=== (U) the transformation rule for R (normal forms Y^4, X^2Y^2+Y^4, XY^3, X^2Y^2)
  ok   (U) R(X, Y+cX) = (r2+3c r3+6c^2 r4) X^2Y^2 + (r3+4c r4) XY^3 + r4 Y^4 mod <X^4, X^3Y>
    R = Y4: dim S_1 o D_4 = 3
    R = X2Y2+Y4: dim S_1 o D_4 = 4
    R = XY3: dim S_1 o D_4 = 4
    R = X2Y2: dim S_1 o D_4 = 3
=== tangent sector: D_5 = <X^5, X^4Y>, D_4 = <X^4, X^3Y, R>; generators P (X^7, tails 6,5,4,3), G (X^4Y, tails 4,3), H (R, tail 3)
--- R = Y4
  ok   R = Y4: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R = Y4: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 58 eliminated with constant pivots; residual equations:
       (2) * (-P_420*G_301*G_211 + 2*P_420*G_102 + 5*P_050*H_102)
       (1/6) * (-P_420*G_211^2 + 12*P_420*G_012 + 30*P_050*H_012)
       (3) * (2*P_420*G_003 + 5*P_050*H_003)
  ok   R = Y4: every closedness condition lies in the ideal of the residual equations after the substitutions
  ok   R = Y4: 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   R = Y4: on {P_420 = 0}: each equation is (P_050) times a linear form; components {P_050 = 0} and {['10*H_102', '5*H_012', '15*H_003'] = 0}
  ok   R = Y4, component W1 (P_420 != 0): a point of the component (residual equations vanish)
  ok   R = Y4, 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 39 (ds vdim), stabilization (length, N) = (39, 11)
      anchor generators: {'P': 'X^7 + X^4*Y^2 - 2*X^2*Y*Z + X*Y^2*Z - 2*X*Y*Z + Y^2*Z + X*Z^2 - Y*Z^2 - 2*Z^3', 'G': 'X^4*Y - X^2*Z + X*Y*Z', 'H': 'Y^4 + X^2*Z - X*Y*Z - Y^2*Z + X*Z^2 + Z^3'}
      triple: ['-x^8 - 2*x^7*y + x^6*y^2 - 3*x^5*y^3 + 3*x^4*y^4 + 2*x^3*y^5 + 2*x^2*y^6 - 2*x*y^7 + 3*x^4*y^3*z - 2*x^3*y^4*z - x^2*y^5*z + 3*x^6*z^2 + 2*x^4*y^2*z^2 - x^3*y^3*z^2 - x^2*y^4*z^2 + 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 + 3*x^2*y^3*z^3 + 2*y^5*z^3 + 2*x^4*z^4 - 2*x^2*y^2*z^4 + x*y^3*z^4 + 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 - x^2*z^6 - x*y*z^6 + y^2*z^6 - 3*x*z^7 + 2*y*z^7 - z^8 + 1/210*x^7 + 3*x^5*y^2 - 2*x^4*y^3 - 2*x^3*y^4 - 3*x^2*y^5 + x*y^6 + y^7 + x^6*z + 2*x^5*y*z + x^4*y^2*z + 2*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 + 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^2*y^2*z^3 - x*y^3*z^3 + y^4*z^3 - 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 + y^2*z^5 - x*z^6 - 2*y*z^6 + z^7 + 13/630*x^6 - 3*x^5*y - x^4*y^2 + x^2*y^4 - 3*x^5*z + 2*x^4*y*z - x^3*y^2*z - 3*x^2*y^3*z - 3*x*y^4*z + 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 - 3*x^2*y*z^3 - 3*x*y^2*z^3 - 2*y^3*z^3 - 2*x^2*z^4 + x*y*z^4 + 2*y*z^5 - 3*z^6 - 2*x^3*y^2 - x^2*y^3 - 3*y^5 + 3*x^4*z - 2*x^2*y^2*z + 2*x*y^3*z - 2*y^4*z - x^3*z^2 - x^2*y*z^2 + x*y^2*z^2 + 2*y^3*z^2 + x^2*z^3 + x*z^4 + 2*y*z^4 - z^5 + x*y^3 + 5/12*y^4 + 2*x^3*z - x^2*y*z - x*y^2*z - 3*y^3*z + x*y*z^2 - y^2*z^2 + 3*x*z^3 + 3*y*z^3 + z^4 + x^2*z + 2*x*y*z + x*z^2 - 2*z^3', '-3*x^8 - 3*x^6*y^2 + 3*x^5*y^3 + x^4*y^4 + x^3*y^5 + 2*x^2*y^6 + 2*x*y^7 - 3*y^8 + 3*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 + y^7*z - 2*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*y^6*z^2 - x^5*z^3 - 2*x^4*y*z^3 + 3*x^3*y^2*z^3 - 3*x*y^4*z^3 + x^4*z^4 + 3*x^2*y^2*z^4 - x*y^3*z^4 - 2*x^3*z^5 + 2*x^2*y*z^5 + 2*x*y^2*z^5 + 2*y^3*z^5 - 3*x^2*z^6 - x*y*z^6 + 2*x*z^7 - y*z^7 - 1/252*x^7 + 3*x^5*y^2 - 3*x^4*y^3 - 2*x^3*y^4 - 3*x^2*y^5 - 3*x*y^6 + 2*y^7 + x^6*z - 2*x^5*y*z - x^4*y^2*z + 3*x^2*y^4*z - x*y^5*z + y^6*z + 2*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 + 3*y^5*z^2 + x^4*z^3 + x^3*y*z^3 - x^2*y^2*z^3 + x*y^3*z^3 - 3*y^4*z^3 - 3*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 + y^2*z^5 + y*z^6 + z^7 - 37/1260*x^6 - x^3*y^3 + x^2*y^4 - x*y^5 + 3*y^6 - x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z + 2*y^5*z + 3*x^4*z^2 + 2*x^3*y*z^2 + 2*x^2*y^2*z^2 + x*y^3*z^2 + 3*y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 + x*y^2*z^3 - x^2*z^4 + 3*x*y*z^4 - y^2*z^4 + 3*x*z^5 - 3*y*z^5 - z^6 - 1/105*x^5 - 1/24*x^4*y + 3*x^3*y^2 + x^2*y^3 - 2*x*y^4 - y^5 - 2*x^4*z + x^3*y*z + x^2*y^2*z + 3*x*y^3*z + y^4*z - x^3*z^2 + 3*x*y^2*z^2 + 2*y^3*z^2 - x^2*z^3 - 2*x*y*z^3 - y^2*z^3 + x*z^4 - 3*y*z^4 - 3*z^5 + x^2*y^2 + 19/24*y^4 - 2*x^3*z + 3*x^2*y*z + 3*x*y^2*z - 3*y^3*z + x^2*z^2 - 3*x*y*z^2 + x*z^3 + 3*z^4 - x^2*z - x*y*z - 3*x*z^2 - 3*y*z^2 - 2*z^3', '-2*x^7*y + 2*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 + y^8 + 2*x^7*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 + 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 - x^3*y^3*z^2 - 3*x^2*y^4*z^2 + 2*x*y^5*z^2 - 3*y^6*z^2 - 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*y^4*z^4 + 2*x^3*z^5 - x^2*y*z^5 + y^3*z^5 + 3*x^2*z^6 + x*y*z^6 - 3*y^2*z^6 - 3*y*z^7 + 3*z^8 + 29/1260*x^7 - 3*x^6*y - 3*x^5*y^2 + x^4*y^3 + 2*x^3*y^4 + x^6*z - 2*x^5*y*z + 2*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 + 2*x^2*y^3*z^2 + x*y^4*z^2 + 3*y^5*z^2 - 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 - 2*y^3*z^4 + 3*y^2*z^5 - 3*x*z^6 - y*z^6 + z^7 - 4/315*x^6 - 2*x^5*y - 2*x^4*y^2 + x^3*y^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 - y^5*z + 2*x^4*z^2 - 3*x^3*y*z^2 + x^2*y^2*z^2 + 2*x*y^3*z^2 - 3*y^4*z^2 + x^3*z^3 + 3*x^2*y*z^3 + 2*y^3*z^3 + 3*x^2*z^4 + x*y*z^4 + 3*y^2*z^4 - x*z^5 - 2*y*z^5 - z^6 - 2/105*x^5 + 5/24*x^4*y + x^3*y^2 - 2*x^2*y^3 + x*y^4 + x^4*z - x^3*y*z + x^2*y^2*z - x*y^3*z + y^4*z - 3*x^3*z^2 + 2*x^2*y*z^2 - x*y^2*z^2 - 3*x^2*z^3 - 3*x*y*z^3 - z^5 + 2*x^2*y^2 - 3*x*y^3 - 1/24*y^4 - x^3*z + 3*x^2*y*z + 3*x*y^2*z + 2*y^3*z + x*y*z^2 - 3*y^2*z^2 - x*z^3 - y*z^3 - z^4 + x^2*z - 3*x*y*z + 2*y^2*z - 3*x*z^2 + 3*y*z^2 + z^3']
  ok   R = Y4, component W2 (P_420 = 0 = P_050): a point of the component (residual equations vanish)
  ok   R = Y4, component W2 (P_420 = 0 = P_050) anchor (A): fixed {'P_420': 0, 'P_050': 0}, solved []; member closed with H and the prescribed graded data: True; a triple of I of local length 41 (ds vdim), stabilization (length, N) = (41, 13)
      anchor generators: {'P': 'X^7 + 2*X^2*Z - 2*X*Y*Z + X*Z^2 + 2*Y*Z^2 - 2*Z^3', 'G': 'X^4*Y - 2*X*Y*Z - Y^2*Z + 2*X*Z^2 - Z^3', 'H': 'Y^4 - X^2*Z + 2*Y*Z^2 - Z^3'}
      triple: ['x^8 - 2*x^7*y - 3*x^6*y^2 + 3*x^5*y^3 - x^4*y^4 - 3*x^3*y^5 + 3*y^8 + x^7*z - 2*x^6*y*z - 3*x^5*y^2*z - 2*x^4*y^3*z - 2*x^3*y^4*z + 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 - x^4*y^2*z^2 + 3*x^2*y^4*z^2 - 2*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 - 3*x*y^4*z^3 + y^5*z^3 - 3*x^3*y*z^4 - 2*x*y^3*z^4 + 2*y^4*z^4 + 3*x^2*y*z^5 - 3*x*y^2*z^5 + 3*y^3*z^5 - 2*x^2*z^6 - 3*x*y*z^6 + x*z^7 + 3*y*z^7 + 1/168*x^7 + 3*x^6*y - x^4*y^3 + 3*x^3*y^4 - x^2*y^5 + 3*x*y^6 - 3*y^7 + x^6*z - 2*x^5*y*z - 3*x^4*y^2*z + 2*x^3*y^3*z - 3*x*y^5*z + 3*y^6*z - 2*x^5*z^2 - 2*x^4*y*z^2 + x^3*y^2*z^2 + 3*x*y^4*z^2 - 3*y^5*z^2 + x^4*z^3 - x^2*y^2*z^3 - x*y^3*z^3 + 2*x^3*z^4 + x^2*y*z^4 + x*y^2*z^4 - y^3*z^4 - x*y*z^5 + 3*y^2*z^5 + 2*y*z^6 - 3*z^7 + 3*x^5*y - 2*x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 - 2*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 + x^2*y^2*z^2 - 2*x*y^3*z^2 + 2*x*y^2*z^3 + y^3*z^3 - x*y*z^4 - 2*y^2*z^4 + 3*x*z^5 - y*z^5 + 5/12*x^4*y + 3*x^3*y^2 - 3*x^2*y^3 + x*y^4 + 2*y^5 - 3*x^4*z - 2*x^3*y*z + x^2*y^2*z + 2*x*y^3*z - 3*x^3*z^2 - 2*x^2*y*z^2 - y^3*z^2 + x^2*z^3 + 3*x*y*z^3 + y^2*z^3 - 2*x*z^4 + 2*y*z^4 + 2*z^5 + 5/6*y^4 + x^2*y*z + 2*x*y^2*z - y^3*z + 3*x^2*z^2 - 3*x*y*z^2 + 3*y^2*z^2 - 2*x*z^3 - 2*y*z^3 - z^4 + x^2*z + 2*x*y*z + 3*x*z^2 + 3*z^3', 'x^8 - 2*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 - 2*x^7*z + 2*x^6*y*z + 2*x^5*y^2*z - 3*x^4*y^3*z - x^3*y^4*z - 2*x*y^6*z + 3*x^5*y*z^2 - 2*x^3*y^3*z^2 - 3*x^2*y^4*z^2 - 3*x*y^5*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*y^4*z^3 - 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 + x^3*z^5 - 2*x^2*y*z^5 - x*y^2*z^5 + 2*y^3*z^5 - 2*x^2*z^6 + 2*y^2*z^6 + 3*x*z^7 - 3*y*z^7 - 1/180*x^7 + 3*x^6*y + x^5*y^2 + x^4*y^3 + 3*x^3*y^4 + 3*x^2*y^5 - x*y^6 - 2*y^7 - 2*x^6*z + x^5*y*z + x^4*y^2*z + 2*x^3*y^3*z + 3*x^2*y^4*z - x*y^5*z + y^6*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 + x^3*y*z^3 - 2*x^2*y^2*z^3 - 2*x*y^3*z^3 - 2*x^2*y*z^4 + x*y^2*z^4 + 3*y^3*z^4 - x^2*z^5 + x*y*z^5 + 2*y^2*z^5 + x*z^6 - z^7 - x^5*y + 2*x^4*y^2 + 3*x^3*y^3 - 3*x^2*y^4 + x*y^5 + y^6 + 3*x^4*y*z - 2*x^2*y^3*z + x*y^4*z + 2*y^5*z - 3*x^4*z^2 - 3*x^3*y*z^2 - x^2*y^2*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 + 3*y^2*z^4 - 2*x*z^5 + 3*y*z^5 + 3*z^6 - 1/2*x^4*y - 3*x^3*y^2 - x^2*y^3 + 2*x*y^4 + 2*y^5 - 2*x^4*z - x^3*y*z + x^2*y^2*z + x*y^3*z - y^4*z - x^3*z^2 + 2*x*y^2*z^2 - 2*x^2*z^3 - x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 - y*z^4 + 2*z^5 + x^2*y^2 - 11/12*y^4 - x^3*z + 2*x^2*y*z + 2*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 + 2*y*z^3 - z^4 - 2*x^2*z + 3*y^2*z - 3*z^3', '-x^8 + x^7*y - 2*x^5*y^3 - 2*x^4*y^4 - 2*x^3*y^5 - x^2*y^6 - 3*x*y^7 + 2*y^8 - 3*x^7*z + 2*x^6*y*z - x^4*y^3*z + 2*x^3*y^4*z + x^2*y^5*z - 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 + x^3*y^3*z^2 + 3*x^2*y^4*z^2 + x*y^5*z^2 + 3*y^6*z^2 - 2*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 - x^4*z^4 + x^3*y*z^4 + 3*x^2*y^2*z^4 + x*y^3*z^4 - 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 - x^2*z^6 - x*y*z^6 + 3*y^2*z^6 + 3*x*z^7 - 2*z^8 + 17/2520*x^7 + x^6*y + 2*x^5*y^2 + 3*x^4*y^3 + 3*x^3*y^4 - 2*x^2*y^5 - 3*x*y^6 - 3*x^6*z + 2*x^5*y*z + 2*x^3*y^3*z + 3*x^2*y^4*z + 3*x*y^5*z - 2*y^6*z - 3*x^5*z^2 + x^4*y*z^2 - 2*x^3*y^2*z^2 + 3*x*y^4*z^2 + x^4*z^3 + x^2*y^2*z^3 + 2*x*y^3*z^3 + 2*y^4*z^3 + 3*x^3*z^4 + 3*x^2*y*z^4 + 3*x*y^2*z^4 + 3*y^3*z^4 - x^2*z^5 - 2*x*y*z^5 - y^2*z^5 - x*z^6 + y*z^6 - 3*z^7 - 3*x^4*y^2 - 3*x^3*y^3 + x^2*y^4 + 3*x*y^5 + 3*y^6 - x^5*z + 3*x^4*y*z + 3*x^2*y^3*z - 3*x*y^4*z - 3*y^5*z + x^4*z^2 + x^2*y^2*z^2 + 2*x*y^3*z^2 + 3*y^4*z^2 + x^3*z^3 - 3*x^2*y*z^3 - 3*y^3*z^3 + 3*x*y*z^4 + 3*y^2*z^4 + x*z^5 + 3*y*z^5 + 3*z^6 + 1/3*x^4*y - 3*x^3*y^2 + x^2*y^3 - x*y^4 - 3*y^5 - x^4*z - 3*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 - 3*x^2*z^3 + 2*y^2*z^3 + 2*x*z^4 - 3*y*z^4 - 2*z^5 + 3*x^2*y^2 + 2*x*y^3 + 7/12*y^4 + x^3*z + 3*x^2*y*z + 2*y^3*z - 2*x^2*z^2 - x*y*z^2 + 2*y^2*z^2 + y*z^3 - z^4 - 2*x^2*z - 2*x*y*z - 3*y^2*z - 3*x*z^2 - 3*y*z^2 + z^3']
  ok   R = Y4, component W3 (P_420 = 0 = H_102 = H_012 = H_003): a point of the component (residual equations vanish)
  ok   R = Y4, component W3 (P_420 = 0 = H_102 = H_012 = H_003) anchor (A): fixed {'P_420': 0, 'H_102': 0, 'H_012': 0, 'H_003': 0}, solved []; member closed with H and the prescribed graded data: True; a triple of I of local length 40 (ds vdim), stabilization (length, N) = (40, 12)
      anchor generators: {'P': 'X^7 - 2*Y^5 + 5*X*Y^2*Z - 20/3*Y^3*Z - 2*X^2*Z + X*Y*Z - 2*Y^2*Z - 2*Y*Z^2', 'G': 'X^4*Y - X^2*Z + X*Y*Z + Y*Z^2 - 2*Z^3', 'H': 'Y^4 - X*Y*Z + 2*Y^2*Z'}
      triple: ['-2*x^7*y + 3*x^6*y^2 - 2*x^5*y^3 - x^3*y^5 - 2*x^2*y^6 + 2*x*y^7 + 2*y^8 - 2*x^7*z + x^6*y*z + 3*x^5*y^2*z - x^3*y^4*z + x^2*y^5*z + x*y^6*z + 3*y^7*z + x^6*z^2 + x^5*y*z^2 - 2*x^4*y^2*z^2 + x^3*y^3*z^2 + x^2*y^4*z^2 - x*y^5*z^2 - 2*y^6*z^2 + 3*x^5*z^3 + 3*x^4*y*z^3 + x^3*y^2*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*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 - 3*y^3*z^5 + 2*x^2*z^6 + 2*y^2*z^6 - 3*x*z^7 + 3*y*z^7 - z^8 - 379/5040*x^7 + 2*x^6*y - x^5*y^2 + x^4*y^3 - x^3*y^4 - x*y^6 - 2*y^7 + 2*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 + x^5*z^2 - x^4*y*z^2 - x^3*y^2*z^2 - x^2*y^3*z^2 - 3*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 - y^4*z^3 - 3*x^3*z^4 + 2*x^2*y*z^4 + 3*x*y^2*z^4 - 3*x^2*z^5 + 2*x*y*z^5 - 2*y^2*z^5 - x*z^6 + y*z^6 - 3*z^7 + 1/504*x^6 - 2*x^5*y - 2*x^4*y^2 + 3*x^3*y^3 + x^2*y^4 + 3*y^6 - x^5*z - x^3*y^2*z - x^2*y^3*z - 2*x*y^4*z + y^5*z + 2*x^4*z^2 - x^3*y*z^2 - 2*x^2*y^2*z^2 - 3*x*y^3*z^2 - y^4*z^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 - 2*x*y*z^4 - 2*y^2*z^4 - 2*x*z^5 - 2*y*z^5 + 35/24*x^4*y - 3*x^3*y^2 - 3*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*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 + x^2*z^3 + 2*x*y*z^3 + 2*y*z^4 + 1/24*y^4 + 2*x^3*z + x*y^2*z + 3*y^3*z - x^2*z^2 + 2*x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 - 2*y*z^3 - 3*z^4 - 2*x^2*z - 3*x*y*z - y^2*z + 2*x*z^2 + 3*z^3', '3*x^8 + 3*x^7*y - 3*x^6*y^2 - 2*x^5*y^3 - 3*x^3*y^5 - 3*x^2*y^6 - 2*x*y^7 + 3*y^8 + x^7*z + 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 - 3*x*y^6*z - 3*y^7*z + 3*x^6*z^2 - 3*x^5*y*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^5*z^3 - 2*x^4*y*z^3 - 3*x^3*y^2*z^3 + x^2*y^3*z^3 - 2*x*y^4*z^3 + y^5*z^3 + x^4*z^4 + x^3*y*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 - 2*x^2*z^6 - 2*x*y*z^6 + y^2*z^6 - 2*x*z^7 - y*z^7 - z^8 + 557/5040*x^7 - 2*x^6*y + x^5*y^2 - 2*x^4*y^3 + x^3*y^4 - 2*x^2*y^5 - x*y^6 + y^7 - 2*x^6*z + x^5*y*z - x^4*y^2*z - 2*x^3*y^3*z + 2*x^2*y^4*z + y^6*z + 3*x^5*z^2 - x^4*y*z^2 - 3*x^3*y^2*z^2 + x^2*y^3*z^2 - 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 + 2*x*y^3*z^3 + 2*y^4*z^3 + 2*x^3*z^4 + x^2*y*z^4 - 2*x*y^2*z^4 + 3*y^3*z^4 - x^2*z^5 - 3*x*y*z^5 - 3*y^2*z^5 - 2*x*z^6 - y*z^6 - 2*z^7 - 1/252*x^6 - 2*x^5*y - 3*x^3*y^3 + 2*x^2*y^4 + 2*x*y^5 + 2*y^6 + 3*x^5*z + 3*x^4*y*z - 3*x^3*y^2*z + 3*x^2*y^3*z - x*y^4*z + 3*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 - 3*x^3*z^3 - 3*x^2*y*z^3 + 3*x*y^2*z^3 - 2*y^3*z^3 + 2*x*y*z^4 - 2*y^2*z^4 + x*z^5 - 3*y*z^5 - 3*z^6 - 7/24*x^4*y + x^3*y^2 - x^2*y^3 - x*y^4 + 2*y^5 - 2*x^4*z + x^3*y*z + 2*x^2*y^2*z - 2*x*y^3*z - 3*y^4*z - 2*x^3*z^2 + 2*x^2*y*z^2 + 3*x*y^2*z^2 - 2*y^3*z^2 - 3*x^2*z^3 - x*y*z^3 + 2*y^2*z^3 - y*z^4 + 2*z^5 + x^2*y^2 - 2*x*y^3 - 3/8*y^4 - 3*x^3*z - 2*x*y^2*z + y^3*z + 2*x^2*z^2 + 3*x*y*z^2 + y^2*z^2 - 3*y*z^3 - z^4 + 2*x^2*z - x*y*z + 2*y^2*z + 3*x*z^2 - z^3', '-3*x^7*y + 3*x^6*y^2 + 3*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*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 + x^2*y^4*z^2 + 2*x*y^5*z^2 + y^6*z^2 + x^5*z^3 + 3*x^4*y*z^3 + x^3*y^2*z^3 - 2*x^2*y^3*z^3 - x*y^4*z^3 - 3*y^5*z^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 + y^3*z^5 - 3*x^2*z^6 + x*y*z^6 - x*z^7 + y*z^7 + 253/1680*x^7 + 2*x^6*y - 3*x^5*y^2 + 2*x^4*y^3 + x^2*y^5 - x*y^6 - 2*y^7 + x^6*z + 2*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 - 2*x^5*z^2 - x^4*y*z^2 - 3*x^3*y^2*z^2 - 2*x^2*y^3*z^2 - y^5*z^2 - 3*x^4*z^3 + x^3*y*z^3 - 3*x^2*y^2*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*y*z^5 - 2*y^2*z^5 - x*z^6 - 3*y*z^6 - z^7 - 1/504*x^6 - 3*x^5*y + 3*x^4*y^2 - x^3*y^3 - 3*x^2*y^4 - 3*x*y^5 + x^5*z + 2*x^4*y*z - x^3*y^2*z + 3*x^2*y^3*z - 3*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 + 3*y^4*z^2 + x^3*z^3 + 2*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*y^2*z^4 + 2*x*z^5 - 29/24*x^4*y + 2*x^2*y^3 - 2*x*y^4 + 3*y^5 - 2*x^4*z + 2*x^3*y*z - 2*x^2*y^2*z - 3*x*y^3*z - 3*x^3*z^2 + 3*x^2*y*z^2 + 2*y^3*z^2 + 3*x^2*z^3 + x*y*z^3 - 3*y^2*z^3 + 2*x*z^4 - 2*y*z^4 + 2*z^5 + 2*x^2*y^2 + x*y^3 - 1/8*y^4 - 2*x^3*z - 2*x^2*y*z + 2*x*y^2*z + y^3*z + 2*x^2*z^2 - 2*x*y*z^2 - y^2*z^2 + 3*x*z^3 - 2*z^4 + x^2*z + x*y*z + y^2*z - x*z^2 + 3*y*z^2 - 2*z^3']
--- R = X2Y2+Y4
  ok   R = X2Y2+Y4: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R = X2Y2+Y4: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 58 eliminated with constant pivots; residual equations:
       (2) * (-P_420*G_301*G_211 + 2*P_420*G_102 + 5*P_050*H_102)
       (1/6) * (-P_420*G_211^2 + 12*P_420*G_012 + 30*P_050*H_012)
       (3) * (2*P_420*G_003 + 5*P_050*H_003)
  ok   R = X2Y2+Y4: every closedness condition lies in the ideal of the residual equations after the substitutions
  ok   R = X2Y2+Y4: 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   R = X2Y2+Y4: on {P_420 = 0}: each equation is (P_050) times a linear form; components {P_050 = 0} and {['10*H_102', '5*H_012', '15*H_003'] = 0}
  ok   R = X2Y2+Y4, component W1 (P_420 != 0): a point of the component (residual equations vanish)
  ok   R = X2Y2+Y4, 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 39 (ds vdim), stabilization (length, N) = (39, 11)
      anchor generators: {'P': 'X^7 + X^4*Y^2 + 2/3*Y^3*Z + 2*X^2*Z + 2*X*Y*Z - X*Z^2 - Y*Z^2', 'G': 'X^4*Y + Y^2*Z', 'H': 'X^2*Y^2 + Y^4 - X^2*Z + 2*X*Y*Z - 2*Y^2*Z + Y*Z^2'}
      triple: ['3*x^8 + 2*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 + 2*y^8 - 3*x^7*z + 2*x^5*y^2*z + 3*x^4*y^3*z + x^3*y^4*z - 2*x*y^6*z - 3*y^7*z - x^6*z^2 - 2*x^5*y*z^2 - x^4*y^2*z^2 - x^3*y^3*z^2 + x^2*y^4*z^2 - 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 - 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 - y^3*z^5 + 2*x^2*z^6 + x*y*z^6 + 2*y^2*z^6 + 2*x*z^7 - 2*y*z^7 + 2*z^8 - 1/35*x^7 + 2*x^6*y + x^5*y^2 + 3*x^4*y^3 + 2*x^3*y^4 + x^2*y^5 - 3*x*y^6 + 3*x^5*y*z + x^4*y^2*z + x^3*y^3*z + 3*x*y^5*z + x^5*z^2 - 3*x^3*y^2*z^2 - 2*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 + 2*x^2*y^2*z^3 - 3*x*y^3*z^3 - y^4*z^3 - 3*x^3*z^4 - 2*x^2*y*z^4 + 3*x*y^2*z^4 + 2*y^3*z^4 + 3*x^2*z^5 - 2*y^2*z^5 - y*z^6 + 2*z^7 + 3*x^4*y^2 + x^3*y^3 + 2*x^2*y^4 - 3*x*y^5 + y^6 + 2*x^5*z + 3*x^4*y*z - 3*x^3*y^2*z - 3*x^2*y^3*z + x^4*z^2 + x^3*y*z^2 - x*y^3*z^2 - y^4*z^2 + x^3*z^3 - 2*x^2*y*z^3 + 3*x*y^2*z^3 + 2*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 + 1/70*x^5 + 1/6*x^4*y + x^2*y^3 + 3*y^5 + x^2*y^2*z - 3*x*y^3*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 + 3*x^2*z^3 - 2*x*y*z^3 + 3*y^2*z^3 + 3*x*z^4 + 2*z^5 - 3/2*x^2*y^2 + x^3*z + x^2*y*z - x*y^2*z - 3*y^3*z + 2*x^2*z^2 - 2*x*y*z^2 + 2*y^2*z^2 + 3*x*z^3 - y*z^3 + x*y*z - 2*y^2*z - 3*x*z^2 - 2*y*z^2 + z^3', '-3*x^8 + x^7*y + x^6*y^2 + 3*x^5*y^3 - 3*x^4*y^4 - x^3*y^5 - 3*x^2*y^6 + 2*x*y^7 + y^8 - 2*x^7*z + 3*x^6*y*z - 3*x^5*y^2*z - x^4*y^3*z - x^2*y^5*z - x*y^6*z + 3*y^7*z - x^6*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 + 3*x*y^5*z^2 + y^6*z^2 - 2*x^5*z^3 - 2*x^4*y*z^3 - 2*x^3*y^2*z^3 + 3*y^5*z^3 + 3*x^4*z^4 + 2*x^3*y*z^4 + x^2*y^2*z^4 - 2*x*y^3*z^4 - 2*y^4*z^4 - x^3*z^5 + x^2*y*z^5 + 3*x*y^2*z^5 - 2*y^3*z^5 - 2*x^2*z^6 - 2*x*y*z^6 + y^2*z^6 - 3*x*z^7 + 3*y*z^7 + 3*z^8 + 3/140*x^7 + 2*x^6*y - 2*x^5*y^2 - 3*x^4*y^3 - 3*x^3*y^4 - 3*x^2*y^5 + 3*x*y^6 + y^7 - x^6*z + 2*x^5*y*z + 3*x^4*y^2*z - 2*x^3*y^3*z + x^2*y^4*z + 2*x*y^5*z + 2*y^6*z - x^5*z^2 - 2*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^3*y*z^3 - 3*x^2*y^2*z^3 + 3*x*y^3*z^3 - 3*x^3*z^4 - 3*x^2*y*z^4 + x*y^2*z^4 - 2*y^3*z^4 + x^2*z^5 + 3*x*y*z^5 + y^2*z^5 + 3*y*z^6 + 3*z^7 + 1/105*x^6 - 3*x^5*y - 2*x^4*y^2 + x^3*y^3 - x^2*y^4 - x*y^5 - 3*x^5*z - 3*x^4*y*z - 2*x^3*y^2*z + 2*y^5*z - x^3*y*z^2 - 2*x^2*y^2*z^2 - x*y^3*z^2 + y^4*z^2 + 3*x^3*z^3 + x^2*y*z^3 - 3*x*y^2*z^3 - 3*y^3*z^3 - x^2*z^4 + 2*x*y*z^4 - y^2*z^4 - 3*x*z^5 - 2*y*z^5 + 1/21*x^5 - 1/12*x^4*y - x^3*y^2 - x*y^4 - y^5 + 3*x^4*z - x^3*y*z + x^2*y^2*z + 2*x*y^3*z - x^3*z^2 + 2*x^2*y*z^2 - 2*x*y^2*z^2 - y^3*z^2 - x^2*z^3 + y^2*z^3 + 3*y*z^4 - 3*z^5 - 5*x^2*y^2 + y^4 - 3*x^3*z - x^2*y*z - 2*x*y^2*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*z - 3*x*y*z + y^2*z - x*z^2 + 2*y*z^2 - 3*z^3', 'x^8 + 3*x^5*y^3 + 2*x^4*y^4 + 2*x^3*y^5 + x^2*y^6 + x*y^7 + y^8 + x^7*z - 3*x^6*y*z - x^4*y^3*z - 2*x^3*y^4*z - x^2*y^5*z + x*y^6*z + 2*y^7*z + 3*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 - y^6*z^2 - 2*x^5*z^3 - 3*x^4*y*z^3 - x^2*y^3*z^3 + 3*x*y^4*z^3 - 2*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 - 2*y^4*z^4 + 3*x^3*z^5 - 3*x^2*y*z^5 - 2*x*y^2*z^5 + 3*x^2*z^6 + x*y*z^6 - y^2*z^6 - 2*x*z^7 - 2*y*z^7 + 2*z^8 - 2/315*x^7 + x^6*y - 2*x^5*y^2 + 2*x^4*y^3 + 2*x^3*y^4 - x^2*y^5 - 2*x*y^6 + 3*y^7 + 2*x^6*z + 3*x^5*y*z - 2*x^3*y^3*z + x^2*y^4*z - 3*x*y^5*z + 3*y^6*z + 3*x^5*z^2 + x^4*y*z^2 + x^2*y^3*z^2 - 2*x*y^4*z^2 - 2*y^5*z^2 - 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 + x^3*z^4 + 2*x^2*y*z^4 + x*y^2*z^4 + y^3*z^4 + 2*x^2*z^5 - 3*x*y*z^5 - x*z^6 + 2*y*z^6 + 2/105*x^6 - 3*x^5*y + x^4*y^2 + x^3*y^3 - 2*x^2*y^4 + x*y^5 + y^6 + 2*x^5*z - 2*x^4*y*z - 2*x^3*y^2*z + 3*x*y^4*z + 2*y^5*z - 3*x^3*y*z^2 - x^2*y^2*z^2 + 3*x*y^3*z^2 + y^4*z^2 - 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 + 3*y^2*z^4 + 2*y*z^5 + 11/210*x^5 - 1/6*x^4*y - 2*x^3*y^2 - 3*x^2*y^3 + 3*x*y^4 - 3*y^5 + 2*x^4*z + 3*x*y^3*z + 2*x^3*z^2 + 2*x^2*y*z^2 - 2*x*y^2*z^2 + y^3*z^2 - 3*x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 - 2*y*z^4 - 11/2*x^2*y^2 - 2*x*y^3 + y^4 - 3*x^3*z + x^2*y*z + 3*x*y^2*z - 3*y^3*z + 2*x^2*z^2 - 2*x*y*z^2 - 3*y^2*z^2 - 3*y*z^3 + 3*z^4 + 2*x*y*z + 2*y^2*z + 3*x*z^2 + y*z^2 - 3*z^3']
  ok   R = X2Y2+Y4, component W2 (P_420 = 0 = P_050): a point of the component (residual equations vanish)
  ok   R = X2Y2+Y4, component W2 (P_420 = 0 = P_050) anchor (A): fixed {'P_420': 0, 'P_050': 0}, solved []; member closed with H and the prescribed graded data: True; a triple of I of local length 41 (ds vdim), stabilization (length, N) = (41, 13)
      anchor generators: {'P': 'X^7 - 2*X^2*Z - X*Y*Z + 2*Y^2*Z - X*Z^2 + 2*Y*Z^2', 'G': 'X^4*Y + X^2*Z + 2*Y^2*Z - X*Z^2 - 2*Y*Z^2 + 2*Z^3', 'H': 'X^2*Y^2 + Y^4 + 2*X^2*Z + 2*X*Y*Z - Y^2*Z - 2*X*Z^2 - Y*Z^2'}
      triple: ['2*x^8 + x^7*y - 2*x^6*y^2 + 2*x^5*y^3 + x^4*y^4 - x^3*y^5 - x^2*y^6 + 3*x*y^7 + 3*y^8 - 2*x^7*z - 2*x^6*y*z - 3*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 + 3*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 + 2*x^2*y^4*z^2 - x*y^5*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 - 3*x*y^4*z^3 - 2*y^5*z^3 + x^4*z^4 + x*y^3*z^4 + y^3*z^5 - 3*x^2*z^6 + x*y*z^6 + 3*y^2*z^6 + 2*x*z^7 - 2*y*z^7 + 3*z^8 + 1/630*x^7 + 2*x^6*y + 3*x^5*y^2 + 3*x^4*y^3 - x^3*y^4 - 3*x^2*y^5 - 3*y^7 - 2*x^6*z - x^5*y*z + 2*x^3*y^3*z + 3*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 + 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^3*z^4 + 2*x^2*y*z^4 - 3*x*y^2*z^4 + 2*y^3*z^4 + x^2*z^5 - 3*x*y*z^5 - 2*x*z^6 + 3*y*z^6 + 2*z^7 + x^4*y^2 - x^3*y^3 + 3*x^2*y^4 + 2*x*y^5 + 3*y^6 - x^5*z - 3*x^4*y*z - 3*x^3*y^2*z - 2*x^2*y^3*z + 3*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 - 3*x^3*z^3 + 2*x^2*y*z^3 + 3*x*y^2*z^3 + 3*y^3*z^3 + y^2*z^4 + 2*x*z^5 + 3*z^6 - 17/12*x^4*y - x^3*y^2 + x^2*y^3 + x*y^4 + 2*y^5 - 3*x^4*z + 2*x^3*y*z - 3*x^2*y^2*z - y^4*z - 2*x^3*z^2 - x^2*y*z^2 + x*y^2*z^2 - 2*y^3*z^2 + 3*x^2*z^3 + 3*x*y*z^3 - 2*y^2*z^3 - 3*x*z^4 + y*z^4 - 2*z^5 - 17/2*x^2*y^2 + 3*x*y^3 + y^4 - 3*x^3*z - x^2*y*z - 3*x*y^2*z + 2*x^2*z^2 - x*y*z^2 + 2*x*z^3 - y*z^3 - 3*z^4 + 3*x^2*z + y^2*z + 2*z^3', '2*x^8 - 3*x^7*y + 3*x^6*y^2 + 2*x^5*y^3 + 2*x^4*y^4 + 2*x^3*y^5 + 2*x^2*y^6 - x*y^7 + 3*y^8 - 3*x^7*z - 2*x^5*y^2*z - 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^6*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 - 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 + 3*x^2*y^2*z^4 - 2*x*y^3*z^4 + y^4*z^4 - x^3*z^5 + x^2*y*z^5 - x*y^2*z^5 - 2*y^3*z^5 + 2*x^2*z^6 + 2*x*y*z^6 - 2*y^2*z^6 + 2*y*z^7 + 2*z^8 - 11/5040*x^7 - x^6*y - 2*x^5*y^2 - 2*x^4*y^3 + 2*x^3*y^4 + 2*x*y^6 + y^7 - x^5*y*z - 3*x^4*y^2*z - x^3*y^3*z + 2*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 - 3*x*y^4*z^2 + 3*y^5*z^2 - x^2*y^2*z^3 + 2*x*y^3*z^3 + 3*y^4*z^3 - x^3*z^4 - 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 + y^2*z^5 - 3*x*z^6 + y*z^6 + 2*z^7 - 3*x^5*y - 2*x^4*y^2 + 2*x^3*y^3 + 2*x^2*y^4 + 3*x*y^5 + 3*y^6 - 2*x^5*z - 3*x^3*y^2*z - y^5*z + 2*x^4*z^2 - 2*x^3*y*z^2 + 3*x^2*y^2*z^2 + 2*x*y^3*z^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 + x*y*z^4 + x*z^5 + y*z^5 + z^6 + 23/12*x^4*y - x^3*y^2 - x^2*y^3 - 3*x*y^4 + y^5 + 2*x^4*z - x^3*y*z - 3*x^2*y^2*z - 2*x*y^3*z + 2*y^4*z - 2*x^3*z^2 - 2*x^2*y*z^2 + y^3*z^2 + x^2*z^3 - 2*x*y*z^3 + x*z^4 + 2*y*z^4 - 3*z^5 - 19*x^2*y^2 - 3*x*y^3 + 3*y^4 + 3*x^3*z + x*y^2*z - 2*y^3*z - x*y*z^2 - y^2*z^2 + 2*x*z^3 + 3*y*z^3 + 2*z^4 - x^2*z + x*y*z - y^2*z - 2*x*z^2 + 2*y*z^2 - 3*z^3', '-3*x^8 + 2*x^7*y - 2*x^6*y^2 - 2*x^5*y^3 + x^4*y^4 - x^3*y^5 + 3*x*y^7 + 3*y^8 + x^7*z - 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 - 3*y^7*z - x^6*z^2 - 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*x*y^5*z^2 + y^6*z^2 + 2*x^4*y*z^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 - 3*x^3*y*z^4 - x^2*y^2*z^4 - 2*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 + 2*y^2*z^6 - x*z^7 + 2*z^8 - 1/336*x^7 - x^6*y - 3*x^5*y^2 - 3*x^4*y^3 + x^3*y^4 - x^2*y^5 + 3*x*y^6 - 2*x^5*y*z - x^3*y^3*z - x^2*y^4*z + 3*x*y^5*z + y^6*z - 2*x^5*z^2 + 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 + 3*y^5*z^2 - 3*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 - 2*x^2*y*z^4 - 2*y^3*z^4 - 2*x^2*z^5 + 3*x*y*z^5 + y^2*z^5 + 2*y*z^6 + z^7 + x^5*y + 3*x^4*y^2 + x^3*y^3 - x*y^5 + 2*y^6 - x^4*y*z + 2*x^3*y^2*z + x^2*y^3*z - 3*x*y^4*z + x^4*z^2 - 2*x^3*y*z^2 - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 - y^4*z^2 - x^3*z^3 - x^2*y*z^3 - 2*x*y^2*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 + 3*x^3*y^2 - x^2*y^3 - x*y^4 + 3*x^3*y*z + 3*x^2*y^2*z - x*y^3*z + 2*y^4*z + x^3*z^2 - 2*x*y^2*z^2 - 2*y^3*z^2 - 3*x^2*z^3 - 3*y^2*z^3 - x*z^4 - y*z^4 - z^5 + 6*x^2*y^2 - 2*x*y^3 - 2*x^3*z + x^2*y*z + x*y^2*z - y^3*z + 2*x^2*z^2 - x*y*z^2 + 2*y^2*z^2 + 3*x*z^3 + 2*y*z^3 - z^4 - 3*x^2*z + 3*x*y*z + y^2*z + 3*x*z^2 + 2*y*z^2']
  ok   R = X2Y2+Y4, component W3 (P_420 = 0 = H_102 = H_012 = H_003): a point of the component (residual equations vanish)
  ok   R = X2Y2+Y4, component W3 (P_420 = 0 = H_102 = H_012 = H_003) anchor (A): fixed {'P_420': 0, 'H_102': 0, 'H_012': 0, 'H_003': 0}, solved []; member closed with H and the prescribed graded data: True; a triple of I of local length 40 (ds vdim), stabilization (length, N) = (40, 12)
      anchor generators: {'P': 'X^7 + 5/3*X^2*Y^3 + Y^5 - 10*X^2*Y*Z - 5/2*X*Y^2*Z - 5/3*Y^3*Z + X^2*Z - Y^2*Z + 2*X*Z^2 - 2*Y*Z^2 + 2*Z^3', 'G': 'X^4*Y + 2*X^2*Z - 2*X*Z^2 - 2*Y*Z^2 - 2*Z^3', 'H': 'X^2*Y^2 + Y^4 - 2*X^2*Z - X*Y*Z - Y^2*Z'}
      triple: ['x^8 + 3*x^7*y - 3*x^6*y^2 + x^5*y^3 + 2*x^4*y^4 - x^3*y^5 + 2*x^2*y^6 - 3*x*y^7 - 2*x^7*z - x^6*y*z + 2*x^5*y^2*z + 3*x^4*y^3*z + 2*x^3*y^4*z + x^2*y^5*z - 3*x*y^6*z + 2*x^6*z^2 + 2*x^4*y^2*z^2 - x^3*y^3*z^2 + x^2*y^4*z^2 - 2*x*y^5*z^2 - y^6*z^2 + 2*x^5*z^3 + 2*x^3*y^2*z^3 + x^2*y^3*z^3 - 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 - 3*y^4*z^4 - 2*x^3*z^5 - 2*x^2*y*z^5 - 3*x*y^2*z^5 + y^3*z^5 + 2*x^2*z^6 + 3*x*y*z^6 - 3*y^2*z^6 - 2*x*z^7 - y*z^7 - z^8 - 37/840*x^7 + 3*x^6*y + x^5*y^2 - 2*x^4*y^3 + 2*x^3*y^4 - 3*x^2*y^5 + 2*x*y^6 - y^7 - 3*x^6*z - 3*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 + 2*y^6*z + x^5*z^2 + 3*x^2*y^3*z^2 - 2*x*y^4*z^2 - 2*y^5*z^2 - 3*x^4*z^3 + 2*x^3*y*z^3 - 2*x^2*y^2*z^3 - 3*x*y^3*z^3 - y^4*z^3 - 2*x^3*z^4 - 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 - 3*y*z^6 - 2*z^7 + 13/1008*x^6 + 3*x^5*y - x^4*y^2 - 3*x^3*y^3 + x^2*y^4 - 3*x*y^5 + 2*y^6 - 2*x^5*z - 2*x^4*y*z - 3*x^3*y^2*z + 3*x^2*y^3*z + y^5*z - x^4*z^2 - x^2*y^2*z^2 - 3*x*y^3*z^2 - y^4*z^2 + 3*x^3*z^3 + x^2*y*z^3 - 3*x*y^2*z^3 + y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 - 3*y^2*z^4 + 2*x*z^5 + y*z^5 - 2*z^6 - x^4*y - 3*x^3*y^2 + 3*x^2*y^3 + 2*x*y^4 + 2*y^5 + 3*x^4*z - 3*x^3*y*z - 2*x^2*y^2*z - x*y^3*z + y^4*z - 3*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 - 3*x*y*z^3 + 2*y^2*z^3 - 3*x*z^4 + 2*z^5 + 19/4*x^2*y^2 - 3*x*y^3 - y^4 - 2*x^3*z + 3*x^2*y*z - 2*x*y^2*z + y^3*z + 2*x^2*z^2 - x*y*z^2 + y^2*z^2 - 3*x*z^3 - y*z^3 + x*y*z - 3*y^2*z + 3*x*z^2 - 3*z^3', '3*x^8 - 2*x^5*y^3 - x^4*y^4 + x^3*y^5 - 2*x^2*y^6 - 2*x*y^7 + 2*y^8 + 2*x^7*z - 2*x^5*y^2*z + 2*x^4*y^3*z - x^2*y^5*z + 2*x*y^6*z + 3*y^7*z + x^6*z^2 + x^5*y*z^2 + 2*x^2*y^4*z^2 + 2*y^6*z^2 - x^5*z^3 - 2*x^3*y^2*z^3 - x^2*y^3*z^3 - 3*x*y^4*z^3 + y^5*z^3 + x^4*z^4 + x^3*y*z^4 - 3*x^2*y^2*z^4 + 2*x*y^3*z^4 - 3*y^4*z^4 + 3*x^3*z^5 + 2*x^2*y*z^5 + 2*y^3*z^5 - x^2*z^6 + 3*x*y*z^6 - y^2*z^6 - x*z^7 + 3*y*z^7 + 2*z^8 - 79/1680*x^7 + 2*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 - 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 + 2*y^6*z - 3*x^5*z^2 + 2*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 + x^4*z^3 - 2*x^2*y^2*z^3 - 3*y^4*z^3 + 2*x^3*z^4 + x*y^2*z^4 + 2*x^2*z^5 + 2*x*y*z^5 - 2*y^2*z^5 + 3*x*z^6 + y*z^6 - z^7 + 1/336*x^6 - 3*x^5*y + 2*x^4*y^2 + 2*x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 + y^6 - 2*x^5*z + 3*x^4*y*z - 3*x^3*y^2*z + 3*x^2*y^3*z - 2*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*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 + 3*x*y*z^4 - 2*y^2*z^4 - 2*x*z^5 - y*z^5 + 3*z^6 - 1/3*x^4*y - 2*x^2*y^3 - 3*x*y^4 + 2*y^5 + x^4*z - x^3*y*z + x^2*y^2*z + 3*x*y^3*z - 2*y^4*z - x^3*z^2 + 3*x^2*y*z^2 + 2*x*y^2*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 + y*z^4 - 3*z^5 + 29/4*x^2*y^2 - 2*x*y^3 - y^4 + x^3*z - x^2*y*z - x*y^2*z - 3*y^3*z + x^2*z^2 + 2*x*y*z^2 - 2*y^2*z^2 + 3*x*z^3 + 3*y*z^3 + 2*x^2*z - x*y*z - y^2*z + 3*x*z^2 + 3*y*z^2 - 2*z^3', '-3*x^8 - 3*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 + 2*x*y^7 - 2*y^8 - 3*x^7*z - 3*x^5*y^2*z - 2*x^4*y^3*z - x^3*y^4*z + x^2*y^5*z + 2*x*y^6*z - y^7*z - x^5*y*z^2 - x^4*y^2*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^3*y^2*z^3 - y^5*z^3 + 2*x^3*y*z^4 + x*y^3*z^4 + y^4*z^4 - 3*x^3*z^5 + 3*x*y^2*z^5 + 3*x*y*z^6 - y^2*z^6 - x*z^7 - 3*y*z^7 - 3*z^8 - 1/144*x^7 - 2*x^6*y + 3*x^5*y^2 - x^3*y^4 + x*y^6 + 2*y^7 + x^6*z + 2*x^4*y^2*z - x^3*y^3*z - x*y^5*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*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 + 3*y^4*z^3 + 2*x^3*z^4 - 2*x^2*y*z^4 + 3*y^3*z^4 - x^2*z^5 - 2*x*y*z^5 - y^2*z^5 - x*z^6 - z^7 - 1/126*x^6 + 2*x^5*y + x^4*y^2 - x^3*y^3 - 3*x^2*y^4 + x*y^5 - y^6 + x^5*z - 3*x^3*y^2*z + x^2*y^3*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 + 3*x*y^3*z^2 - x^3*z^3 - 3*x^2*y*z^3 + 3*x*y^2*z^3 + 2*y^3*z^3 - 3*x^2*z^4 - 3*x*y*z^4 + 3*y^2*z^4 - x*z^5 + 2*y*z^5 + 2*z^6 - 4/3*x^4*y - 2*x^3*y^2 + 3*x*y^4 + x^4*z + 2*x^3*y*z - x^2*y^2*z - 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 - 3*x^2*z^3 + x*y*z^3 + y^2*z^3 - 2*x*z^4 + y*z^4 - 3*z^5 + 1/4*x^2*y^2 - x*y^3 - 3*x^3*z - x^2*y*z - x*y^2*z - 2*y^3*z - x*y*z^2 - x*z^3 - 3*y*z^3 + z^4 + x^2*z - 3*x*y*z + x*z^2 - 2*y*z^2 - 2*z^3']
--- R = XY3
  ok   R = XY3: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R = XY3: one lift per pivot of D_4..D_7
    134 closedness conditions in 88 tail coefficients; 58 eliminated with constant pivots; residual equations:
       (2) * (-P_420*G_301*G_211 + 2*P_420*G_102 + 4*P_140*H_102)
       (1/6) * (-P_420*G_211^2 + 12*P_420*G_012 + 24*P_140*H_012)
       (6) * (P_420*G_003 + 2*P_140*H_003)
  ok   R = XY3: every closedness condition lies in the ideal of the residual equations after the substitutions
  ok   R = XY3: 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   R = XY3: on {P_420 = 0}: each equation is (P_140) times a linear form; components {P_140 = 0} and {['8*H_102', '4*H_012', '12*H_003'] = 0}
  ok   R = XY3, component W1 (P_420 != 0): a point of the component (residual equations vanish)
  ok   R = XY3, 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 39 (ds vdim), stabilization (length, N) = (39, 11)
      anchor generators: {'P': 'X^7 + X^4*Y^2 + 4*X^2*Y*Z - X*Y^2*Z + 4/3*Y^3*Z + 2*X^2*Z + X*Y*Z - 2*Y^2*Z - 2*X*Z^2 + 2*Y*Z^2 - 2*Z^3', 'G': 'X^4*Y + 2*X^2*Z - X*Y*Z + 2*Y^2*Z', 'H': 'X*Y^3 + 2*X^2*Z + Y^2*Z - X*Z^2 - Y*Z^2 + 2*Z^3'}
      triple: ['3*x^8 - x^7*y + 2*x^6*y^2 - x^5*y^3 - x^4*y^4 - x*y^7 + y^8 + 3*x^7*z - 2*x^6*y*z - 2*x^5*y^2*z + 2*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 - x^6*z^2 - 2*x^5*y*z^2 + x^3*y^3*z^2 - x*y^5*z^2 - 3*y^6*z^2 + x^5*z^3 - 3*x^4*y*z^3 - x^2*y^3*z^3 - 3*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 - 2*y^4*z^4 - x^3*z^5 - 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 - y^2*z^6 - 2*x*z^7 + 3*y*z^7 + 1/420*x^7 - 2*x^6*y + 3*x^5*y^2 + 3*x^4*y^3 + 3*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 - 3*y^6*z - 2*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 + 2*x^4*z^3 + x^2*y^2*z^3 + x*y^3*z^3 - 3*y^4*z^3 - x^3*z^4 - 3*x^2*y*z^4 + 3*x*y^2*z^4 - 2*y^3*z^4 + 3*x^2*z^5 - x*y*z^5 - 2*y^2*z^5 - 3*x*z^6 - 2*z^7 + 61/2520*x^6 + x^5*y + x^3*y^3 + x*y^5 - 3*y^6 + 2*x^5*z - 3*x^4*y*z - 3*x^3*y^2*z - 2*x^2*y^3*z + x*y^4*z + 2*y^5*z + 2*x^4*z^2 - 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 + y^3*z^3 - 2*x^2*z^4 + 3*x*y*z^4 + y^2*z^4 - 3*y*z^5 - 3*z^6 + 2/105*x^5 + 13/12*x^4*y - 3*x^3*y^2 + 2*x^2*y^3 - 2*x*y^4 + 3*y^5 + x^4*z + 3*x^3*y*z - 3*x^2*y^2*z - 2*x*y^3*z + 2*x^3*z^2 + 3*y^3*z^2 - x*y*z^3 - y^2*z^3 + x*z^4 + y*z^4 + z^5 - 2*x^2*y^2 + 11/3*x*y^3 - 3*y^4 - 2*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 + 3*y^2*z^2 + 3*x*z^3 - y*z^3 + 3*z^4 - 3*x^2*z + 2*x*y*z - 3*y^2*z + 2*x*z^2', '-2*x^7*y + 2*x^6*y^2 + 2*x^4*y^4 - 2*x^3*y^5 + 2*x^2*y^6 - 3*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 - 2*x^3*y^4*z - 2*x*y^6*z + y^7*z + 2*x^6*z^2 + 2*x^5*y*z^2 - 3*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 - x^2*y^3*z^3 - 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 + 2*x*y^3*z^4 - y^4*z^4 - x^3*z^5 - 2*x^2*y*z^5 + 2*x*y^2*z^5 - 2*y^3*z^5 - 3*x*y*z^6 - 2*y^2*z^6 - 3*x*z^7 - 3*y*z^7 - 3*z^8 - 11/336*x^7 + x^5*y^2 - 3*x^4*y^3 + 3*x^3*y^4 + 2*y^7 - 2*x^6*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 + 3*x^5*z^2 - 2*x^3*y^2*z^2 - x*y^4*z^2 - 3*y^5*z^2 + 3*x^4*z^3 - 2*x^2*y^2*z^3 + 2*x*y^3*z^3 - y^4*z^3 + 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*z^6 - 3*y*z^6 - 3*z^7 - 47/2520*x^6 + x^5*y + 3*x^4*y^2 + 2*x*y^5 + 3*y^6 + 3*x^5*z - 3*x^4*y*z - 3*x^2*y^3*z + x*y^4*z - 3*x^4*z^2 - 2*x^3*y*z^2 + 3*x*y^3*z^2 + y^4*z^2 - 3*x^3*z^3 - x*y^2*z^3 + 2*y^3*z^3 - 3*x^2*z^4 - 2*y^2*z^4 - 3*x*z^5 + 3*y*z^5 + z^6 + 2/105*x^5 + 7/24*x^4*y + 2*x^3*y^2 - 3*x^2*y^3 + 3*x*y^4 - 2*y^5 - 2*x^4*z - 2*x^3*y*z - x^2*y^2*z + 3*x*y^3*z + 2*x^3*z^2 + 2*x^2*y*z^2 - 2*y^3*z^2 + x^2*z^3 + x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 - y*z^4 - 2*x^2*y^2 + 7*x*y^3 - 2*y^4 + 2*x^3*z - 3*x^2*y*z + 3*x*y^2*z - 3*x^2*z^2 - y^2*z^2 + 2*y*z^3 + 2*z^4 + x^2*z - x*y*z - 3*y^2*z + x*z^2 + y*z^2 - 3*z^3', '-2*x^8 - x^7*y + x^6*y^2 - 3*x^5*y^3 - 2*x^4*y^4 - 2*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 + 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 + x*y^5*z^2 + 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 - 3*y^5*z^3 + 3*x^4*z^4 - 3*x^3*y*z^4 + x^2*y^2*z^4 - 2*x^3*z^5 - x^2*y*z^5 + 3*y^3*z^5 - x^2*z^6 - 3*x*y*z^6 + 2*y^2*z^6 - 3*x*z^7 + 2*y*z^7 - 3*z^8 - 1/72*x^7 + 3*x^6*y + x^5*y^2 - 3*x^2*y^5 + x*y^6 - 3*y^7 - 2*x^6*z + 3*x^4*y^2*z + x^3*y^3*z + 3*x^2*y^4*z - 3*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 + 3*y^5*z^2 - 3*x^4*z^3 - 3*x^3*y*z^3 - x^2*y^2*z^3 - 3*x*y^3*z^3 - 3*x^3*z^4 + 3*x^2*y*z^4 - 2*x*y^2*z^4 + 3*y^3*z^4 + 2*x*y*z^5 - 3*y^2*z^5 - 3*x*z^6 - 2*y*z^6 + 3*z^7 + 19/1260*x^6 + 3*x^5*y + 2*x^4*y^2 - 3*x^3*y^3 + 3*x^2*y^4 + 3*x*y^5 - 2*x^5*z + 3*x^4*y*z - 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*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 + 2*y^3*z^3 + 2*y^2*z^4 + x*z^5 + 1/35*x^5 + 1/12*x^4*y - 2*x^3*y^2 - x^2*y^3 - x*y^4 + y^5 + 3*x^4*z - 3*x^2*y^2*z + 3*x*y^3*z + 2*x^2*y*z^2 + x*y^2*z^2 - y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 - 3*y^2*z^3 - 2*x*z^4 + 3*y*z^4 - 3*z^5 - 3*x^2*y^2 + x*y^3 - 3*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 + 3*z^4 + 2*x^2*z + 2*x*y*z - 2*y^2*z + x*z^2 - 2*y*z^2 - z^3']
  ok   R = XY3, component W2 (P_420 = 0 = P_140): a point of the component (residual equations vanish)
  ok   R = XY3, component W2 (P_420 = 0 = P_140) anchor (A): fixed {'P_420': 0, 'P_140': 0}, solved []; member closed with H and the prescribed graded data: True; a triple of I of local length 41 (ds vdim), stabilization (length, N) = (41, 13)
      anchor generators: {'P': 'X^7 + X^2*Z + 2*X*Y*Z + 2*X*Z^2 - 2*Y*Z^2 + 2*Z^3', 'G': 'X^4*Y + 2*X*Y*Z - 2*Y^2*Z - 2*X*Z^2 + 2*Z^3', 'H': 'X*Y^3 + 2*X^2*Z - X*Y*Z + Y^2*Z - X*Z^2'}
      triple: ['-3*x^8 + 3*x^7*y - x^6*y^2 - 3*x^5*y^3 - x^4*y^4 - 2*x^3*y^5 + 2*x^2*y^6 - 2*x*y^7 - 2*y^8 + x^7*z + x^6*y*z + 3*x^5*y^2*z - 2*x^4*y^3*z + x^3*y^4*z + 2*x^2*y^5*z - x*y^6*z - y^7*z - x^6*z^2 + x^5*y*z^2 - 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 - 2*y^6*z^2 - 2*x^5*z^3 - 3*x^4*y*z^3 + x^3*y^2*z^3 + 2*x*y^4*z^3 - 3*y^5*z^3 + 3*x^3*y*z^4 - 2*x^2*y^2*z^4 + 2*x*y^3*z^4 + 3*x^3*z^5 + 3*x*y^2*z^5 + y^3*z^5 + 2*x^2*z^6 - x*y*z^6 + y^2*z^6 - 3*x*z^7 - 3*y*z^7 - 2*z^8 + 1/1260*x^7 - 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 + 3*x^4*y^2*z + 2*x^3*y^3*z + 2*x^2*y^4*z + 2*x*y^5*z - 3*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 + 3*y^5*z^2 + 3*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 + 2*x^3*z^4 - x^2*y*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 + 2*x^3*y^3 + 2*x^2*y^4 - x*y^5 + 3*x^5*z + x^4*y*z + x^3*y^2*z - x^2*y^3*z + 2*x*y^4*z + 3*y^5*z - x^4*z^2 + 3*x^3*y*z^2 - 2*x^2*y^2*z^2 - 3*x*y^3*z^2 - y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 + 3*x*y^2*z^3 - 2*y^3*z^3 + 3*x^2*z^4 + 2*y^2*z^4 - 2*x*z^5 + 3*y*z^5 - 3*z^6 + 1/4*x^4*y - x^3*y^2 - x^2*y^3 - 3*x*y^4 + 3*y^5 - 3*x^4*z + 3*x*y^3*z + y^4*z - 2*x^2*y*z^2 + 3*x*y^2*z^2 + 3*y^3*z^2 + 2*x^2*z^3 + y^2*z^3 + 3*x*z^4 - 3*y*z^4 + z^5 + 2*x^2*y^2 + 23/6*x*y^3 + 3*y^4 + 2*x^3*z + x^2*y*z + 3*x*y^2*z + y^3*z - 3*x^2*z^2 + 3*x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 + y*z^3 - 3*x^2*z + 3*x*y*z - 2*y^2*z + 2*x*z^2 - z^3', '-3*x^8 + x^7*y + 3*x^6*y^2 + 3*x^5*y^3 + x^2*y^6 - 3*x*y^7 + 2*y^8 - 3*x^7*z - x^6*y*z - 3*x^5*y^2*z + 3*x^3*y^4*z + x^2*y^5*z + 3*x*y^6*z + 2*y^7*z - 3*x^6*z^2 + 3*x^5*y*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 + 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 + 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 - 3*x^3*z^5 - 2*x^2*y*z^5 - 3*x*y^2*z^5 + 2*x^2*z^6 - 3*x*y*z^6 + 3*y^2*z^6 - 3*x*z^7 - y*z^7 + 3*z^8 - 1/504*x^7 + x^6*y - 2*x^4*y^3 - 2*x^3*y^4 + 2*x^2*y^5 + 2*x*y^6 + 2*y^7 - 2*x^6*z - 3*x^4*y^2*z + x^3*y^3*z - 2*x^2*y^4*z - 3*x*y^5*z - 2*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 + 2*x*y^4*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 + 3*x*y^3*z^3 + x^3*z^4 - x^2*y*z^4 - 3*x^2*z^5 + 3*y^2*z^5 - 3*x*z^6 + y*z^6 + z^7 - 3*x^4*y^2 + 2*x^3*y^3 - 3*x^2*y^4 + 3*x*y^5 - 2*y^6 - 2*x^5*z + 2*x^4*y*z - 3*x^3*y^2*z + 3*x^2*y^3*z - 3*y^5*z - x^4*z^2 + x^3*y*z^2 + 3*x*y^3*z^2 - y^4*z^2 - 2*y^3*z^3 - x^2*z^4 + 2*x*y*z^4 + 2*y^2*z^4 + 3*x*z^5 + z^6 + 1/3*x^4*y + 2*x^3*y^2 + x^2*y^3 + 3*x*y^4 - 3*y^5 + 3*x^4*z + 3*x^3*y*z + x^2*y^2*z + 2*x*y^3*z + y^4*z + 3*x^3*z^2 - x^2*y*z^2 - x*y^2*z^2 - 2*y^3*z^2 + 2*y^2*z^3 + 3*x*z^4 - 2*y*z^4 - z^5 - 8/3*x*y^3 - 2*y^4 + 2*x^3*z + 3*x^2*y*z + y^3*z - 3*x^2*z^2 + x*y*z^2 - 3*y^2*z^2 + 3*x*z^3 + y*z^3 - z^4 + 3*x^2*z - 2*x*y*z + y^2*z - 2*y*z^2', 'x^8 - x^7*y + x^6*y^2 + x^5*y^3 - 3*x^4*y^4 + x^3*y^5 - 3*x^2*y^6 - 3*y^8 - 3*x^7*z - 2*x^6*y*z - x^5*y^2*z + x^4*y^3*z - 2*x^3*y^4*z + x^2*y^5*z - 3*x*y^6*z + 3*y^7*z - x^6*z^2 + 2*x^5*y*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 - x^5*z^3 - 3*x^4*y*z^3 - 3*x^3*y^2*z^3 + 2*x*y^4*z^3 - 2*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 - 3*x*y^2*z^5 + 2*y^3*z^5 - 3*x^2*z^6 - x*y*z^6 - 2*y^2*z^6 + 2*x*z^7 + 2*y*z^7 - z^8 + 11/1260*x^7 + 2*x^6*y + x^5*y^2 + x^4*y^3 + 2*x^2*y^5 - 3*x*y^6 + 3*y^7 - 3*x^6*z - x^5*y*z - x^4*y^2*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^3*y^2*z^2 - 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 - 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 + 2*x^2*z^5 + 3*x*y*z^5 + 2*y^2*z^5 + 2*x*z^6 + 3*y*z^6 + z^7 + x^5*y + 2*x^4*y^2 - x^3*y^3 - 2*x^2*y^4 + 3*x*y^5 + 2*y^6 - 3*x^5*z + x^3*y^2*z - 2*x^2*y^3*z - 2*x*y^4*z + y^5*z - x^4*z^2 + 2*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 + 3*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 + 23/12*x^4*y - 3*x^3*y^2 + 3*x*y^4 - 3*y^5 - x^4*z + 2*x^3*y*z - 2*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 + 3*x*y*z^3 - y^2*z^3 + 3*y*z^4 - z^5 + 3*x^2*y^2 + 7/6*x*y^3 + 3*x^3*z - x^2*y*z + 3*x*y^2*z + 3*x*y*z^2 + 2*y^2*z^2 - 2*x*z^3 + 2*y*z^3 - x^2*z - 3*x*y*z - y^2*z + 2*x*z^2 + 2*y*z^2 - 3*z^3']
  ok   R = XY3, component W3 (P_420 = 0 = H_102 = H_012 = H_003): a point of the component (residual equations vanish)
  ok   R = XY3, component W3 (P_420 = 0 = H_102 = H_012 = H_003) anchor (A): fixed {'P_420': 0, 'H_102': 0, 'H_012': 0, 'H_003': 0}, solved []; member closed with H and the prescribed graded data: True; a triple of I of local length 40 (ds vdim), stabilization (length, N) = (40, 12)
      anchor generators: {'P': 'X^7 + 2*X*Y^4 + 8*X^2*Y*Z - 8*X*Y^2*Z - 16/3*Y^3*Z + X*Y*Z + 2*Y^2*Z + 2*X*Z^2 + 2*Y*Z^2 + Z^3', 'G': 'X^4*Y - X^2*Z - Y*Z^2', 'H': 'X*Y^3 + X^2*Z - 2*X*Y*Z - 2*Y^2*Z'}
      triple: ['2*x^8 + 2*x^7*y + 2*x^6*y^2 - x^4*y^4 + x^2*y^6 + 3*x*y^7 + y^8 - 3*x^7*z - x^6*y*z - 2*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 + 2*x^6*z^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 + 3*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 - 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*x^2*y^2*z^4 - 3*x*y^3*z^4 + 3*x^3*z^5 - x^2*y*z^5 - 3*x*y^2*z^5 + 2*y^3*z^5 - 3*x^2*z^6 - 3*x*y*z^6 + 3*y^2*z^6 + 2*x*z^7 - 3*y*z^7 + 3*z^8 - 17/720*x^7 - x^6*y + 2*x^5*y^2 - 2*x^4*y^3 - x^3*y^4 - 3*x^2*y^5 - 3*x*y^6 - 3*y^7 + 2*x^6*z - 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 - 3*x^4*y*z^2 - 2*x^2*y^3*z^2 - y^5*z^2 - x^4*z^3 + x^3*y*z^3 + 2*x^2*y^2*z^3 + 3*x^3*z^4 + x^2*y*z^4 - 2*x*y^2*z^4 + 2*y^3*z^4 - 2*x^2*z^5 + 3*x*y*z^5 - y^2*z^5 + 2*x*z^6 - z^7 + 4/105*x^6 - 3*x^5*y - 3*x^3*y^3 + 3*x^2*y^4 - x*y^5 + 2*y^6 + 2*x^5*z - x^3*y^2*z + x^2*y^3*z - 3*x*y^4*z + 2*y^5*z + x^4*z^2 - 3*x^3*y*z^2 - 3*y^4*z^2 + x^3*z^3 + 2*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 - 3*y^2*z^4 - x*z^5 + 3*y*z^5 + 2*x^3*y^2 + 3*x*y^4 + y^5 + 3*x^4*z + x^3*y*z + 3*x^2*y^2*z - 2*x*y^3*z - 2*y^4*z - 3*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 - y^2*z^3 - 2*x*z^4 - 2*z^5 + 3*x^2*y^2 + 1/3*x*y^3 - 3*y^4 - x^3*z + x^2*y*z + 2*y^3*z - 2*x*y*z^2 - 3*y^2*z^2 - 3*y*z^3 - 3*z^4 + 2*x^2*z - x*y*z + 2*y^2*z + 3*x*z^2 - 2*y*z^2 + 2*z^3', '-2*x^8 + 3*x^7*y - 2*x^5*y^3 + 3*x^4*y^4 + x^2*y^6 + 3*x*y^7 + y^8 + 2*x^7*z + x^6*y*z + 2*x^5*y^2*z + 2*x^4*y^3*z - 2*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^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 - 3*y^6*z^2 + 2*x^5*z^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 + 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^2*y*z^5 - 2*x*y^2*z^5 + 3*y^3*z^5 + x*y*z^6 + 3*y^2*z^6 + 3*x*z^7 + 3*y*z^7 + z^8 + 1/126*x^7 + 3*x^6*y - 3*x^5*y^2 - x^4*y^3 + 2*x^3*y^4 - 3*x^2*y^5 - x*y^6 - 3*y^7 - 3*x^5*y*z - 3*x^4*y^2*z + 3*x^3*y^3*z + 2*x^2*y^4*z + 2*x*y^5*z - 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 + y^5*z^2 - 2*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 - x^2*y*z^4 - x*y^2*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 - 1/315*x^6 - 3*x^5*y + x^4*y^2 - 2*x^3*y^3 - 3*x^2*y^4 - y^6 - 2*x^5*z + 2*x^4*y*z - x^3*y^2*z - 3*x^2*y^3*z + x*y^4*z + 3*y^5*z - 3*x^4*z^2 - 2*x^3*y*z^2 + x*y^3*z^2 + 2*y^4*z^2 - x^3*z^3 + 2*x^2*y*z^3 + 3*y^3*z^3 + 3*x^2*z^4 - 2*x*y*z^4 - 2*x*z^5 + 3*y*z^5 + z^6 - 1/12*x^4*y - x^3*y^2 - x*y^4 - x^2*y^2*z + 3*x*y^3*z - y^4*z + 3*x^2*y*z^2 + 3*x*y^2*z^2 + 3*y^3*z^2 + x^2*z^3 + x*y*z^3 - 3*y^2*z^3 + 2*y*z^4 + 2*z^5 + x^2*y^2 + 2/3*x*y^3 - x^3*z + 2*x*y^2*z - 2*y^3*z - x^2*z^2 - 3*x*y*z^2 + 2*y^2*z^2 + 2*x*z^3 - 3*y*z^3 + z^4 + 2*x^2*z + 2*x*y*z + y^2*z - 3*y*z^2 - 3*z^3', '3*x^8 - x^6*y^2 + x^5*y^3 - 2*x^4*y^4 + 2*x^3*y^5 - 3*x*y^7 - 3*x^6*y*z + x^5*y^2*z - 2*x^4*y^3*z - 2*x^2*y^5*z - 2*x*y^6*z + 3*y^7*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 - 3*y^6*z^2 + 3*x^5*z^3 + x^4*y*z^3 + x^2*y^3*z^3 - 3*x*y^4*z^3 + 3*y^5*z^3 - x^3*y*z^4 - x^2*y^2*z^4 - 2*x*y^3*z^4 + 2*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 + 2*x*y*z^6 + 2*y^2*z^6 - x*z^7 - z^8 + 293/5040*x^7 - 2*x^6*y + 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 + 3*x^4*y^2*z - x^3*y^3*z - 2*x^2*y^4*z + x*y^5*z + 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 + 2*y^5*z^2 + x^4*z^3 - 3*x^3*y*z^3 + 2*x^2*y^2*z^3 - 2*x*y^3*z^3 - 3*y^4*z^3 - 2*x^2*y*z^4 + 3*x*y^2*z^4 + y^3*z^4 - 3*x^2*z^5 + x*y*z^5 + 3*y^2*z^5 + 3*x*z^6 - 3*y*z^6 - 3*z^7 + 4/315*x^6 + 3*x^5*y + 2*x^4*y^2 - x^3*y^3 + x^2*y^4 + 3*x*y^5 - y^6 - 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 - 3*x^4*z^2 + 2*x^3*y*z^2 + x*y^3*z^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 + x*y*z^4 + 2*y^2*z^4 - 2*x*z^5 - y*z^5 - 3*z^6 - 1/4*x^4*y + x^3*y^2 - 3*x*y^4 - x^3*y*z - x^2*y^2*z - 3*y^4*z - x^3*z^2 - x^2*y*z^2 + 3*x*y^2*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 - 2*x^2*y^2 - 5/3*x*y^3 - y^4 + 2*x^3*z - 2*x^2*y*z + 3*y^3*z + 2*x^2*z^2 + 2*x*y*z^2 + 3*y^2*z^2 + 3*x*z^3 + z^4 - 2*x^2*z - 3*x*y*z - 2*y^2*z + 3*x*z^2 - y*z^2 - 3*z^3']
--- R = X2Y2
  ok   R = X2Y2: the graded normal form is closed with H = [1, 3, 6, 4, 3, 2, 1, 1]
  ok   R = X2Y2: 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 - 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 - 12*P_510*P_420*H_012 + 84*P_420*G_012 + 126*P_230*H_012)
       (3/7) * (-2*P_510*P_420*H_003 + 14*P_420*G_003 + 21*P_230*H_003)
  ok   R = X2Y2: every closedness condition lies in the ideal of the residual equations after the substitutions
  ok   R = X2Y2: 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   R = X2Y2: on {P_420 = 0}: each equation is (P_230) times a linear form; components {P_230 = 0} and {['6*H_102', '3*H_012', '9*H_003'] = 0}
  ok   R = X2Y2, component W1 (P_420 != 0): a point of the component (residual equations vanish)
  ok   R = X2Y2, 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 39 (ds vdim), stabilization (length, N) = (39, 11)
      anchor generators: {'P': 'X^7 + X^4*Y^2 - 4*X^2*Y*Z + 2*X*Y^2*Z + 2*X^2*Z + 2*X*Y*Z + 2*Y^2*Z - 2*X*Z^2 - Y*Z^2 + 2*Z^3', 'G': 'X^4*Y - 2*X^2*Z + 2*X*Y*Z', 'H': 'X^2*Y^2 + X^2*Z + X*Z^2 + Y*Z^2'}
      triple: ['3*x^8 + 2*x^7*y - 3*x^6*y^2 - x^4*y^4 + 3*x^3*y^5 - 2*x*y^7 - y^8 + 3*x^7*z + x^5*y^2*z + x^4*y^3*z - 3*x^3*y^4*z + 3*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^3*y^3*z^2 + x^2*y^4*z^2 + 2*x*y^5*z^2 - 2*x^5*z^3 - x^4*y*z^3 - x^3*y^2*z^3 - 2*x^2*y^3*z^3 + 3*x*y^4*z^3 - x^2*y^2*z^4 + 2*x*y^3*z^4 - 3*y^4*z^4 - 2*x^3*z^5 - 3*x*y^2*z^5 - x^2*z^6 + 2*x*y*z^6 + 2*y^2*z^6 + y*z^7 - 3*z^8 + 11/2520*x^7 + 2*x^5*y^2 - x^4*y^3 - 2*x^3*y^4 - x^2*y^5 + 3*x*y^6 - 3*y^7 + 2*x^6*z - 2*x^5*y*z + 2*x^3*y^3*z + 2*x^2*y^4*z - 2*x*y^5*z - 2*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 + 2*x*y^4*z^2 - 2*y^5*z^2 - 2*x^4*z^3 - 3*x^3*y*z^3 - 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^2*y*z^4 - x*y^2*z^4 + 3*y^3*z^4 + 2*x^2*z^5 - 3*y^2*z^5 - 3*x*z^6 + 2*y*z^6 - 5/252*x^6 - x^5*y + 2*x^3*y^3 - 2*x^2*y^4 - 3*x*y^5 - 3*x^5*z + 2*x^4*y*z - x^3*y^2*z - 2*x*y^4*z + 3*y^5*z - 2*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 + x^3*z^3 + 2*x^2*y*z^3 - x*y^2*z^3 - 3*y^3*z^3 + x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 - 2*x*z^5 - 2*y*z^5 - z^6 - 1/35*x^5 + 2*x^3*y^2 - 2*x^2*y^3 - 2*x*y^4 + 2*x^4*z - x^3*y*z + 3*x^2*y^2*z - 3*x*y^3*z - 3*y^4*z + 2*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*z^4 + 2*y*z^4 + 3*x^2*y^2 - x*y^3 - 2*x^3*z + 2*x^2*y*z - 3*x*y^2*z + y^3*z + 2*x^2*z^2 + x*y*z^2 + y^2*z^2 - 3*y*z^3 + 2*z^4 - x^2*z - 2*x*y*z - 3*y^2*z - 2*x*z^2 - 3*y*z^2 + z^3', 'x^8 - x^7*y + 3*x^6*y^2 + 3*x^5*y^3 - 2*x^3*y^5 - x^2*y^6 + 3*y^8 - 3*x^7*z - 2*x^5*y^2*z + x^4*y^3*z - x^3*y^4*z - 2*x^2*y^5*z - x*y^6*z - y^7*z + 2*x^6*z^2 - 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 - x*y^5*z^2 - 2*y^6*z^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 - 3*x^4*z^4 + 3*x^2*y^2*z^4 - 2*x*y^3*z^4 + 3*y^4*z^4 - 2*x^3*z^5 + 2*x^2*y*z^5 + 3*x*y^2*z^5 - y^3*z^5 + x^2*z^6 - x*y*z^6 - y^2*z^6 + x*z^7 - 2*y*z^7 + z^8 - 1/420*x^7 - 3*x^6*y - 3*x^4*y^3 - x^3*y^4 + 3*x^2*y^5 + 2*x*y^6 + y^7 - x^6*z + x^5*y*z + 3*x^4*y^2*z + x^3*y^3*z - 3*x^2*y^4*z + x*y^5*z + y^6*z - 2*x^3*y^2*z^2 - 3*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 + 2*x^3*z^4 - 3*x^2*y*z^4 - 3*x*y^2*z^4 + 2*y^3*z^4 + 2*x*y*z^5 - 2*y^2*z^5 + 2*x*z^6 - 3*y*z^6 + 4/315*x^6 + 3*x^5*y + x^2*y^4 - 2*x*y^5 + 2*y^6 + 2*x^5*z + x^4*y*z + 2*x^3*y^2*z + 2*x^2*y^3*z + 2*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*x*y^3*z^2 + y^4*z^2 + 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 - 3*z^6 + 1/42*x^5 - 1/12*x^4*y - x^3*y^2 + 2*x^2*y^3 - 3*x*y^4 + 2*y^5 + x^4*z - 3*x^3*y*z + x^2*y^2*z + 3*x*y^3*z - 3*y^4*z - 3*x^3*z^2 - 3*x^2*y*z^2 - 3*x*y^2*z^2 - x^2*z^3 - 2*x*y*z^3 + x*z^4 + y*z^4 - z^5 - 5/2*x^2*y^2 + x*y^3 + y^4 - 3*x^2*y*z + x*y^2*z + y^3*z + 2*x^2*z^2 - x*y*z^2 - 3*y^2*z^2 - 2*x*z^3 + y*z^3 + 3*z^4 + x^2*z + 3*x*y*z + 2*y^2*z + x*z^2 + 3*y*z^2 - 2*z^3', '3*x^8 - x^7*y + x^6*y^2 + 3*x^5*y^3 - 3*x^4*y^4 + 2*x^3*y^5 - x^2*y^6 - 3*x*y^7 + y^8 - 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^5*y*z^2 + 2*x^2*y^4*z^2 + 3*x*y^5*z^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 - 2*x*y^4*z^3 - 2*y^5*z^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*y^2*z^5 - x^2*z^6 + 2*x*y*z^6 + 3*y^2*z^6 - 3*x*z^7 + y*z^7 - z^8 - 1/120*x^7 + 2*x^6*y - x^5*y^2 - 2*x^3*y^4 - 3*x^2*y^5 + x*y^6 - y^7 + 2*x^6*z + 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 - y^6*z + 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 - 2*y^5*z^2 + 2*x^4*z^3 - 2*x^3*y*z^3 + 2*x^2*y^2*z^3 + 3*x*y^3*z^3 - 2*y^4*z^3 - x^3*z^4 - 2*x^2*y*z^4 - 2*x*y^2*z^4 - 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 - 2*z^7 - 19/1260*x^6 + 3*x^5*y + 2*x^4*y^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 - 3*x^3*y^2*z + x^2*y^3*z - x*y^4*z - y^5*z + x^4*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 + 2*x^2*z^4 + 3*x*y*z^4 - y^2*z^4 + 2*x*z^5 + y*z^5 + z^6 + 1/105*x^5 + 1/12*x^4*y + 2*x^3*y^2 - 3*x^2*y^3 + 3*x*y^4 - 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 - 2*x^3*z^2 - x^2*y*z^2 - x*y^2*z^2 + 2*x*y*z^3 - x*z^4 + 2*y*z^4 + 3*z^5 - x^2*y^2 + 3*x*y^3 - 2*y^4 + 2*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 + 2*y*z^3 + x^2*z + x*y*z - 3*y^2*z + 3*x*z^2 - 2*y*z^2 - 3*z^3']
  ok   R = X2Y2, component W2 (P_420 = 0 = P_230): a point of the component (residual equations vanish)
  ok   R = X2Y2, component W2 (P_420 = 0 = P_230) anchor (A): fixed {'P_420': 0, 'P_230': 0}, solved []; member closed with H and the prescribed graded data: True; a triple of I of local length 41 (ds vdim), stabilization (length, N) = (41, 13)
      anchor generators: {'P': 'X^7 - X^2*Z + X*Y*Z - 2*X*Z^2 - 2*Y*Z^2', 'G': 'X^4*Y - X^2*Z - X*Y*Z + 2*Y^2*Z + 2*X*Z^2 + Y*Z^2 + 2*Z^3', 'H': 'X^2*Y^2 + 2*Y^2*Z + 2*X*Z^2 + 2*Z^3'}
      triple: ['2*x^7*y + 3*x^6*y^2 - 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 + 2*x^6*y*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^6*z^2 - x^5*y*z^2 - 2*x^4*y^2*z^2 - x^3*y^3*z^2 + x^2*y^4*z^2 - 2*x*y^5*z^2 - 2*y^6*z^2 - 3*x^5*z^3 + x^4*y*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 - 3*x^3*y*z^4 - 3*y^4*z^4 + x^3*z^5 - x*y^2*z^5 + y^3*z^5 + 2*x^2*z^6 - x*y*z^6 + 2*y^2*z^6 + x*z^7 - y*z^7 - z^8 - 1/1008*x^7 + x^6*y + 3*x^4*y^3 - 2*x^3*y^4 - 3*x*y^6 + 2*y^7 - 2*x^6*z - 2*x^5*y*z + 3*x^3*y^3*z - 3*x^2*y^4*z - x*y^5*z + 3*y^6*z + 3*x^5*z^2 - 3*x^4*y*z^2 - 3*x^2*y^3*z^2 + 3*x*y^4*z^2 - y^5*z^2 + x^4*z^3 + x^3*y*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 - 3*y^3*z^4 - 2*x^2*z^5 + 2*x*y*z^5 - x*z^6 - y*z^6 - z^7 + 3*x^5*y + 2*x^4*y^2 - x^3*y^3 + 3*x^2*y^4 + 2*x*y^5 - y^6 + 2*x^5*z - 2*x^4*y*z - x^3*y^2*z - y^5*z - 2*x^4*z^2 + 3*x^3*y*z^2 + 3*x*y^3*z^2 + y^4*z^2 - 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 + y^2*z^4 - x*z^5 + 3*y*z^5 + 3*z^6 + 41/24*x^4*y + 2*x^3*y^2 + x^2*y^3 - x*y^4 + 2*x^3*y*z - x^2*y^2*z - 3*x*y^3*z - 3*y^4*z - 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 + 3*x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 + 3*z^5 + 8*x^2*y^2 + 2*x*y^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 - 2*x*y*z^2 - y^2*z^2 - x*z^3 - y*z^3 - z^4 + x^2*z + 3*x*y*z - 3*y^2*z + x*z^2 - 2*y*z^2 - 2*z^3', '-x^8 - 3*x^7*y - x^6*y^2 + x^5*y^3 - x^4*y^4 + 2*x^3*y^5 - 2*x*y^7 - 3*y^8 - x^7*z - 2*x^6*y*z - x^5*y^2*z - x^4*y^3*z + 3*x^3*y^4*z - x*y^6*z + 3*y^7*z + 2*x^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 + x^5*z^3 + 2*x^4*y*z^3 - 2*x^3*y^2*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 + 3*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 - 3*y^3*z^5 + 3*x^2*z^6 + 2*x*y*z^6 + y^2*z^6 - 3*y*z^7 + 3*z^8 + 1/840*x^7 - 2*x^6*y + 3*x^5*y^2 + x^4*y^3 - x^3*y^4 - 2*x^2*y^5 + 2*x*y^6 + 2*y^7 + 2*x^6*z + x^5*y*z - 3*x^4*y^2*z - 2*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 + 2*x*y^4*z^2 + 2*y^5*z^2 - x^4*z^3 - 2*x^3*y*z^3 - 2*x^2*y^2*z^3 - 2*x*y^3*z^3 + x^3*z^4 + 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 - y^2*z^5 + x*z^6 + y*z^6 + 3*z^7 - 3*x^5*y + 2*x^4*y^2 - x^3*y^3 + 3*x^2*y^4 - 3*x*y^5 + 2*y^6 + x^5*z + 2*x^3*y^2*z + x^2*y^3*z - x*y^4*z - y^5*z + x^4*z^2 - 3*x^3*y*z^2 + x^2*y^2*z^2 + 3*y^4*z^2 + x^2*y*z^3 - 2*x*y^2*z^3 + y^2*z^4 + 2*x*z^5 - y*z^5 - z^6 + 19/12*x^4*y - 2*x^3*y^2 + x^2*y^3 + x*y^4 + 3*y^5 - x^4*z + 2*x^3*y*z - x^2*y^2*z - x*y^3*z - 2*y^4*z - 3*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 + 9*x^2*y^2 - 3*x*y^3 - y^4 - 3*x^3*z - x^2*y*z - 3*y^3*z + 2*x^2*z^2 + x*y*z^2 - y^2*z^2 - 2*x*z^3 + 2*z^4 + 2*x^2*z - 2*x*y*z - 3*y^2*z - 2*z^3', '-x^8 - 2*x^6*y^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 + x^6*y*z - 3*x^5*y^2*z - x^4*y^3*z + 3*x^3*y^4*z - 2*x^2*y^5*z + 3*x^6*z^2 + 2*x^5*y*z^2 - 2*x^3*y^3*z^2 - 2*x^2*y^4*z^2 + 2*x*y^5*z^2 + y^6*z^2 + 2*x^5*z^3 - 3*x^4*y*z^3 + 3*x^3*y^2*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 - 2*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 + x^2*z^6 + 2*x*y*z^6 - 3*x*z^7 + 3*y*z^7 + 2*z^8 + 1/336*x^7 - x^6*y - 3*x^5*y^2 - 3*x^3*y^4 - 2*x*y^6 - y^7 + 2*x^6*z - x^5*y*z - x^3*y^3*z + 3*x^2*y^4*z + 3*x*y^5*z + x^5*z^2 + 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 - 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*y^4*z^3 + x^3*z^4 - 3*x^2*y*z^4 + 3*x*y^2*z^4 - y^3*z^4 + 2*y^2*z^5 - 3*x*z^6 - y*z^6 - 3*z^7 - x^5*y - x^3*y^3 - 3*x^2*y^4 + 3*x*y^5 + 2*y^6 + 2*x^5*z + 3*x^4*y*z + x^3*y^2*z - 3*x^2*y^3*z - 3*x*y^4*z + y^5*z - x^2*y^2*z^2 - 2*x*y^3*z^2 + 2*y^4*z^2 - x^2*y*z^3 + 3*x*y^2*z^3 + 3*y^3*z^3 + 2*x*y*z^4 - 3*x*z^5 - 3*y*z^5 + z^6 + 19/24*x^4*y - 3*x^3*y^2 + 3*x^2*y^3 + 2*x*y^4 - 2*y^5 + 2*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 + 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 + y^2*z^3 + 2*x*z^4 + 3*y*z^4 - 2*z^5 + 6*x^2*y^2 - 2*x*y^3 - 3*y^4 - x^3*z + 3*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 - 3*x*z^3 - 3*y*z^3 + 3*z^4 - 3*x*y*z + y^2*z + 2*x*z^2 + y*z^2 - 3*z^3']
  ok   R = X2Y2, component W3 (P_420 = 0 = H_102 = H_012 = H_003): a point of the component (residual equations vanish)
  ok   R = X2Y2, component W3 (P_420 = 0 = H_102 = H_012 = H_003) anchor (A): fixed {'P_420': 0, 'H_102': 0, 'H_012': 0, 'H_003': 0}, solved []; member closed with H and the prescribed graded data: True; a triple of I of local length 40 (ds vdim), stabilization (length, N) = (40, 12)
      anchor generators: {'P': 'X^7 + X^2*Y^3 + 3*X^2*Y*Z - 3/2*X*Y^2*Z - Y^3*Z - X*Y*Z + 2*Y^2*Z + Z^3', 'G': 'X^4*Y - X*Y*Z + Y^2*Z - 2*Y*Z^2 + Z^3', 'H': 'X^2*Y^2 + X^2*Z - X*Y*Z - Y^2*Z'}
      triple: ['-3*x^8 + x^7*y - x^6*y^2 - 3*x^5*y^3 + x^3*y^5 - 2*x^2*y^6 + 2*y^8 - 2*x^7*z + x^5*y^2*z - x^4*y^3*z + x^3*y^4*z + x^2*y^5*z - 3*x*y^6*z + y^7*z - 2*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 + 2*y^6*z^2 - x^5*z^3 + 3*x*y^4*z^3 - y^5*z^3 - 3*x^4*z^4 - 3*x^2*y^2*z^4 - 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 - x^2*z^6 - 3*x*y*z^6 + 3*y^2*z^6 + 2*x*z^7 - y*z^7 - 3*z^8 - 11/2520*x^7 - 3*x^6*y + 3*x^4*y^3 + 2*x^3*y^4 - 3*x*y^6 - y^7 - 2*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 + x*y^5*z - 2*y^6*z - 3*x^5*z^2 - 2*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 - 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 + 3*y^4*z^3 + 3*x^3*z^4 - 3*x*y^2*z^4 - y^3*z^4 - 2*x^2*z^5 + 3*x*y*z^5 - y^2*z^5 - 3*x*z^6 - y*z^6 + 3*z^7 - 1/240*x^6 + 2*x^5*y + 2*x^4*y^2 - 3*x^3*y^3 - x^2*y^4 - x*y^5 + 3*x^5*z - 3*x^4*y*z - x^3*y^2*z + 2*x*y^4*z + y^5*z - x^3*y*z^2 + 2*x^2*y^2*z^2 - x*y^3*z^2 - 3*y^4*z^2 - 2*x^3*z^3 + 2*x^2*y*z^3 + 3*x*y^2*z^3 - y^3*z^3 - x^2*z^4 + 3*x*y*z^4 - 3*y^2*z^4 + x*z^5 + 3*y*z^5 - 11/12*x^4*y + x^3*y^2 - 2*x*y^4 - y^5 + 3*x^4*z + 2*x^2*y^2*z + x*y^3*z - 3*y^4*z + x^3*z^2 + 2*x^2*y*z^2 + 2*x^2*z^3 - 2*x*y*z^3 - y^2*z^3 + 2*x*z^4 + y*z^4 + z^5 - 5/2*x^2*y^2 - y^4 + 2*x^2*y*z - 2*x*y^2*z + 3*x^2*z^2 - x*y*z^2 - y^2*z^2 - y*z^3 + 2*z^4 + 3*x^2*z + 2*x*y*z - 3*y^2*z + x*z^2 - 3*y*z^2 + 3*z^3', '2*x^8 - 2*x^7*y + x^6*y^2 + 2*x^5*y^3 - 2*x^4*y^4 - x^3*y^5 + 2*x^2*y^6 - x*y^7 + 2*y^8 - 3*x^7*z - 3*x^6*y*z + 3*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 - 2*y^7*z - 3*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 + 3*y^6*z^2 + x^5*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 - 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 + 3*x^3*z^5 + 2*x*y^2*z^5 + 2*y^3*z^5 + 2*x^2*z^6 - 2*x*y*z^6 + y^2*z^6 + x*z^7 + 1/252*x^7 - x^6*y + 3*x^5*y^2 - x^4*y^3 - 2*x^3*y^4 + 2*x^2*y^5 - x*y^6 - 3*y^7 + 2*x^6*z - x^5*y*z - x^3*y^3*z - 2*x^2*y^4*z + 2*x*y^5*z - 3*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 + 3*y^5*z^2 - 2*x^4*z^3 - 3*x^3*y*z^3 + 3*x^2*y^2*z^3 + 3*x*y^3*z^3 - x^3*z^4 + 2*x*y^2*z^4 - y^3*z^4 + x^2*z^5 - 2*y^2*z^5 + y*z^6 - 2*z^7 - 1/210*x^6 - 3*x^5*y + 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 - x^2*y^3*z + x*y^4*z + 2*y^5*z + x^4*z^2 + 2*x^3*y*z^2 - 3*x^2*y^2*z^2 + 2*x*y^3*z^2 + 3*y^4*z^2 + x^3*z^3 - x*y^2*z^3 + y^3*z^3 + 2*x^2*z^4 + 3*x*y*z^4 - y^2*z^4 + y*z^5 - 3*z^6 + 11/24*x^4*y + 2*x^3*y^2 - 2*x^2*y^3 + x*y^4 + y^5 + x^4*z - x^3*y*z - x^2*y^2*z + 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 - x*y*z^3 - y^2*z^3 - x*z^4 - 2*y*z^4 + 2*z^5 - 11/4*x^2*y^2 + 3*x*y^3 - 3*y^4 - x^3*z + x^2*y*z + x*y^2*z - 2*y^3*z - x^2*z^2 - x*y*z^2 - y^2*z^2 + y*z^3 + 2*z^4 + 2*x^2*z - 3*x*y*z - 2*y^2*z - x*z^2 + y*z^2 - z^3', 'x^7*y + 2*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^7*z - 3*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 - 2*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 - 3*y^6*z^2 + x^5*z^3 + x^4*y*z^3 - 3*x^3*y^2*z^3 + x^2*y^3*z^3 - 2*x*y^4*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 - x^3*z^5 + 2*x^2*y*z^5 + 3*y^3*z^5 + x*y*z^6 - y^2*z^6 - 2*x*z^7 + 3*y*z^7 - 1/144*x^7 - x^5*y^2 - 2*x^4*y^3 + x^2*y^5 - x*y^6 - 3*y^7 + 2*x^6*z - x^5*y*z + x^3*y^3*z - x^2*y^4*z - 3*x*y^5*z - 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 - x^4*z^3 - 3*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 + y^3*z^4 + 2*x*y*z^5 - 3*y^2*z^5 - 3*x*z^6 - y*z^6 + 1/105*x^6 + 2*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^4*y*z + 3*x^3*y^2*z - 2*x^2*y^3*z + 2*x*y^4*z - 2*y^5*z - 2*x^4*z^2 + 2*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 + x^2*y*z^3 - 2*x*y^2*z^3 + 2*y^3*z^3 - 3*x^2*z^4 + x*y*z^4 - y^2*z^4 + 2*x*z^5 + 3*y*z^5 - 3*z^6 + 1/6*x^4*y + 2*x^2*y^3 + 3*x*y^4 - 3*y^5 - 2*x^4*z + x^3*y*z - 2*x^2*y^2*z + 2*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 + x^2*z^3 + 2*x*y*z^3 - y^2*z^3 - z^5 - x^2*y^2 - 3*x*y^3 + x^3*z + x^2*y*z - x*y^2*z - 3*y^3*z - 2*x^2*z^2 + x*y*z^2 + 2*y^2*z^2 + x*z^3 + 2*y*z^3 - 2*z^4 + x^2*z - 2*x*y*z - 2*x*z^2 - 3*y*z^2 - 3*z^3']
time 11.8 s
anchor lengths (W1, W2, W3): {'Y4': [39, 41, 40], 'X2Y2+Y4': [39, 41, 40], 'XY3': [39, 41, 40], 'X2Y2': [39, 41, 40]}
ALL CHECKS PASSED
