Part B: binary sextic F, slide of K_{r_2} by a binary quintic w
  ok   F = Y^6 + 2*Y^4*Z^2 - Y^3*Z^3 + 3*Y*Z^5 + Z^6, r_2 = y*z: H = [1, 3, 5, 6, 3, 2, 1], gamma_f = 0, x w in I: True, w nonzero at the roots of p: True
  ok     tau = 1: slid ideal colength 21, H = [1, 3, 5, 6, 3, 2, 1], contains f, P, K + tau w: True
  ok     tau = 2: slid ideal colength 21, H = [1, 3, 5, 6, 3, 2, 1], contains f, P, K + tau w: True
  ok     CI(f, P, K + 3 w) local length 36 <= 40
  ok   F = Y^6 - Y^5*Z + 2*Y^2*Z^4 + Z^6, r_2 = z^2: H = [1, 3, 5, 6, 3, 2, 1], gamma_f = 0, x w in I: True, w nonzero at the roots of p: True
  ok     tau = 1: slid ideal colength 21, H = [1, 3, 5, 6, 3, 2, 1], contains f, P, K + tau w: True
  ok     tau = 2: slid ideal colength 21, H = [1, 3, 5, 6, 3, 2, 1], contains f, P, K + tau w: True
  ok     CI(f, P, K + 3 w) local length 32 <= 40
  ok   F = -2*Y^6 + Y^5*Z + 3*Y^3*Z^3 + Z^6, r_2 = y^2 + y*z - z^2: H = [1, 3, 5, 6, 3, 2, 1], gamma_f = 0, x w in I: True, w nonzero at the roots of p: True
  ok     tau = 1: slid ideal colength 21, H = [1, 3, 5, 6, 3, 2, 1], contains f, P, K + tau w: True
  ok     tau = 2: slid ideal colength 21, H = [1, 3, 5, 6, 3, 2, 1], contains f, P, K + tau w: True
  ok     CI(f, P, K + 3 w) local length 32 <= 40
  ok   F = Y^6 + Y^4*Z^2 + 5*Y^2*Z^4 - Z^6, r_2 = y^2: H = [1, 3, 5, 6, 3, 2, 1], gamma_f = 0, x w in I: True, w nonzero at the roots of p: True
  ok     tau = 1: slid ideal colength 21, H = [1, 3, 5, 6, 3, 2, 1], contains f, P, K + tau w: True
  ok     tau = 2: slid ideal colength 21, H = [1, 3, 5, 6, 3, 2, 1], contains f, P, K + tau w: True
  ok     CI(f, P, K + 3 w) local length 32 <= 40
  ok   Part B: 4 accepted samples (of 4 cases)
  ok   Part B anchor certified by stabilization: 32 (N = 9) <= 40
Part N: F = X Y^5 (nonbinary), all tails symbolic
  ok   N1 (yz): the conditions (16) kill exactly the coefficients outside the tail space (17)
  ok   N1 (z^2): the conditions (16) kill exactly the coefficients outside the tail space (17)
  ok   N2 rho = 0, r_2 = yz or z^2 (C_4 = nu0 Y^4 + sig Y^3 Z), p in z bS_2: T o Phi in T_{<=1} modulo the 2 linear condition(s) on p; T_3 kills X Y^5, Y^5, X Y^4
  ok   N2 r_2 = yz, rho != 0 (T_3 = 12 rho p - [Z^2](p o B5) x z^2): T o Phi in T_{<=1} modulo the 1 linear condition(s) on p; T_3 kills X Y^5, Y^5, X Y^4
  ok   N2 r_2 = z^2, rho != 0 (T_3 = 4 rho p - [YZ](p o B5) x y z): T o Phi in T_{<=1} modulo the 1 linear condition(s) on p; T_3 kills X Y^5, Y^5, X Y^4
  ok   N3: the conditions on p are homogeneous linear: 2 on 3 unknowns (rho = 0), 1 on 2, 1 on 2 (rho != 0), so a nonzero p exists for every value of the parameters; the binary part of T_3 is (1, 12*rho, 4*rho) p, injective in p (rank 3, 2, 2), so it is nonzero
Part NA: actual algebras with F = X Y^5: a turning operator of type (b) in (I : m^2)
  ok   r_2 = y*z, E_4 = Y^2*Z^2 + X*Z^3 + 2*Y*Z^3 + Z^4: H = [1, 3, 5, 6, 3, 2, 1]; binary cubic parts of (I : m^2) cap m^3: [z^3, y*z^2]
  ok   r_2 = z^2, E_4 = X*Y^2*Z + Y^2*Z^2 - Y*Z^3 + 3*Z^4: H = [1, 3, 5, 6, 3, 2, 1]; binary cubic parts of (I : m^2) cap m^3: [z^3, y*z^2]
  ok   r_2 = y*z, E_4 = Y^3*Z + Z^4: H = [1, 3, 5, 6, 3, 2, 1]; binary cubic parts of (I : m^2) cap m^3: [z^3, y*z^2]
  ok   r_2 = z^2, E_4 = Y*Z^3 + Z^4: H = [1, 3, 5, 6, 3, 2, 1]; binary cubic parts of (I : m^2) cap m^3: [z^3, y*z^2]
  ok   Part NA: 4 accepted samples
ALL CHECKS PASSED
