Part O: tangent out, D_k = <Y^k, X Y^(k-1)>, F = Y^7 + P6 + ..., G = X Y^6 + Q6 + ...
   shear effects: [(42*Y^5*Z, 30*X*Y^4*Z), (0, 6*Y^5*Z)]
  ok   every (P6,Q6) in N becomes binary in X,Y after the shear z -> z + a y^2 + c xy  (dim N = 12)
  ok   leading effects 42 Z Y^5 on F and 30 Z X Y^4, 6 Z Y^5 on G
  ok   z o F, z o G have no part of degree >= 5
  ok   then P5, Q5 have Z-degree <= 1
  ok   U = y z^2: U o F, U o G in T_{<=1} (all tails symbolic), U_3 kills D_5 = <Y^5, X Y^4>
Part I: tangent in, D_k = <Y^k, Y^(k-1) Z>, F = Y^7 + P6 + ..., G = Y^6 Z + Q6 + ...
   dim N = 8
  ok   N = <(lam Y^4Z^2, (4lam/21) Y^3Z^3)> + shears x -> x + a y^2 + c yz, z -> z + e y^2 + gauges (ranks 8, 8)
  ok   leading effects: 42 X Y^5 | 30 X Y^4 Z, 6 X Y^5 | 42 Y^5 Z, 30 Y^4 Z^2
  ok   x o F, x o G, z o F - (lam/15) y^2 o G, z o G - (1/7) y o F have no part of degree >= 5
   containing space: P5 = 7/4*Q5_11*X*Y^4 + P5_15*Y^5 + P5_10*Y^4*Z + 7*Q5_3*Y^3*Z^2 + 2/105*lam^2*Y*Z^4
                     Q5 = Q5_16*X*Y^4 + Q5_15*Y^5 + Q5_11*X*Y^3*Z + Q5_10*Y^4*Z + Q5_6*Y^3*Z^2 + Q5_3*Y^2*Z^3 + 2/3675*lam^2*Z^5
  ok   U = y z^2 - (lam/105) y^4 - (p/420) y^5 - (d/60) y^4 z: U o F, U o G in T_{<=1}, U_3 kills D_5
Part S (sanity, class S): actual algebras
   trial 0 (secant): H ok, N1 complete intersection local length 36 (stable at N = 11)
   trial 1 rejected (binary H [1, 2, 3, 4, 3, 2, 2, 2])
   trial 2 (secant): H ok, N1 complete intersection local length 36 (stable at N = 11)
   trial 3 rejected (binary H [1, 2, 3, 4, 3, 2, 2, 2])
  ok   N1 sanity: 2 accepted algebras, all complete intersections of local length <= 40
   trial 0 (out) rejected: H = [1, 3, 6, 6, 5, 4, 3, 2]
  ok      trial 1 (tangent in): H ok, D_3 = <Y^3, Y^2Z, YZ^2, XY^2> (cube branch), U o M in T_{<=1} for the whole actual inverse system
   trial 2 (out) rejected: H = [1, 3, 6, 5, 3, 3, 3, 2]
  ok      trial 3 (tangent in): H ok, D_3 = <Y^3, Y^2Z, YZ^2, XY^2> (cube branch), U o M in T_{<=1} for the whole actual inverse system
   trial 4 (out) rejected: H = [1, 3, 6, 6, 5, 4, 3, 2]
  ok      trial 5 (tangent in): H ok, D_3 = <Y^3, Y^2Z, YZ^2, XY^2> (cube branch), U o M in T_{<=1} for the whole actual inverse system
  ok   cube branch: 3 accepted actual samples
time 9.9 s
ALL CHECKS PASSED
