Part U0 (U): structure of the cube branch
  ok   k = 3: {F in T_k : I*_3 o F = 0} = <Y^k, Y^(k-1)Z, Y^(k-2)Z^2, XY^(k-1)> (dim 4)
  ok   k = 4: {F in T_k : I*_3 o F = 0} = <Y^k, Y^(k-1)Z, Y^(k-2)Z^2, XY^(k-1)> (dim 4)
  ok   k = 5: {F in T_k : I*_3 o F = 0} = <Y^k, Y^(k-1)Z, Y^(k-2)Z^2, XY^(k-1)> (dim 4)
  ok   k = 6: {F in T_k : I*_3 o F = 0} = <Y^k, Y^(k-1)Z, Y^(k-2)Z^2, XY^(k-1)> (dim 4)
  ok   k = 7: {F in T_k : I*_3 o F = 0} = <Y^k, Y^(k-1)Z, Y^(k-2)Z^2, XY^(k-1)> (dim 4)
  ok   the substitution y -> y + a z maps I*_3 into itself
  ok   the substitution z -> b z maps I*_3 into itself
  ok   the substitution y -> y + a x maps I*_3 into itself
  ok   the substitution x -> b x maps I*_3 into itself
  ok   the substitution z -> z + a x maps I*_3 into itself
  ok   the substitution y -> b y maps I*_3 into itself
  ok   control: x -> x + a y does not map I*_3 into itself
  ok   dual action: y -> y + az  <->  Z -> Z + aY;  y -> y + ax  <->  X -> X + aY;  z -> z + ax  <->  X -> X + aZ
  ok   X -> X + alpha Z maps Y^4(aX + bZ) to Y^4(aX + (a alpha + b)Z): tangent out after alpha = -b/a
  ok   tangent in (D_6 = <Y^6, Y^5Z>): S_1 o F in D_6 iff C = E = 0
  ok   tangent out (D_6 = <Y^6, XY^5>): S_1 o F in D_6 iff B = C = 0
  ok   Z -> Z + aY: A Y^7 + B Y^6Z -> (A + aB) Y^7 + B Y^6Z;  X -> X + aY: A Y^7 + E XY^6 -> (A + aE) Y^7 + E XY^6
Part UF (U): Lemma F, step 3, and the operator y^5 for the heads Y^7, XY^6
  ok   x^2 o Xi = R, eps(x^2 rho) = <rho, R> for all rho in S_2 (R symbolic)
  ok   for every cubic monomial w not divisible by x^2: eps(x w) = <w, X R_0>, eps(y w) = eps(z w) = 0 (R symbolic)
  ok   y^5 o (Y^7 + P6 + P5 + P4) = 2520*Y^2 + T_{<=1} (all tails symbolic); y^5 o (generic sextic) in T_{<=1}
  ok   y^5 o (XY^6 + P6 + P5 + P4) = 720*X*Y + T_{<=1} (all tails symbolic); y^5 o (generic sextic) in T_{<=1}
  ok   contractions: y^3*z o Y^6*Z = 120*Y^3, y^4 o Y^6*Z = 360*Y^2*Z, y^5 o Y^6*Z = 720*Y*Z, y^4*z o Y^6*Z = 360*Y^2, z^3 o Y*Z^4 = 24*Y*Z, x*y*z o X*Y^2*Z^2 = 4*Y*Z, z^3 o Y^3*Z^3 = 6*Y^3, z^3 o Y^2*Z^4 = 24*Y^2*Z, y^5 o Y^7 = 2520*Y^2, y^5 o X*Y^6 = 720*X*Y, x^2 o X^2*Y^3 = 2*Y^3, y*z o Y^6*Z = 6*Y^5, y^2 o Y^6*Z = 30*Y^4*Z, z o Y^6*Z = Y^6, y o Y^6*Z = 6*Y^5*Z
Part UY (U): the head Y^6 Z, all tails symbolic
  ok   P6: {x o P6 in <Y^5, Y^4Z>, z^2 o P6 in <Y^4, Y^3Z, Y^2Z^2, XY^3>} = span of X Y^5, X Y^4 Z, Y^6, Y^5 Z, Y^4 Z^2, Y^3 Z^3, Y^2 Z^4
  ok   P6: the condition z^2 o P6 in C(uY^2Z^2 + vXY^3) + <Y^4, Y^3Z> is 12 v eps = 0 on that span (eps = [Y^2Z^4]P6)
  ok   shear x -> x + a yz + b y^2: degree 7 kept, degree 6 becomes P6 + X(6a Y^5 + 30b Y^4 Z) (tails symbolic)
  ok   shear z -> z + c y^2: degree 7 kept, degree 6 becomes P6 + 30c Y^4 Z^2 (tails symbolic)
  ok   gauge Phi - a (z o Phi) - (b/6)(y o Phi): degree 6 becomes P6 - a Y^6 - b Y^5 Z
  ok   step 2: [Y^3] deg_3(g0 o Phi) = 6 delta + 120 [y^3z]g0_4,  [Y^2Z] = 24 eps + 360 [y^4]g0_4 (P6 of the step-1 shape, all tails symbolic)
  ok   P5: {x o P5 in <Y^4, Y^3Z, Y^2Z^2, XY^3>, z^2 o P5 in D_3} = span of XY^4, XY^3Z, XY^2Z^2, X^2Y^3 and the binary quintics without Z^5
  ok   P5: the D_4 condition on that span is v [XY^2Z^2]P5 - 2u [X^2Y^3]P5 = 0, i.e. ([XY^2Z^2], [X^2Y^3]) = C (u, v/2)
  ok   step 3: deg_4(f o Phi) = 0 identically; [Y^3] deg_3 = Cv + 120 [y^3z]f_4, [Y^2Z] deg_3 = 360 [y^4]f_4 (P6 = 0, tails symbolic)
  ok   step 4: [YZ] deg_2(g0 o Phi) = 24 f' + 720 [y^5]g0_5, f' = [YZ^4]B5 (P6 = 0, tails symbolic)
  ok   step 6: deg_3(g1 o Phi) = 360 [y^4]g1_4 Y^2Z + 120 [y^3z]g1_4 Y^3, [YZ] deg_2 = 4Cu + 720 [y^5]g1_5 (u, v symbolic)
  ok   step 5: V = xy^2 - (A/30) y^4 z - (B/120) y^5 has V o Phi, V o (z o Phi), V o (y o Phi), V o (D_5-lift) in T_{<=1} (C = 0, tails symbolic)
  ok   step 5 control: with C != 0, V o Phi has quadratic part 2Cu Z^2 + 6Cv XY... (not in T_{<=1})
  ok   split: xi = -L2/2 + O(3); g_3 = alpha z^3; [y^4]g = [y^4]f_4 - k^2/4; [y^3z]g = [y^3z]f_4 - k l/2 (all coefficients symbolic)
  ok   split with k = 0: xi(y, 0) = O(y^3) and [y^5]g = [y^5]f_5 (all other coefficients symbolic)
  ok   split(f + t y^5) = split(f) + t y^5 modulo m^6 (d_x y^5 = 0)
  ok   split(f + t x y^2): [y^4] = [y^4]f_4 - (k + t)^2/4 (leading term -t^2/4: [15, Lemma F.4])
Part F (S): the Lemma F family (u = y^5) for the heads Y^7 (tangent in, out) and XY^6
  ok   Y^7 in, E4 = Y^2Z^2 [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 in, E4 = Y^2Z^2 [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 in, E4 = Y^2Z^2 [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 in, E4 = Y^2Z^2 [tails]: split of f (cube coefficient -1/9): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 in, E4 = XY^3 [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 in, E4 = XY^3 [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 in, E4 = XY^3 [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 in, E4 = XY^3 [tails]: split of f (cube coefficient -1/6): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 in, E4 = Y^2Z^2 + XY^3 [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 in, E4 = Y^2Z^2 + XY^3 [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 in, E4 = Y^2Z^2 + XY^3 [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 in, E4 = Y^2Z^2 + XY^3 [tails]: split of f (cube coefficient -1/2): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 out, E4 = Y^3Z [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 out, E4 = Y^3Z [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 out, E4 = Y^3Z [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 out, E4 = Y^3Z [tails]: split of f (cube coefficient 59/105): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 out, E4 = Y^2Z^2 [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 out, E4 = Y^2Z^2 [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 out, E4 = Y^2Z^2 [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 out, E4 = Y^2Z^2 [tails]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 out, E4 = Y^2Z^2 - Y^3Z [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 out, E4 = Y^2Z^2 - Y^3Z [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 out, E4 = Y^2Z^2 - Y^3Z [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 out, E4 = Y^2Z^2 - Y^3Z [tails]: split of f (cube coefficient 2/3): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   XY^6, E4 = Y^3Z [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C X*Y: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   XY^6, E4 = Y^3Z [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   XY^6, E4 = Y^3Z [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C X*Y: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   XY^6, E4 = Y^3Z [tails]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   XY^6, E4 = Y^2Z^2 [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C X*Y: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   XY^6, E4 = Y^2Z^2 [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   XY^6, E4 = Y^2Z^2 [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C X*Y: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   XY^6, E4 = Y^2Z^2 [tails]: split of f (cube coefficient -2/9): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   XY^6, E4 = Y^2Z^2 + Y^3Z [graded]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C X*Y: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   XY^6, E4 = Y^2Z^2 + Y^3Z [graded]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 0 -> predicted E8; mu(f + 3 y^5) = 8
  ok   XY^6, E4 = Y^2Z^2 + Y^3Z [tails]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C X*Y: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   XY^6, E4 = Y^2Z^2 + Y^3Z [tails]: split of f (cube coefficient 1): [y^4] = 0, [y^3z] = 0, [y^5] = 1/60 -> predicted E8; mu(f + 3 y^5) = 8
  ok   Y^7 - 420 X^2Y^3 out (x^2 + y^4 in I), E4 = Y^3Z [fixed]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 - 420 X^2Y^3 out (x^2 + y^4 in I), E4 = Y^3Z [fixed]: split of f (cube coefficient 1): [y^4] = 1, [y^3z] = 0, [y^5] = 0 -> predicted E6; mu(f + 3 y^5) = 6
  ok   Y^7 - 420 X^2Y^3 out (x^2 + y^4 in I), E4 = Y^3Z [sheared]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 - 420 X^2Y^3 out (x^2 + y^4 in I), E4 = Y^3Z [sheared]: split of f (cube coefficient 1): [y^4] = 1, [y^3z] = 0, [y^5] = 0 -> predicted E6; mu(f + 3 y^5) = 6
  ok   Y^7 in, E4 = Y^2Z^2, lift XY^2 - X^2 (k = 1) [fixed]: H ok, cube branch True; u = y^5 has u o M in T_<=1 + C Y^2: True; dim I, I cap m^4, ker eps, K (mod m^8) = (99, 92, 91, 94); family at t = 0, 3, -2: span closed (ideal), colength 21, contains f + t y^5: True; I_0 = I: True
  ok   Y^7 in, E4 = Y^2Z^2, lift XY^2 - X^2 (k = 1) [fixed]: split of f (cube coefficient 1): [y^4] = -1/4, [y^3z] = 0, [y^5] = 0 -> predicted E6; mu(f + 3 y^5) = 6
    (Y^7 in, E4 = Y^2Z^2, lift XY^2 - X^2 (k = 1) [tails]: the random tails changed the graded data; sample not counted)
  ok   Part F: 21 accepted algebras; cases {'E8': 18, 'E6': 3}
Part Y (S): the head Y^6 Z (tangent in): normalization, the step that applies, the E-type on actual equations
  ok   graded, E4 = Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    graded, E4 = Y^2*Z^2 [fixed]: A = 0, B = 0, C = 0, f' = 0, k = 0
  ok   graded, E4 = Y^2*Z^2 [fixed]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, 0, 0) -> E6: True; mu = 6
  ok   graded, E4 = Y^2*Z^2 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    graded, E4 = Y^2*Z^2 [tails]: A = 0, B = 0, C = 0, f' = 0, k = 0
  ok   graded, E4 = Y^2*Z^2 [tails]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, 0, 0) -> E6: True; mu = 6
  ok   graded, E4 = X*Y^3 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    graded, E4 = X*Y^3 [fixed]: A = 0, B = 0, C = 0, f' = 0, k = 0
  ok   graded, E4 = X*Y^3 [fixed]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, 0, 0) -> E6: True; mu = 6
  ok   graded, E4 = X*Y^3 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    graded, E4 = X*Y^3 [tails]: A = 0, B = 0, C = 0, f' = 0, k = 0
  ok   graded, E4 = X*Y^3 [tails]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, 0, 0) -> E6: True; mu = 6
  ok   graded, E4 = X*Y^3 + Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3 + Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    graded, E4 = X*Y^3 + Y^2*Z^2 [fixed]: A = 0, B = 0, C = 0, f' = 0, k = 0
  ok   graded, E4 = X*Y^3 + Y^2*Z^2 [fixed]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, 0, 0) -> E6: True; mu = 6
  ok   graded, E4 = X*Y^3 + Y^2*Z^2 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, 15/13*X*Y^3 + Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 1/30) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    graded, E4 = X*Y^3 + Y^2*Z^2 [tails]: A = 0, B = 0, C = 0, f' = 0, k = 0
  ok   graded, E4 = X*Y^3 + Y^2*Z^2 [tails]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, 0, 9541/4050) -> E6: True; mu = 6
  ok   eps: Y^6Z + Y^2Z^4, E4 = Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 1; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
  ok   eps: Y^6Z + Y^2Z^4, E4 = Y^2*Z^2 [fixed]: step 2 (E6); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, -8/15, 0, 0) -> E6: True; mu = 6
  ok   eps: Y^6Z + Y^2Z^4, E4 = Y^2*Z^2 [sheared]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (-2, 1, -3) ([16, Lemma B.4] checked: True): delta = 0, eps = 1; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
  ok   eps: Y^6Z + Y^2Z^4, E4 = Y^2*Z^2 [sheared]: step 2 (E6); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, -8/15, 0, 0) -> E6: True; mu = 6
  ok   eps: Y^6Z + Y^2Z^4, E4 = Y^2*Z^2 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    eps: Y^6Z + Y^2Z^4, E4 = Y^2*Z^2 [tails]: A = 0, B = -2, C = 0, f' = 3, k = 0
  ok   eps: Y^6Z + Y^2Z^4, E4 = Y^2*Z^2 [tails]: step 4 (f' != 0, E8); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, 0, -4/5) -> E8: True; mu = 8
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 1, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = Y^2*Z^2 [fixed]: step 2 (E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, -2/5, 0) -> E7: True; mu = 7
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = Y^2*Z^2 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 1, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = Y^2*Z^2 [tails]: step 2 (E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (83/9, 0, -83/180, -63/3200) -> E7: True; mu = 7
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = X*Y^3 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 1, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = X*Y^3 [fixed]: step 2 (E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, -2/5, 0) -> E7: True; mu = 7
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = X*Y^3 [sheared]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (-2, 1, -3) ([16, Lemma B.4] checked: True): delta = 1, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = X*Y^3 [sheared]: step 2 (E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, -2/5, 0) -> E7: True; mu = 7
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = X*Y^3 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, 1/3*X*Y^3 + Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, -1/15) ([16, Lemma B.4] checked: True): delta = 1, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
  ok   delta: Y^6Z + Y^3Z^3 + 3/200 Z^5, E4 = X*Y^3 [tails]: step 2 (E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, -2/5, 0) -> E7: True; mu = 7
  ok   k: lift XY^2 - X^2, E4 = Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    k: lift XY^2 - X^2, E4 = Y^2*Z^2 [fixed]: A = 0, B = 0, C = 0, f' = 0, k = 1
  ok   k: lift XY^2 - X^2, E4 = Y^2*Z^2 [fixed]: step 3 (k != 0, E6); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -1/4, 0, 0) -> E6: True; mu = 6
  ok   k: lift XY^2 - X^2, E4 = Y^2*Z^2 [sheared]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (-2, 1, -3) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    k: lift XY^2 - X^2, E4 = Y^2*Z^2 [sheared]: A = 0, B = -720, C = 0, f' = 0, k = 1
  ok   k: lift XY^2 - X^2, E4 = Y^2*Z^2 [sheared]: step 3 (k != 0, E6); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -1/4, 0, 3) -> E6: True; mu = 6
  ok   k: lift XY^3 - X^2Y of E4, E4 = X*Y^3 - X^2*Y [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    k: lift XY^3 - X^2Y of E4, E4 = X*Y^3 - X^2*Y [fixed]: A = 0, B = 0, C = 0, f' = 0, k = 1/3
  ok   k: lift XY^3 - X^2Y of E4, E4 = X*Y^3 - X^2*Y [fixed]: step 3 (k != 0, E6); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -1/36, 0, 0) -> E6: True; mu = 6
  ok   k: lift Y^2Z^2 + XY^3 - X^2Y of E4, E4 = X*Y^3 + Y^2*Z^2 - X^2*Y [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3 + Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    k: lift Y^2Z^2 + XY^3 - X^2Y of E4, E4 = X*Y^3 + Y^2*Z^2 - X^2*Y [fixed]: A = 0, B = 0, C = 0, f' = 0, k = 1/3
  ok   k: lift Y^2Z^2 + XY^3 - X^2Y of E4, E4 = X*Y^3 + Y^2*Z^2 - X^2*Y [fixed]: step 3 (k != 0, E6); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -1/36, 0, 0) -> E6: True; mu = 6
  ok   Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [fixed]: A = 0, B = 0, C = 1, f' = 0, k = 0
  ok   Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [fixed]: step 3 (Cv != 0, E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, 0, -1/120, 0) -> E7: True; mu = 7
  ok   Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [sheared]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (-2, 1, -3) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [sheared]: A = 0, B = -720, C = 1, f' = 0, k = 0
  ok   Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [sheared]: step 3 (Cv != 0, E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, 0, -1/120, 0) -> E7: True; mu = 7
  ok   Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [tails]: A = 0, B = 0, C = 1, f' = 0, k = 0
  ok   Cv: Y^6Z + X^2Y^3/2, E4 = X*Y^3 [tails]: step 3 (Cv != 0, E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, 0, -1/120, 0) -> E7: True; mu = 7
  ok   Cv: Y^6Z + XY^2Z^2 + X^2Y^3/2, E4 = X*Y^3 + Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3 + Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    Cv: Y^6Z + XY^2Z^2 + X^2Y^3/2, E4 = X*Y^3 + Y^2*Z^2 [fixed]: A = 0, B = 0, C = 1, f' = 0, k = 0
  ok   Cv: Y^6Z + XY^2Z^2 + X^2Y^3/2, E4 = X*Y^3 + Y^2*Z^2 [fixed]: step 3 (Cv != 0, E7); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, 0, -1/120, 0) -> E7: True; mu = 7
  ok   f': Y^6Z + YZ^4, E4 = X*Y^3 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    f': Y^6Z + YZ^4, E4 = X*Y^3 [fixed]: A = 0, B = 0, C = 0, f' = 1, k = 0
  ok   f': Y^6Z + YZ^4, E4 = X*Y^3 [fixed]: step 4 (f' != 0, E8); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, 0, -4/15) -> E8: True; mu = 8
  ok   f': Y^6Z + YZ^4, E4 = X*Y^3 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 1/15) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    f': Y^6Z + YZ^4, E4 = X*Y^3 [tails]: A = 0, B = 1, C = 0, f' = 1, k = 0
  ok   f': Y^6Z + YZ^4, E4 = X*Y^3 [tails]: step 4 (f' != 0, E8); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, 0, -4/15) -> E8: True; mu = 8
  ok   f': Y^6Z + YZ^4 + XY^4, E4 = Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    f': Y^6Z + YZ^4 + XY^4, E4 = Y^2*Z^2 [fixed]: A = 1, B = 0, C = 0, f' = 1, k = 0
  ok   f': Y^6Z + YZ^4 + XY^4, E4 = Y^2*Z^2 [fixed]: step 4 (f' != 0, E8); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, 0, -4/15) -> E8: True; mu = 8
  ok   f': Y^6Z + YZ^4 + XY^4, E4 = Y^2*Z^2 [sheared]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (-2, 1, -3) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    f': Y^6Z + YZ^4 + XY^4, E4 = Y^2*Z^2 [sheared]: A = 1, B = -720, C = 0, f' = 1, k = 0
  ok   f': Y^6Z + YZ^4 + XY^4, E4 = Y^2*Z^2 [sheared]: step 4 (f' != 0, E8); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (8, 0, 0, -4/15) -> E8: True; mu = 8
  ok   C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [fixed]: A = 0, B = 0, C = 1, f' = 0, k = 0
  ok   C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [fixed]: step 6 (C != 0, v = 0, E8 for f + c g0 + t g1); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, 0, 0, -7/180) -> E8: True; mu = 8
  ok   C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [sheared]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (-2, 1, -3) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [sheared]: A = 0, B = -720, C = 1, f' = 0, k = 0
  ok   C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [sheared]: step 6 (C != 0, v = 0, E8 for f + c g0 + t g1); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, 0, 0, -7/180) -> E8: True; mu = 8
  ok   C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [tails]: A = 0, B = 0, C = 1, f' = 0, k = 0
  ok   C, v = 0: Y^6Z + XY^2Z^2, E4 = Y^2*Z^2 [tails]: step 6 (C != 0, v = 0, E8 for f + c g0 + t g1); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1/3, 0, 0, -7/180) -> E8: True; mu = 8
  ok   C, v = 0: Y^6Z + XY^2Z^2 + XY^3Z + Y^3Z^2, E4 = Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    C, v = 0: Y^6Z + XY^2Z^2 + XY^3Z + Y^3Z^2, E4 = Y^2*Z^2 [fixed]: A = 0, B = 1, C = 1, f' = 0, k = 0
  ok   C, v = 0: Y^6Z + XY^2Z^2 + XY^3Z + Y^3Z^2, E4 = Y^2*Z^2 [fixed]: step 6 (C != 0, v = 0, E8 for f + c g0 + t g1); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, 0, 0, -7/180) -> E8: True; mu = 8
  ok   C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [fixed]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3 + Y^2*Z^2>) True; normalized by shears (a, b, c) = (0, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [fixed]: A = 1, B = 1, C = 0, f' = 0, k = 0
  ok   C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [fixed]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, 0, -7/120) -> E6: True; mu = 6
  ok   C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [sheared]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, X*Y^3 + Y^2*Z^2>) True; normalized by shears (a, b, c) = (-2, 1, -3) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [sheared]: A = 1, B = -719, C = 0, f' = 0, k = 0
  ok   C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [sheared]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, 0, 1809367/86280) -> E6: True; mu = 6
  ok   C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [tails]: data ok (D_7 = C Y^6Z, D_4 = <Y^4, Y^3Z, 1/2*X*Y^3 + Y^2*Z^2>) True; normalized by shears (a, b, c) = (-1/2, 0, 0) ([16, Lemma B.4] checked: True): delta = 0, eps = 0; [y^4]g0 = -eps/15, [y^3z]g0 = -delta/20: True
    C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [tails]: A = 1, B = 1, C = 0, f' = 0, k = 0
  ok   C = 0, A, B: Y^6Z + XY^4 + XY^3Z, E4 = X*Y^3 + Y^2*Z^2 [tails]: step 5 (V in (I : m^2): True, E6 for f + t V); forced coefficients ok: True; split jets of the equation (z^3, y^4, y^3z, y^5) = (1, -49/4, -7/2, -7/120) -> E6: True; mu = 6
  ok   Part Y: 33 accepted algebras; steps {'step 5': 9, 'step 2': 7, 'step 4': 5, 'step 3': 8, 'step 6': 4}
ALL CHECKS PASSED
