(S) shear duality: <g(x + q(y,z), y, z), F> = <g, exp(X q(dY,dZ)) F> for all monomials g, F of degree <= 6, q a general quadric
  ok   shear duality (all monomials of degree <= 6)

(0) shapes of the sextic tail Q6 of the lift of F (before normalization)
   secant, F = Y^7+Z^7: Q6 in [Z^6, Y*Z^5, X*Z^5, Y^5*Z, Y^6, X*Y^5]
  ok   secant nonpure shape
   secant, F = Y^7: Q6 in [Z^6, Y^5*Z, Y^6, X*Y^5]
  ok   secant pure shape
   tangent in, F = Y^6 Z: Q6 in [Y^3*Z^3, Y^4*Z^2, Y^5*Z, X*Y^4*Z, Y^6, X*Y^5]
  ok   tangent-in nonpure shape
   tangent in, F = Y^7: Q6 in [Y^4*Z^2, Y^5*Z, Y^6, X*Y^5]
  ok   tangent-in pure shape
   tangent out, F = X Y^6: Q6 in [Y^5*Z, X*Y^4*Z, Y^6, X*Y^5, X^2*Y^4, X^3*Y^3, X^4*Y^2, X^5*Y, X^6]
  ok   tangent-out nonpure shape
   tangent out, F = Y^7: Q6 in [Y^5*Z, Y^6, X*Y^5, X^2*Y^4]
  ok   tangent-out pure shape

(0') normalization: leading effects of gauges and shears on F (degree 6 part of exp(V q) F - F)
   exp(X y^2) Y^7, exp(Z y^2) Y^7: 42*X*Y^5 , 42*Y^5*Z
   exp(X(y^2), X(z^2), Z y^2, Y z^2) on Y^7+Z^7: [42*X*Y^5, 42*X*Z^5, 42*Y^5*Z, 42*Y*Z^5]
   exp(X yz), exp(X y^2), exp(Z y^2) on Y^6 Z: [6*X*Y^5, 30*X*Y^4*Z, 30*Y^4*Z^2]
   exp(Z xy), exp(Z y^2) on X Y^6: [6*Y^5*Z, 30*X*Y^4*Z]
  ok   normalizing effects as stated

(1)-(2) the six cases
   secant Y^7+Z^7: 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 Y^7+Z^7: high part of u o Phi = 12 (d3 p1 + d2 p2) YZ   [restriction of u_3 to x = 0: p2*y^2*z + p1*y*z^2]
   secant Y^7: Q5 = Q5_16*X*Y^4 + Q5_15*Y^5 + Q5_10*Y^4*Z + Q5_0*Z^5 ;  R5 = R5_15*Y^5 + R5_2*X*Z^4 + R5_1*Y*Z^4 + R5_0*Z^5
  ok   secant Y^7: u = yz^2 - (g/30) z^4, g = [YZ^4] R5   [restriction of u_3 to x = 0: y*z^2]
   tangent in Y^6 Z: 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 Y^6 Z: high part of U o Phi = ((60 xi - 9 d^2/10) p0 + 12 kap p1) Z^2   [restriction of u_3 to x = 0: p1*y*z^2 + p0*z^3]
  ok   tangent in Y^6 Z: V = x y^2 - (A/30) y^4 z - (B/120) y^5   [restriction of u_3 to x = 0: 0]
  ok   z o Psi - y^2 o Phi/42 and z o Phi - (2lam/5) y o Psi have degree <= 4 with the stated quartic parts
   tangent in Y^7: Q5 = Q5_16*X*Y^4 + Q5_15*Y^5 + 8/5*lam*R5_16*X*Y^3*Z + Q5_10*Y^4*Z + Q5_6*Y^3*Z^2 + 2/5*lam*R5_6*Y^2*Z^3 + 2/105*lam^2*Y*Z^4 ;  R5 = R5_16*X*Y^4 + R5_15*Y^5 + R5_10*Y^4*Z + R5_6*Y^3*Z^2 + 2/21*lam*Y^2*Z^3
  ok   tangent in Y^7: u = yz^2 - (lam/105) y^4 - (D2/10) y^3 z - (C/420) y^5   [restriction of u_3 to x = 0: y*z^2]
   tangent out X Y^6: 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 X Y^6: u = yz^2   [restriction of u_3 to x = 0: y*z^2]
   tangent out Y^7: 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 ;  R5 = R5_20*X^5 + R5_19*X^4*Y + R5_18*X^3*Y^2 + R5_17*X^2*Y^3 + R5_16*X*Y^4 + R5_15*Y^5 + R5_11*X*Y^3*Z + R5_10*Y^4*Z
  ok   tangent out Y^7: u = yz^2   [restriction of u_3 to x = 0: y*z^2]

total time 6.8 s
ALL CHECKS PASSED
