(0) shapes of Q7 (x o Q7, z o Q7 in C Y^6) and of Q6 after Q7 = 0 (x o Q6, z o Q6 in D_5)
   Q7 in [Y^6*Z, Y^7, X*Y^6]
  ok   Q7 shape
   Q6 (sec) in [Z^6, Y^5*Z, Y^6, X*Y^5]
  ok   Q6 shape sec
   Q6 (tin) in [Y^4*Z^2, Y^5*Z, Y^6, X*Y^5]
  ok   Q6 shape tin
   Q6 (tout) in [Y^5*Z, Y^6, X*Y^5, X^2*Y^4]
  ok   Q6 shape tout
   degree-7 effect of exp(X y^2), exp(Z y^2) on Y^8: 56*X*Y^6 , 56*Y^6*Z
   degree-6 effect of exp(X y^3), exp(Z y^3) on Y^8: 336*X*Y^5 , 336*Y^5*Z ; degree-7 effect: 0 0
  ok   shear effects
   (by hand) the gauge by y^2 o Phi/56 does not touch the quintic tail when Q7 = 0: y^2 maps Q6 to degree 4

(1)-(2) the cases
   secant, sig != 0: Q5 = Q5_16*X*Y^4 + Q5_15*Y^5 + Q5_10*Y^4*Z + Q5_6*Y^3*Z^2 + Q5_3*Y^2*Z^3 + Q5_2*X*Z^4 + Q5_1*Y*Z^4 + Q5_0*Z^5
  ok   secant sig != 0: high part of sig*u o Phi = 12 sig (d3 p1 + d2 p2) YZ   [restriction of u_3 to x = 0: sig*p2*y^2*z + sig*p1*y*z^2]
   secant, sig = 0: Q5 = Q5_16*X*Y^4 + Q5_15*Y^5 + Q5_10*Y^4*Z + Q5_0*Z^5
  ok   secant sig = 0: u = yz^2   [restriction of u_3 to x = 0: y*z^2]
   tangent in, lam = 0: Q5 = Q5_16*X*Y^4 + Q5_15*Y^5 + Q5_10*Y^4*Z + Q5_6*Y^3*Z^2
  ok   tangent in lam = 0: u = yz^2 - (eta/3360) y^6, eta = [Y^3Z^2] Q5   [restriction of u_3 to x = 0: y*z^2]
   tangent in, lam != 0: 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 + Q5_1*Y*Z^4 + Q5_0*Z^5
  ok   tangent in lam != 0: high part of 48 lam U o Phi = 48 lam (60 xi p0 + 12 kap p1) Z^2   [restriction of u_3 to x = 0: 48*lam*p1*y*z^2 + 48*lam*p0*z^3]
  ok   tangent in lam != 0: 8 lam V, V = x y^2 - B/(8 lam) y^3 z - (A/1680) y^6   [restriction of u_3 to x = 0: 0]
   tangent out: Q5 = Q5_20*X^5 + Q5_19*X^4*Y + Q5_18*X^3*Y^2 + Q5_17*X^2*Y^3 + Q5_16*X*Y^4 + Q5_15*Y^5 + Q5_11*X*Y^3*Z + Q5_10*Y^4*Z
  ok   tangent out: u = yz^2   [restriction of u_3 to x = 0: y*z^2]

total time 0.7 s
ALL CHECKS PASSED
