2*x^6*z + 2*x^5*y*z - 3*x^3*y^3*z + 2*x^2*y^4*z - 3*x*y^5*z - 3*x^5*z^2 + x^4*y*z^2 - 3*x^3*y^2*z^2 + 2*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*y^4*z^3 + 2*x^2*y*z^4 + 3*x*y^2*z^4 + y^3*z^4 - 3*x^2*z^5 - 2*x*y*z^5 - 2*y^2*z^5 - 2*x*z^6 - 3*y*z^6 + 3*z^7 - 3*x^4*y^2 - 3*x^3*y^3 + 3*x^2*y^4 - 2*x*y^5 + y^6 - 2*x^5*z + x^4*y*z + x^3*y^2*z - 3*x^2*y^3*z - x*y^4*z + 3*x^4*z^2 - x^3*y*z^2 + x*y^3*z^2 + 2*y^4*z^2 - x^2*y*z^3 - 3*x*y^2*z^3 + 2*y^3*z^3 - x^2*z^4 + x*y*z^4 - 2*y^2*z^4 + 2*x*z^5 - 3*z^6 + 2/3*x^4*y + x^3*y^2 + 2*x*y^4 + y^5 - 3*x^4*z + x^3*y*z + 3*x^2*y^2*z - x*y^3*z - 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 + 3*x*y*z^3 - y^2*z^3 + 2*x*z^4 - y*z^4 + z^5 + 53/4*x^2*y^2 - 2*x*y^3 - 2*y^4 + 2*x^3*z - 3*x^2*y*z - x*y^2*z - 2*y^3*z + 3*x^2*z^2 - 2*x*y*z^2 - y^2*z^2 - x*z^3 + 2*z^4 + 2*y^3 - 2*x^2*z - 3*x*y*z + 3*y^2*z - x*z^2 - 3*y*z^2 + 2*z^3', '2*x^8 + 2*x^7*y + x^6*y^2 + 2*x^5*y^3 - x^4*y^4 - 3*x^3*y^5 - 2*x^2*y^6 + 3*x^7*z - 3*x^6*y*z + x^5*y^2*z - 2*x^4*y^3*z + 3*x^3*y^4*z - 2*x^2*y^5*z - 3*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 - 2*x^2*y^4*z^2 - 3*x*y^5*z^2 + y^6*z^2 - 3*x^5*z^3 + 3*x^2*y^3*z^3 + 2*x*y^4*z^3 + x^4*z^4 + 3*x^2*y^2*z^4 - y^4*z^4 - 2*x^2*y*z^5 + 2*x*y^2*z^5 - 2*x^2*z^6 - 2*x*y*z^6 - 3*y^2*z^6 - 2*y*z^7 - 2*z^8 - 1/280*x^7 + 2*x^6*y - 3*x^5*y^2 + 3*x^4*y^3 + 3*x^3*y^4 - 2*y^7 - x^6*z - 2*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 - y^6*z + x^5*z^2 + x^4*y*z^2 - 2*x^3*y^2*z^2 + x^2*y^3*z^2 - x*y^4*z^2 + y^5*z^2 + x^3*y*z^3 + 3*x^2*y^2*z^3 - 2*x*y^3*z^3 - 3*y^4*z^3 + x^3*z^4 + 2*x^2*y*z^4 - x*y^2*z^4 - 2*y^3*z^4 + 3*x^2*z^5 - 2*x*y*z^5 + 2*y^2*z^5 - 2*x*z^6 + y*z^6 + 3*z^7 + x^5*y + 3*x^4*y^2 - 2*x^3*y^3 - x^2*y^4 - 2*x*y^5 + 2*y^6 + 2*x^5*z + 3*x^3*y^2*z + y^5*z - 3*x^4*z^2 - 2*x^3*y*z^2 + 3*x^2*y^2*z^2 + 2*x*y^3*z^2 - y^4*z^2 + 3*x^3*z^3 - 2*x^2*y*z^3 + 3*x*y^2*z^3 + 3*y^3*z^3 - 2*x^2*z^4 - 3*x*y*z^4 + 3*y^2*z^4 + 2*x*z^5 + 2*z^6 - 5/6*x^4*y - x^3*y^2 + 2*x^2*y^3 - x*y^4 - y^5 + 2*x^4*z - 3*x^3*y*z - x^2*y^2*z + x*y^3*z + 2*x^2*y*z^2 + 2*x*y^2*z^2 - 2*y^3*z^2 - x*y*z^3 - y^2*z^3 + 3*x*z^4 - 2*y*z^4 + 3*z^5 - 19/4*x^2*y^2 - 2*x*y^3 + 3*y^4 + 2*x^3*z + x^2*y*z + 2*x*y^2*z - y^3*z - x*y*z^2 - y^2*z^2 + x*z^3 - 2*y*z^3 + 3*z^4 - 2*y^3 + 2*x^2*z - x*y*z - y^2*z - 2*x*z^2 - y*z^2 - z^3', 'x^8 - 3*x^7*y - 3*x^6*y^2 + 2*x^5*y^3 - 2*x^3*y^5 + 3*x^2*y^6 + x*y^7 + 2*y^8 - 3*x^7*z - x^6*y*z - 2*x^5*y^2*z - 2*x^4*y^3*z - 3*x^3*y^4*z - 2*x^2*y^5*z - x*y^6*z + 3*y^7*z - 2*x^6*z^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 + y^6*z^2 + 3*x^5*z^3 + 2*x^4*y*z^3 - 2*x^3*y^2*z^3 + x^2*y^3*z^3 + 2*y^5*z^3 + 3*x^4*z^4 + x^2*y^2*z^4 + 3*x*y^3*z^4 - y^4*z^4 + x^3*z^5 + x^2*y*z^5 + x*y^2*z^5 + x^2*z^6 - 3*x*y*z^6 + x*z^7 - 3*y*z^7 + z^8 + 1/504*x^7 + x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 - 2*x^2*y^5 + 3*x*y^6 - y^7 - x^6*z - 3*x^5*y*z + 3*x^4*y^2*z - 2*x^3*y^3*z + x^2*y^4*z - x*y^5*z - y^6*z + 2*x^4*y*z^2 - 3*x^2*y^3*z^2 - 3*x*y^4*z^2 + 2*x^4*z^3 + 3*x^3*y*z^3 + 2*x^2*y^2*z^3 - x*y^3*z^3 - y^4*z^3 - 3*x^3*z^4 + 2*x^2*y*z^4 - 3*y^3*z^4 - x*y*z^5 - 3*y^2*z^5 - x*z^6 + 3*y*z^6 + 3*x^5*y + x^3*y^3 + 3*x^2*y^4 + 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 - 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 + x*y^2*z^3 + 3*y^3*z^3 - 2*x^2*z^4 - 3*x*y*z^4 + y^2*z^4 + 2*x*z^5 + y*z^5 + 3*z^6 + 5/3*x^4*y - 2*x^3*y^2 + 3*x^2*y^3 - 3*x*y^4 + x^4*z - 3*x^3*y*z + 2*x^2*y^2*z + x*y^3*z + 3*y^4*z + 2*x^3*z^2 - x*y^2*z^2 + 3*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 - 2*z^5 + 3*x^2*y^2 - x*y^3 + y^4 + 2*x^3*z + 3*x^2*y*z + 2*x*y^2*z + 3*y^3*z + 3*x^2*z^2 + x*y*z^2 - 2*y^2*z^2 + 2*x*z^3 + 2*y*z^3 + 3*y^3 - 3*x^2*z + 2*x*y*z - 3*y^2*z + x*z^2 + 2*y*z^2 + z^3']
  ok   R1 inflectional, component W3 (P_420 = 0, linear): a point of the component (residual equations vanish)
      timing: member+triples 0.4 s, stabilization 0.2 s
  ok   R1 inflectional, component W3 (P_420 = 0, linear) anchor (A): fixed {'P_420': 0}, solved ['H_102', 'H_012', 'H_003']; member closed with H and the prescribed graded data: True; a triple of I of local length 38 (ds), stabilization (38, 12)
      anchor generators: {'P': 'X^7 - X^2*Y^3 + 18*X^2*Y*Z - 3*X*Y^2*Z - 2*Y^3 - X*Y*Z - 2*Y^2*Z + X*Z^2 + 2*Y*Z^2', 'G': 'X^4*Y + Y^3 + X*Y*Z + 2*Y^2*Z + 2*X*Z^2 + Y*Z^2 - Z^3', 'H': 'X^2*Y^2 + 2*Y^3 + 2*X*Y*Z'}
      anchor triple: ['-3*x^8 + x^7*y - 2*x^6*y^2 - 3*x^5*y^3 + x^4*y^4 - 2*x^3*y^5 + 3*x^2*y^6 - 3*x*y^7 + y^8 - 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 + y^7*z - x^6*z^2 + 2*x^5*y*z^2 - 2*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 + 2*x*y^4*z^3 - y^5*z^3 + x^4*z^4 - 2*x^3*y*z^4 - 2*x^2*y^2*z^4 - 2*x*y^3*z^4 - 3*x^3*z^5 - 2*x^2*y*z^5 + 2*x*y^2*z^5 - 2*y^3*z^5 - 2*y^2*z^6 - 3*x*z^7 + 2*y*z^7 - z^8 - 61/5040*x^7 - 3*x^6*y + x^5*y^2 - 3*x^4*y^3 + x^2*y^5 + x*y^6 - 2*y^7 + 2*x^5*y*z + x^4*y^2*z - 3*x^3*y^3*z + 2*x^2*y^4*z - 3*x*y^5*z - y^6*z - 3*x^5*z^2 - x^4*y*z^2 - x^3*y^2*z^2 + 3*x^2*y^3*z^2 - 3*x*y^4*z^2 + 3*y^5*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 - 3*x^3*z^4 + x^2*y*z^4 + x*y^2*z^4 + 2*x^2*z^5 - 2*x*y*z^5 - 3*y^2*z^5 + 2*y*z^6 + 5/168*x^6 - 2*x^5*y - 2*x^4*y^2 + x^3*y^3 + 2*x^2*y^4 + 2*y^6 + 3*x^5*z + 3*x^4*y*z - 3*x^3*y^2*z + x^2*y^3*z + 2*x*y^4*z - 3*y^5*z + 3*x^4*z^2 - 2*x^2*y^2*z^2 + 3*x*y^3*z^2 - 3*y^4*z^2 - 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*y^2*z^4 - 3*x*z^5 - 2*y*z^5 + 1/420*x^5 - 29/24*x^4*y - x^3*y^2 - 2*x^2*y^3 - 2*y^5 - 3*x^3*y*z - 3*x^2*y^2*z - 2*x*y^3*z + y^4*z + 2*x^3*z^2 - 3*x^2*y*z^2 + 2*x*y^2*z^2 - y^3*z^2 - 2*x^2*z^3 + 3*x*y*z^3 - y^2*z^3 + 2*x*z^4 + 2*y*z^4 + 3*z^5 - 3/2*x^2*y^2 + 2*x*y^3 + 2*x^3*z + 2*x^2*y*z + 2*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 - 3*y*z^3 - z^4 + y^3 - x^2*z - 3*x*y*z + 3*y^2*z - x*z^2 - 3*z^3', '-3*x^8 - x^6*y^2 - 3*x^5*y^3 - 2*x^4*y^4 + 3*x^3*y^5 + 2*x^2*y^6 + 2*x*y^7 - y^8 - x^7*z + x^5*y^2*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 + x^6*z^2 + 3*x^5*y*z^2 - 2*x^4*y^2*z^2 + 2*x^3*y^3*z^2 - 2*x*y^5*z^2 - 3*y^6*z^2 - 3*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^4*z^4 + 3*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 + 3*x^2*y*z^5 - y^3*z^5 + x^2*z^6 - x*y*z^6 - 2*x*z^7 + 2*y*z^7 - 2*z^8 - 31/1680*x^7 - x^6*y + 3*x^4*y^3 - x^3*y^4 + 3*x^2*y^5 - x*y^6 + x^6*z - 2*x^5*y*z - 2*x^4*y^2*z + 3*x^3*y^3*z + 3*x^2*y^4*z - 3*x*y^5*z - x^5*z^2 - 3*x^4*y*z^2 - 2*x^3*y^2*z^2 - x^2*y^3*z^2 + x*y^4*z^2 - y^5*z^2 - x^4*z^3 + 2*x^3*y*z^3 + x^2*y^2*z^3 - x*y^3*z^3 + 3*x^3*z^4 - 3*x*y^2*z^4 - y^3*z^4 - x*y*z^5 - y^2*z^5 - x*z^6 - 3*y*z^6 + 2*z^7 + 19/840*x^6 + x^5*y + x^4*y^2 - 3*x^3*y^3 + 3*x^2*y^4 + 2*x*y^5 - 2*y^6 - 3*x^5*z - x^3*y^2*z - x^2*y^3*z + x*y^4*z + y^5*z - 2*x^4*z^2 - 2*x^3*y*z^2 + 3*x*y^3*z^2 - 3*y^4*z^2 + 2*x^3*z^3 - 3*x^2*y*z^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 - 2*x*z^5 + y*z^5 - z^6 - 1/420*x^5 + 5/8*x^4*y - 2*x*y^4 + 3*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 + 2*x^2*y*z^2 + x*y^2*z^2 + 2*y^3*z^2 - 2*x^2*z^3 - 2*x*z^4 - 3*y*z^4 + 9/2*x^2*y^2 + x*y^3 + y^4 - 3*x^3*z + 2*x^2*y*z - 3*x*y^2*z + 3*y^3*z + 3*x^2*z^2 + 2*x*y*z^2 - y^2*z^2 + 2*x*z^3 - y*z^3 + 2*z^4 - y^3 + x^2*z - 3*x*y*z - y^2*z - 2*x*z^2 - 3*y*z^2 - 2*z^3', '2*x^8 - 2*x^7*y + 3*x^6*y^2 - 3*x^5*y^3 + 3*x^3*y^5 - x^2*y^6 + x*y^7 + y^8 - 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 + x*y^6*z - 2*y^7*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 - 3*x*y^5*z^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*x*y^4*z^3 - y^5*z^3 + 2*x^3*y*z^4 - 3*x^2*y^2*z^4 + 3*x*y^3*z^4 + y^4*z^4 + 2*x^3*z^5 + 3*x^2*y*z^5 - 2*x*y^2*z^5 + 2*y^3*z^5 + 2*x^2*z^6 - 2*y^2*z^6 - 2*y*z^7 + 2*z^8 + 13/560*x^7 - 3*x^6*y - 2*x^5*y^2 - 3*x^3*y^4 + x^2*y^5 - 3*y^7 + 2*x^6*z + 3*x^5*y*z + 3*x^4*y^2*z - 2*x^3*y^3*z + 3*x^2*y^4*z + 3*x*y^5*z - y^6*z - x^5*z^2 - 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 - 2*x^4*z^3 + x^3*y*z^3 - 2*x^2*y^2*z^3 + x*y^3*z^3 - 2*y^4*z^3 + x^3*z^4 - 2*x^2*y*z^4 + 3*x*y^2*z^4 + y^3*z^4 + 2*y^2*z^5 + 2*x*z^6 + 2*y*z^6 - z^7 - 2/105*x^6 - 3*x^5*y - 3*x^4*y^2 - 3*x^3*y^3 + 2*x^2*y^4 + 3*y^6 - 3*x^5*z + 2*x^4*y*z + 2*x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z + 3*y^5*z - 2*x^4*z^2 - x^3*y*z^2 + 2*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 + 2*y^3*z^3 + 3*x*y*z^4 - y^2*z^4 - 3*x*z^5 - y*z^5 + 1/140*x^5 - 11/8*x^4*y + 2*x*y^4 + 2*y^5 - x^4*z - x^3*y*z + x^2*y^2*z - 3*y^4*z - x^3*z^2 - 2*x^2*y*z^2 + 3*y^3*z^2 - 2*x^2*z^3 - 3*x*y*z^3 - y^2*z^3 - x*z^4 - 2*y*z^4 - 3*z^5 - 21/2*x^2*y^2 + 2*x*y^3 + 3*y^4 - 2*x^3*z - 2*x^2*y*z + 3*x*y^2*z + 3*y^3*z + 3*x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 + 3*z^4 + 3*y^3 - 3*x^2*z + 3*x*y*z - 2*y^2*z + y*z^2 - 3*z^3']
time 13.4 s
anchor lengths: {'R5 l=Y': [36, 39, 35], 'R5 l=Y+Z': [35, 39, 35], 'R1 conic': [35, 38, 40], 'R1 inflectional': [35, 38, 38]}
ALL CHECKS PASSED
