(U1) D_4(l)
  [ok] (U1) z o G_l = X^4, and D_4(l) = <X^4, G_x, G_y> has dimension 3 for every l (constant 3x3 minor 20)
(U2) P(l) = S_1 o D_4(l)
  [ok] (U2) P(l) = <X^3, x o G_x, y o G_x, y o G_y> (all nine derivatives in its span over Q(l)) has dimension 4 for every l (constant 4x4 minor 1440), and P(l) lies in C[X,Y]_3 + C X^2Z
(U3) N_X o P(l)
  [ok] (U3) y o P(l) + z o P(l) = C[X,Y]_2 for every l (contained in it; constant 3x3 minor -864)
(U4) the A-space
  [ok] (U4) {A : A_Y, A_Z in D_4(l)} = <X^5, X^4Y, X^4Z, G_0(l)> for every l: the map (A,a,b) has rank 23 everywhere (constant 23x23 minor -165888000), the four quintics lie in the space and are independent for every l (constant minor -1)
(U5) the shift
  [ok] (U5) x^2 o A/30 = (2/5)X^2(c1 Y + c2 Z); (s_B)_Y = c1 x^2oA/30, (s_B)_Z = c2 x^2oA/30, (s_P)_Z = x^2oA/30 (symbolic c1, c2)
(U6) the map Lambda_l
  [ok] (U6) image of Lambda_l lies in W (symbolic in l), dim W = 17, and rank Lambda_l = 17 for every l (constant 17x17 minor -995328); kernel of rank 6
(U7) the spaces V_delta
  [ok] (U7) z delta o : T_3 -> T_1 has rank 3 for every (a,b) != 0 (radical of the 3x3 minors = (a,b)), so dim V_delta = 7; P(l) lies in V_delta identically in (l, a, b)
(A8) members and certificates
  [ok] (A8) piece (alpha), l = 17/5: member closed with H, D_3 = N_3 (direct), in the piece; S6.2 triple of local length 34 <= 41 (ds = stabilization), explicit M_Q closed with H and the triple in Ann(M_Q); unsolvable B-systems: 0
      D_3 = [-1461/200*X^2*Y + 3/4*X*Y*Z - 5/4*Y^2*Z + 3/8*X*Z^2 - 15/8*Y*Z^2 + Z^3, -583/100*X^2*Y + X^2*Z, 3/10*X^2*Y + Y^3, 17/5*X^2*Y + X*Y^2, X^3]
      triple: [x^6 + 5*x^5*y + 5*x^4*y^2 + 2*x^3*y^3 - 5*x^2*y^4 + 5*x*y^5 - 3*y^6 - 7*x^5*z - 5*x^4*y*z - x^3*y^2*z + 7*x*y^4*z + y^5*z + 7*x^4*z^2 + 2*x^3*y*z^2 - 6*x^2*y^2*z^2 + 2*x*y^3*z^2 - 2*y^4*z^2 + 3*x^3*z^3 - 2*x^2*y*z^3 - 7*y^3*z^3 + x*y*z^4 - 7*y^2*z^4 + 7*x*z^5 + 6*y*z^5 + 6*z^6 - 4*x^4*y - 245/17*x^3*y^2 - 5*x^2*y^3 + 7*x*y^4 + 5*y^5 + 2*x^4*z - 2*x^3*y*z + 6*x^2*y^2*z + 7*x*y^3*z - 4*y^4*z + 5*x^3*z^2 + 7*x^2*y*z^2 - 6*x*y^2*z^2 - x^2*z^3 - x*y*z^3 - 3*y^2*z^3 - 3*x*z^4 - y*z^4 - 2*z^5 + 2025/289*x^3*y - 65/17*x^2*y^2 + 7*x*y^3 - 2*y^4 + 3*x^3*z + 4*x^2*y*z + 3*x*y^2*z + 3*y^3*z + 6*x^2*z^2 + 6*x*y*z^2 + x*z^3 - 6*y*z^3 + 4*z^4 + 1425/487*x^2*y - 4845/487*x*y^2 - 285/974*y^3 + 33231/1948*x^2*z - 2*x*y*z + 3*y^2*z + 2*x*z^2 - 7*y*z^2 + 4*z^3, 2*x^6 + 5*x^5*y - 6*x^4*y^2 - 4*x^3*y^3 - 4*x^2*y^4 + 6*x*y^5 - 2*y^6 - 2*x^5*z - 6*x^4*y*z + 2*x^3*y^2*z + x^2*y^3*z + 2*x*y^4*z + 2*y^5*z - 2*x^4*z^2 - 6*x^3*y*z^2 + 4*x^2*y^2*z^2 + 4*x*y^3*z^2 - 6*y^4*z^2 + 5*x^3*z^3 - 2*x^2*y*z^3 + 3*x*y^2*z^3 + 3*y^3*z^3 + 4*x^2*z^4 - 6*x*y*z^4 - 2*y^2*z^4 - 7*x*z^5 + 2*z^6 - x^4*y + 435/17*x^3*y^2 - 3*x^2*y^3 - 5*x*y^4 - 7*y^5 - 7*x^4*z + 7*x^3*y*z + 7*x^2*y^2*z - 3*x*y^3*z - 2*x^3*z^2 - 4*x^2*y*z^2 + 4*x*y^2*z^2 + y^3*z^2 - 5*x^2*z^3 + 3*x*y*z^3 + 2*y^2*z^3 - x*z^4 - y*z^4 - 2*z^5 + 1975/289*x^3*y - 55/17*x^2*y^2 - x*y^3 - 2*y^4 + 6*x^3*z - 6*x^2*y*z + 7*x^2*z^2 - x*y*z^2 - 7*y^2*z^2 - 6*x*z^3 + 2*y*z^3 + 1825/1461*x^2*y - 6205/1461*x*y^2 - 365/2922*y^3 + 42559/5844*x^2*z + 4*x*y*z - 7*y^2*z + 6*x*z^2 + 5*y*z^2 + 2*z^3, -3*x^6 + x^5*y + 3*x^4*y^2 - 2*x^3*y^3 - 4*x^2*y^4 + 2*y^6 + 3*x^5*z - 4*x^4*y*z + 4*x^3*y^2*z + 5*x^2*y^3*z - x*y^4*z - 5*y^5*z - 4*x^4*z^2 - 6*x^3*y*z^2 + 6*x^2*y^2*z^2 - 7*x*y^3*z^2 + 7*y^4*z^2 + 4*x^3*z^3 - 3*x^2*y*z^3 - 3*x*y^2*z^3 + 5*y^3*z^3 - 2*x^2*z^4 + x*y*z^4 + 2*y^2*z^4 + 2*x*z^5 - 3*y*z^5 + 5*z^6 - 3*x^4*y - 205/17*x^3*y^2 + 7*x^2*y^3 - 7*x*y^4 + 2*y^5 + 7*x^4*z + 7*x^3*y*z - 4*x^2*y^2*z + 2*x*y^3*z - 2*y^4*z - 3*x^3*z^2 + 7*x^2*y*z^2 - 2*x*y^2*z^2 + 2*y^3*z^2 + x^2*z^3 + x*y*z^3 + 4*y^2*z^3 + 2*x*z^4 + 5*y*z^4 - 2*z^5 + 5350/289*x^3*y - 50/17*x^2*y^2 - 6*y^4 + 5*x^3*z - 3*x^2*y*z - 5*x*y^2*z - y^3*z + 6*x^2*z^2 - 7*y^2*z^2 + 6*x*z^3 + 4*y*z^3 - 6*z^4 + 1150/487*x^2*y - 3910/487*x*y^2 - 115/487*y^3 + 13409/974*x^2*z + 3*x*y*z - 6*y^2*z - 3*x*z^2 - 2*y*z^2 + 2*z^3]
  [ok] (A8) piece (alpha), l = -1: member closed with H, D_3 = N_3 (direct), in the piece; S6.2 triple of local length 34 <= 41 (ds = stabilization), explicit M_Q closed with H and the triple in Ann(M_Q); unsolvable B-systems: 0
      D_3 = [-53/40*X^2*Y + 1/2*X*Y*Z + 5/2*Y^2*Z - 15/4*X*Z^2 + 3/2*Y*Z^2 + Z^3, -11/20*X^2*Y + X^2*Z, 3/10*X^2*Y + Y^3, -X^2*Y + X*Y^2, X^3]
      triple: [4*x^6 + 7*x^5*y + 4*x^4*y^2 + 4*x^3*y^3 - 3*x^2*y^4 - 2*x*y^5 + 7*y^6 + 7*x^5*z - 2*x^4*y*z - x^3*y^2*z + 4*x^2*y^3*z + 7*x*y^4*z + 6*y^5*z + 5*x^4*z^2 + x^3*y*z^2 - 5*x^2*y^2*z^2 + 5*x*y^3*z^2 - 6*y^4*z^2 + 7*x^3*z^3 - x^2*y*z^3 - 2*x*y^2*z^3 - 6*y^3*z^3 - 7*x^2*z^4 - 4*x*y*z^4 - 3*y^2*z^4 - 6*x*z^5 - 4*y*z^5 + 4*z^6 + 6*x^4*y - 2*x^3*y^2 + 2*x^2*y^3 - 6*x*y^4 + y^5 - 7*x^4*z - x^3*y*z + 2*x^2*y^2*z + 6*x*y^3*z - 5*x^3*z^2 - 5*x^2*y*z^2 - 7*x*y^2*z^2 - 4*y^3*z^2 + 6*x*y*z^3 + 4*y^2*z^3 - 5*x*z^4 + 6*y*z^4 - 6*z^5 + 30*x^3*y - 10*x^2*y^2 + 2*x*y^3 + 4*y^4 - 6*x^3*z - x^2*y*z + x*y^2*z + 3*y^3*z - 4*x^2*z^2 - x*y*z^2 + 5*y^2*z^2 + 7*y*z^3 + 4*z^4 + 500/53*x^2*y + 500/53*x*y^2 - 50/53*y^3 + 275/53*x^2*z - 3*x*y*z + 2*y^2*z - x*z^2 - 3*y*z^2 + 3*z^3, 2*x^6 - 2*x^4*y^2 + 7*x^3*y^3 + 3*x^2*y^4 + x*y^5 + 6*y^6 - 3*x^5*z - x^4*y*z - x^3*y^2*z - 4*x^2*y^3*z + 6*x*y^4*z + 3*x^4*z^2 + x^3*y*z^2 - 3*x^2*y^2*z^2 - 4*x*y^3*z^2 - 7*y^4*z^2 + 7*x^3*z^3 - 5*x^2*y*z^3 + 3*x*y^2*z^3 - 4*y^3*z^3 - 3*x^2*z^4 - 6*x*y*z^4 + 5*y^2*z^4 + x*z^5 + 5*z^6 + 6*x^4*y - 65*x^3*y^2 + 3*x^2*y^3 - 6*y^5 - 4*x^4*z - 6*x^3*y*z - 3*x^2*y^2*z + 7*x*y^3*z - 5*y^4*z - x^3*z^2 - x^2*y*z^2 + 3*x*y^2*z^2 - 4*y^3*z^2 - 7*x^2*z^3 + 4*y^2*z^3 - 7*x*z^4 - 6*y*z^4 - 5*z^5 + 62*x^3*y + 12*x^2*y^2 + 6*x*y^3 + 5*y^4 + 3*x^3*z + 4*x^2*y*z - 6*x*y^2*z - 2*y^3*z - x^2*z^2 + 3*x*y*z^2 + 4*y^2*z^2 - 5*x*z^3 - 3*y*z^3 + 6*z^4 - 1340/53*x^2*y - 1340/53*x*y^2 + 134/53*y^3 - 737/53*x^2*z + 6*x*y*z - 2*y^2*z - 6*y*z^2 - 7*z^3, -4*x^6 + 4*x^5*y - 6*x^4*y^2 - 7*x^3*y^3 - x^2*y^4 - 4*x*y^5 - 5*y^6 + 3*x^5*z + 7*x^4*y*z + 4*x^3*y^2*z + 7*x^2*y^3*z + x*y^4*z + 5*x^4*z^2 - x^2*y^2*z^2 - 4*x*y^3*z^2 + y^4*z^2 + 3*x^3*z^3 - 5*x^2*y*z^3 + 5*x*y^2*z^3 + 5*x^2*z^4 - 6*x*y*z^4 - 6*y^2*z^4 + 4*x*z^5 + 2*y*z^5 - 3*z^6 - 7*x^4*y + 33*x^3*y^2 - 5*x^2*y^3 + 7*x*y^4 + 5*y^5 - 6*x^4*z - x^3*y*z + 7*x^2*y^2*z + 7*x*y^3*z + 7*y^4*z - 4*x^3*z^2 - 6*x*y^2*z^2 - 5*y^3*z^2 + 3*x^2*z^3 + 3*x*y*z^3 - 5*y^2*z^3 + 6*x*z^4 + y*z^4 - 4*z^5 - 5*x^3*y + 5*x^2*y^2 + 5*x*y^3 - y^4 + 2*x^2*y*z + 4*x*y^2*z - 7*x^2*z^2 + 2*x*y*z^2 - 6*y^2*z^2 - 4*x*z^3 - 4*y*z^3 + 6*z^4 - 690/53*x^2*y - 690/53*x*y^2 + 69/53*y^3 - 759/106*x^2*z + x*y*z - 4*y^2*z + y*z^2 - 3*z^3]
  [ok] (A8) piece (beta), l = 17/5: member closed with H, D_3 = N_3 (direct), in the piece; S6.2 triple of local length 34 <= 41 (ds = stabilization), explicit M_Q closed with H and the triple in Ann(M_Q); unsolvable B-systems: 0
      D_3 = [1359/400*X^2*Y + 10/3*X*Y*Z + 16/3*Y^2*Z + 5/4*X*Z^2 + 4*Y*Z^2 + Z^3, -583/100*X^2*Y + X^2*Z, 3/10*X^2*Y + Y^3, 17/5*X^2*Y + X*Y^2, X^3]
      triple: [7*x^6 + 2*x^5*y - 7*x^4*y^2 - x^3*y^3 + 4*x^2*y^4 - 3*x*y^5 + y^6 - 7*x^5*z - 6*x^3*y^2*z - 5*x^2*y^3*z - 6*x*y^4*z + 7*y^5*z - x^4*z^2 + 4*x^3*y*z^2 - 5*x^2*y^2*z^2 - 4*y^4*z^2 + 6*x^3*z^3 - 4*x^2*y*z^3 + 3*x*y^2*z^3 - 3*y^3*z^3 - 3*x^2*z^4 - 7*x*y*z^4 + 7*y^2*z^4 + 7*x*z^5 - 3*y*z^5 - 6*z^6 + 2*x^4*y + 10*x^3*y^2 + 6*x^2*y^3 - 2*x*y^4 - 4*y^5 - 4*x^3*y*z - 2*x^2*y^2*z - 4*x*y^3*z - y^4*z + 3*x^3*z^2 - 6*x^2*y*z^2 - 2*x*y^2*z^2 + y^3*z^2 + 6*x^2*z^3 + 4*x*y*z^3 - y^2*z^3 - 7*y*z^4 - 4*z^5 - 1300/289*x^3*y + 90/17*x^2*y^2 - 4*x*y^3 + y^4 - 7*x^3*z - 5*x*y^2*z + 2*y^3*z + 4*x^2*z^2 - 7*x*y*z^2 - 5*y^2*z^2 + 2*x*z^3 - 4*y*z^3 - 2*z^4 + 2900/453*x^2*y - 9860/453*x*y^2 - 290/453*y^3 + 16907/453*x^2*z - 7*x*z^2 - 7*y*z^2 + 5*z^3, -7*x^6 - 6*x^4*y^2 - 3*x^3*y^3 - 5*x^2*y^4 - 6*x*y^5 - 6*y^6 + 2*x^5*z + 6*x^4*y*z - 4*x^3*y^2*z + 2*x^2*y^3*z + 4*x*y^4*z + 4*y^5*z - 7*x^4*z^2 - 2*x^3*y*z^2 - 5*x^2*y^2*z^2 + 5*x*y^3*z^2 - 2*y^4*z^2 + 2*x^3*z^3 + 6*x^2*y*z^3 + 6*x*y^2*z^3 - 4*y^3*z^3 - 5*x^2*z^4 - x*y*z^4 + 5*y^2*z^4 - 4*x*z^5 + 5*y*z^5 + 4*z^6 - x^4*y - 45/17*x^3*y^2 + 7*x^2*y^3 + x*y^4 + x^4*z + 4*x^3*y*z - 5*x^2*y^2*z + 2*x*y^3*z + 5*y^4*z + 4*x^3*z^2 - 2*x^2*y*z^2 + x*y^2*z^2 - 6*y^3*z^2 - 5*x^2*z^3 - y^2*z^3 + 5*y*z^4 + 5*z^5 - 3350/289*x^3*y - 10/17*x^2*y^2 - 4*x*y^3 + 4*y^4 + 3*x^3*z - 6*x^2*y*z + 2*x*y^2*z - y^3*z + 2*x*y*z^2 + 6*y^2*z^2 - 3*x*z^3 - 6*y*z^3 + 7*z^4 - 12800/4077*x^2*y + 43520/4077*x*y^2 + 1280/4077*y^3 - 74624/4077*x^2*z + 3*x*y*z + 2*y^2*z + 4*x*z^2 - y*z^2 - 2*z^3, 2*x^6 - 6*x^5*y - 2*x^3*y^3 + 7*x^2*y^4 - 3*x*y^5 - 5*y^6 - 3*x^5*z + 7*x^4*y*z + 6*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 - 4*x^3*y*z^2 - 6*x^2*y^2*z^2 - 5*x*y^3*z^2 - 5*y^4*z^2 + x^3*z^3 + 7*x^2*y*z^3 + x*y^2*z^3 + 6*y^3*z^3 + 5*x^2*z^4 - 2*x*y*z^4 + 5*y^2*z^4 + x*z^5 + 4*y*z^5 + 5*z^6 - x^4*y - 280/17*x^3*y^2 - 4*x^2*y^3 - 7*x*y^4 + 7*y^5 - 5*x^4*z - 4*x^3*y*z + 7*x^2*y^2*z + 6*x*y^3*z + 7*y^4*z - 7*x^3*z^2 - x^2*y*z^2 + 5*x*y^2*z^2 + 4*y^3*z^2 - 2*x^2*z^3 - x*y*z^3 - 4*y^2*z^3 + 7*x*z^4 - 7*y*z^4 - z^5 + 100/289*x^3*y - 20/17*x^2*y^2 + 2*x*y^3 + x^3*z + 5*x^2*y*z - 7*x*y^2*z + 5*y^3*z + 5*x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 - 7*y*z^3 - 6*z^4 - 1000/4077*x^2*y + 3400/4077*x*y^2 + 100/4077*y^3 - 5830/4077*x^2*z + 4*x*y*z + 2*y^2*z - 6*x*z^2 - 3*y*z^2 + z^3]
  [ok] (A8) piece (beta), l = -1: member closed with H, D_3 = N_3 (direct), in the piece; S6.2 triple of local length 34 <= 41 (ds = stabilization), explicit M_Q closed with H and the triple in Ann(M_Q); unsolvable B-systems: 0
      D_3 = [-3*X*Y*Z + 27*Y^2*Z + 1/2*X*Z^2 - 9*Y*Z^2 + Z^3, -11/20*X^2*Y + X^2*Z, 3/10*X^2*Y + Y^3, -X^2*Y + X*Y^2, X^3]
      triple: [-x^6 - 6*x^5*y - 4*x^4*y^2 - 6*x^3*y^3 - 5*x^2*y^4 + 4*x*y^5 - 2*y^6 + 2*x^5*z - 4*x^4*y*z - 3*x^3*y^2*z - 6*x^2*y^3*z - 3*x*y^4*z + 6*y^5*z + 6*x^4*z^2 - 5*x^3*y*z^2 + 7*x^2*y^2*z^2 + 3*x*y^3*z^2 + 7*y^4*z^2 - 5*x^3*z^3 - 3*x^2*y*z^3 + 4*x*y^2*z^3 + 6*y^3*z^3 - 6*x^2*z^4 - 5*x*y*z^4 + y^2*z^4 - 7*x*z^5 + 6*y*z^5 + z^6 - 4*x^4*y + 46*x^3*y^2 + 3*x*y^4 + 5*y^5 - 2*x^4*z + 2*x^3*y*z - 6*x^2*y^2*z - 3*x*y^3*z + y^4*z + 5*x^3*z^2 + 7*x^2*y*z^2 + 5*y^3*z^2 - 2*x^2*z^3 - 6*x*y*z^3 + 6*y^2*z^3 + 3*x*z^4 + y*z^4 + 4*z^5 - 15*x^3*y + 15*x^2*y^2 + 3*x*y^3 - 3*y^4 + 6*x^3*z + 7*x^2*y*z - x*y^2*z - 5*y^3*z - 5*x^2*z^2 - 2*x*y*z^2 + 6*y^2*z^2 - 232/3*x*y*z - 4*y^2*z - 4*x*z^2 + 2*y*z^2 + 4*z^3, 6*x^6 - 2*x^5*y - 7*x^4*y^2 + 6*x^3*y^3 - 5*x^2*y^4 + 6*x*y^5 + y^6 + 2*x^5*z + 3*x^4*y*z - x^3*y^2*z - 4*x^2*y^3*z - 6*x*y^4*z + 7*y^5*z + 2*x^4*z^2 + 2*x^3*y*z^2 - 5*x^2*y^2*z^2 + 2*x*y^3*z^2 + 6*y^4*z^2 - 7*x^3*z^3 - 5*x^2*y*z^3 - 7*x*y^2*z^3 + 2*y^3*z^3 + 2*x^2*z^4 - 5*x*y*z^4 - 5*y^2*z^4 - 4*x*z^5 + 6*y*z^5 + 4*z^6 - 35*x^3*y^2 + 5*x^2*y^3 + 3*x*y^4 - 3*y^5 - 5*x^4*z + 3*x^3*y*z + x^2*y^2*z + 7*x*y^3*z - 7*y^4*z + 4*x^3*z^2 - 2*x^2*y*z^2 - 2*x*y^2*z^2 + 5*y^3*z^2 + 2*x*y*z^3 - 5*y^2*z^3 - 2*x*z^4 + 3*y*z^4 - 2*z^5 - 37*x^3*y + 3*x^2*y^2 + 3*x*y^3 - 4*y^4 + 5*x^2*y*z - x*y^2*z - 4*y^3*z - 5*x^2*z^2 + 5*x*y*z^2 - 4*y^2*z^2 - 4*x*z^3 - 20/11*x^2*y - 20/11*x*y^2 + 2/11*y^3 - x^2*z + 51*x*y*z + 4*y^2*z + 3*x*z^2 + 3*y*z^2 - 2*z^3, 5*x^6 - x^5*y + 2*x^4*y^2 - 4*x^2*y^4 + 7*y^6 - x^5*z + 7*x^4*y*z - 7*x^3*y^2*z - 7*x^2*y^3*z + 5*x*y^4*z + 3*y^5*z - 6*x^4*z^2 + 2*x^3*y*z^2 - 7*x^2*y^2*z^2 - 7*x*y^3*z^2 - y^4*z^2 + 3*x^3*z^3 - x^2*y*z^3 + 7*x*y^2*z^3 + 7*y^3*z^3 + 4*x^2*z^4 - 5*x*y*z^4 + y^2*z^4 + 7*x*z^5 - 4*y*z^5 + 3*z^6 + 67*x^3*y^2 + 7*x^2*y^3 - 2*x*y^4 + 6*y^5 - 3*x^3*y*z + x^2*y^2*z + 7*x*y^3*z + 7*y^4*z + 3*x^3*z^2 + 6*x^2*y*z^2 - 4*x*y^2*z^2 - 4*y^3*z^2 + 5*x^2*z^3 - 4*x*y*z^3 - 5*y^2*z^3 + 7*x*z^4 + 7*y*z^4 + 4*z^5 + 34*x^3*y - 6*x^2*y^2 + 2*x*y^3 + 4*y^4 - 4*x^3*z + 3*x^2*y*z - 2*x*y^2*z + 6*y^3*z + 5*x^2*z^2 + 2*x*y*z^2 + 7*y^2*z^2 + 5*x*z^3 - 6*y*z^3 + 5*z^4 - 140/11*x^2*y - 140/11*x*y^2 + 14/11*y^3 - 7*x^2*z - 117*x*y*z - 6*y^2*z - 3*x*z^2 - 4*z^3]
(S9) actual algebras of the line stratum (D_3 = C[X,Y]_3 + C X^2Z) with random tails
  [info] l = 17/5: gauge A = -3 X^4Y + -6 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = 17/5: gauge A = -3 X^4Y + 0 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = 17/5: gauge A = -2 X^4Y + -3 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = 0: gauge A = 5 X^4Y + 5 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = 0: gauge A = -5 X^4Y + -5 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = 0: gauge A = 4 X^4Y + -9 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = -2: gauge A = -2 X^4Y + -1 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = -2: gauge A = -2 X^4Y + -1 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = -2: gauge A = -5 X^4Y + 7 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = 1: gauge A = -5 X^4Y + 2 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = 1: gauge A = 3 X^4Y + -2 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [info] l = 1: gauge A = 1 X^4Y + -1 X^4Z; kind beta; presentation reproduces M: True; N_3 formula = direct: True
  [ok] (S9) 12 actual algebras of the line stratum: presentation, N_3 formula and piece membership confirmed (kinds {'alpha': 0, 'beta': 12, 'notN': 0})
(S10) line-stratum members of both pieces, built from the family
  [ok] (S10) l = 17/5, piece (alpha): 4 of 4 family members built on the line stratum are closed with H and D_3 = N_3 = C[X,Y]_3 + C X^2Z
  [ok] (S10) l = 17/5, piece (beta): 4 of 4 family members built on the line stratum are closed with H and D_3 = N_3 = C[X,Y]_3 + C X^2Z
  [ok] (S10) l = 0, piece (alpha): 4 of 4 family members built on the line stratum are closed with H and D_3 = N_3 = C[X,Y]_3 + C X^2Z
  [ok] (S10) l = 0, piece (beta): 4 of 4 family members built on the line stratum are closed with H and D_3 = N_3 = C[X,Y]_3 + C X^2Z
  [ok] (S10) l = -2, piece (alpha): 4 of 4 family members built on the line stratum are closed with H and D_3 = N_3 = C[X,Y]_3 + C X^2Z
  [ok] (S10) l = -2, piece (beta): 4 of 4 family members built on the line stratum are closed with H and D_3 = N_3 = C[X,Y]_3 + C X^2Z
18 checks, 0 failed
ALL CHECKS PASSED
