Part R: base-free W_2, radial costs with the turning power b^5
  ok   F = 2*Y^6 + 6*Y^5*Z + 15*Y^4*Z^2 + 20*Y^3*Z^3 + 15*Y^2*Z^4 + 6*Y*Z^5 + 2*Z^6, Q_D = Y*Z: H = [1, 3, 5, 5, 3, 3, 1], r = y^2 + 2*z^2 avoids the roots of p = -4*y^3*z + 3*y^2*z^2 + y*z^3: True; CI(f + 3 b^5, K_r, P) = 36 <= 36
  ok   F = 2*Y^6 + 12*Y^5*Z + 60*Y^4*Z^2 + 160*Y^3*Z^3 + 240*Y^2*Z^4 + 192*Y*Z^5 + 65*Z^6, Q_D = Y^2 + Z^2: H = [1, 3, 5, 5, 3, 3, 1], r = y^2 + 2*y*z - z^2 avoids the roots of p = -10*y^3*z + 3*y^2*z^2 + y*z^3: True; CI(f + 3 b^5, K_r, P) = 35 <= 36
  ok   F = 2*Y^6 - 6*Y^5*Z + 15*Y^4*Z^2 - 20*Y^3*Z^3 + 15*Y^2*Z^4 - 6*Y*Z^5 + 2*Z^6, Q_D = Y^2 + Y*Z + Z^2: H = [1, 3, 5, 5, 3, 3, 1], r = y^2 + 2*y*z - 2*z^2 avoids the roots of p = 2*y^3*z + 3*y^2*z^2 + y*z^3: True; CI(f + 3 b^5, K_r, P) = 35 <= 36
  ok   Part R: 3 accepted samples
  ok   Part R anchor certified: 35 (N = 10) <= 36
Part B: W_2 = l_0 <y,z>, F binary: pencil slide
  ok   F = 2*Y^6 + 6*Y^5*Z + 15*Y^4*Z^2 + 20*Y^3*Z^3 + 15*Y^2*Z^4 + 6*Y*Z^5 + 2*Z^6, Q_D = Y^2: H = [1, 3, 5, 5, 3, 3, 1], x phi(W_2) in I and phi nonzero at the roots of p = -4*y^3*z + 3*y^2*z^2 + y*z^3: True
  ok     tau = 1: slid ideal colength 21, H = [1, 3, 5, 5, 3, 3, 1], contains f, P, K + tau phi: True
  ok     tau = -2: slid ideal colength 21, H = [1, 3, 5, 5, 3, 3, 1], contains f, P, K + tau phi: True
  ok     CI(f, P, K + 3 phi) local length 36 <= 40
  ok   F = Y^6, Q_D = Y^2: H = [1, 3, 5, 5, 3, 3, 1], x phi(W_2) in I and phi nonzero at the roots of p = -4*y^3*z + 3*y^2*z^2 + y*z^3: True
  ok     tau = 1: slid ideal colength 21, H = [1, 3, 5, 5, 3, 3, 1], contains f, P, K + tau phi: True
  ok     tau = -2: slid ideal colength 21, H = [1, 3, 5, 5, 3, 3, 1], contains f, P, K + tau phi: True
  ok     CI(f, P, K + 3 phi) local length 40 <= 40
  ok   F = 2*Y^6 + 12*Y^5*Z + 60*Y^4*Z^2 + 160*Y^3*Z^3 + 240*Y^2*Z^4 + 192*Y*Z^5 + 65*Z^6, Q_D = Y^2 - 2*Y*Z + Z^2: H = [1, 3, 5, 5, 3, 3, 1], x phi(W_2) in I and phi nonzero at the roots of p = -10*y^3*z + 3*y^2*z^2 + y*z^3: True
  ok     tau = 1: slid ideal colength 21, H = [1, 3, 5, 5, 3, 3, 1], contains f, P, K + tau phi: True
  ok     tau = -2: slid ideal colength 21, H = [1, 3, 5, 5, 3, 3, 1], contains f, P, K + tau phi: True
  ok     CI(f, P, K + 3 phi) local length 36 <= 40
  ok   F = 2*Y^6 + 6*Y^5*Z + 15*Y^4*Z^2 + 20*Y^3*Z^3 + 15*Y^2*Z^4 + 6*Y*Z^5 + 2*Z^6, Q_D = Z^2: H = [1, 3, 5, 5, 3, 3, 1], x phi(W_2) in I and phi nonzero at the roots of p = -4*y^3*z + 3*y^2*z^2 + y*z^3: True
  ok     tau = 1: slid ideal colength 21, H = [1, 3, 5, 5, 3, 3, 1], contains f, P, K + tau phi: True
  ok     tau = -2: slid ideal colength 21, H = [1, 3, 5, 5, 3, 3, 1], contains f, P, K + tau phi: True
  ok     CI(f, P, K + 3 phi) local length 38 <= 40
  ok   Part B: 4 accepted samples
  ok   Part B anchor certified: 38 (N = 11) <= 40
Part N: nonbinary F, all tails symbolic
  ok   N0 (d = 3): x^2, xyz, xz^2 annihilate exactly B_d + C X Y^(d-1)
  ok   N0 (d = 4): x^2, xyz, xz^2 annihilate exactly B_d + C X Y^(d-1)
  ok   N0 (d = 5): x^2, xyz, xz^2 annihilate exactly B_d + C X Y^(d-1)
  ok   N0 (d = 6): x^2, xyz, xz^2 annihilate exactly B_d + C X Y^(d-1)
  ok   N1 XY^5 + Z^6: dim E_2 = S_4 o F_6 = 3, spanned by the listed images ['60*Y^2', '120*X*Y', '360*Z^2']
  ok   N1 XY^5 + Z^6: binary quadrics of E_2: [Y^2, Z^2]; the allowed A_4 are spanned by [Y^4, Y^3*Z, Z^4] (expected [Y^4, Y^3*Z, Z^4])
  ok   N2 XY^5 + Z^6: T_3 = s*(y^2*z) + t*(y*z^2): T_3 o P_5 has 1 component(s) outside E_2, linear in (s, t); T_3 kills F_6: True
  ok   N2 XY^5 + Z^6: T = T_3 + T_4 sends Phi = F_6 + X A_4 + B_5 into T_{<=1} modulo the linear condition (all coefficients symbolic)
  ok   N1 XY^5 + Y^4 Z^2: dim E_2 = S_4 o F_6 = 3, spanned by the listed images ['60*Y^2', '48*Y*Z', '120*X*Y + 24*Z^2']
  ok   N1 XY^5 + Y^4 Z^2: binary quadrics of E_2: [Y^2, Y*Z]; the allowed A_4 are spanned by [Y^4, Y^3*Z, Y^2*Z^2] (expected [Y^4, Y^3*Z, Y^2*Z^2])
  ok   N2 XY^5 + Y^4 Z^2: T_3 = s*((-2/5)*x*y^2 + y*z^2) + t*(z^3): T_3 o P_5 has 1 component(s) outside E_2, linear in (s, t); T_3 kills F_6: True
  ok   N2 XY^5 + Y^4 Z^2: T = T_3 + T_4 sends Phi = F_6 + X A_4 + B_5 into T_{<=1} modulo the linear condition (all coefficients symbolic)
  ok   N2 XY^5, third quintic Z^5: y*z^2 kills D_5 and sends Phi = X Y^5 + P_5 into T_{<=1} whenever z o P_5 lies in D_4 = [Y^4, X*Y^3, Z^4]
  ok   N2 XY^5, third quintic Y^4*Z: z^3 kills D_5 and sends Phi = X Y^5 + P_5 into T_{<=1} whenever z o P_5 lies in D_4 = [Y^4, X*Y^3, Y^3*Z]
Part NA: actual algebras with nonbinary F: binary cubic parts of (I : m^2) cap m^3
  ok   [X*Y^5 + Z^6]: H = [1, 3, 5, 5, 3, 3, 1]; binary cubic parts: [y*z^2]
  ok   [X*Y^5 + Y^4*Z^2]: H = [1, 3, 5, 5, 3, 3, 1]; binary cubic parts: [z^3, y*z^2]
  ok   [X*Y^5, Z^5]: H = [1, 3, 5, 5, 3, 3, 1]; binary cubic parts: [y*z^2, y^2*z]
  ok   [X*Y^5, Y^4*Z]: H = [1, 3, 5, 5, 3, 3, 1]; binary cubic parts: [z^3, y*z^2]
  ok   Part NA: 4 accepted samples
ALL CHECKS PASSED
