Part R: radial branch
   D_3 = [Y*Z^2, Y^2*Z, Y^3, X*Y^2]
  ok   D_3 = <Y^3, Y^2 Z, Y Z^2, X Y^2>
   P6 in [Y^3*Z^3, Y^4*Z^2, Y^5*Z, X*Y^4*Z, Y^6, X*Y^5, X^2*Y^4]
  ok   P6 in <X^2Y^4, XY^5, XY^4Z, Y^6, Y^5Z, Y^4Z^2, Y^3Z^3>
  ok   contractions: x^2 o X^2Y^4 = 2Y^4, y^3 o Y^7 = 210 Y^4, xyz o XY^4Z = 4Y^3, y^4 o Y^7 = 840 Y^3, z^3 o Y^3Z^3 = 6 Y^3
  ok   delta = 0: W = y^3 z gives W o Phi in T_{<=1}
  ok   delta arbitrary: W = y^2 z^2 - (delta/105) y^5 gives W o Phi in T_{<=1}
Part Z: binary branch, gcd(P) = z^2, V = <Y^5, Y^4 Z>, sextic tail delta Y^4 Z^2 with delta != 0
  ok   u4 o (delta Y^4 Z^2) in <Y^2, YZ> when [y^4] u4 = 0
   Z^2-coefficient of r2 o A4 = 2*a2*r0 + 3*a3*r1 + 12*a4*r2  (vanishing for all r2 forces a2 = a3 = a4 = 0, i.e. A4 in <Y^4, Y^3 Z>)
   matrix (rows r0, r1, r2; columns a0..a4): [(0, 0, 2, 0, 0), (0, 0, 0, 3, 0), (0, 0, 0, 0, 12)]
  ok   the Z^2-coefficient of r2 o A4 vanishes for all r2 iff a2 = a3 = a4 = 0
   high part of 48 delta U0 o Phi: (-384/35*dl^3*p1 + 576*dl*p1*b4 + 2880*dl*p0*b5)*Z^2
  ok   48 delta U0 o Phi has high part 48 delta (60 xi p0 + (12 kap - 8 delta^2/35) p1) Z^2
  ok   cubic part of U0 kills V = <Y^5, Y^4 Z>
Part N: norm formula length_0(x^2 + g, x r + k, p) = i_0(k^2 + g r^2, p)
   trial 0 : length 40  i_0 = 40
   trial 1 : length 32  i_0 = 32
   trial 2 : length 40  i_0 = 40
   trial 3 : length 41  i_0 = 41
   trial 4 : length 40  i_0 = 40
   trial 5 : length 45  i_0 = 45
  ok   norm formula on 6 random examples (finite lengths)
Part T: complete intersections in the tangent cone I* (binary branch), exact local lengths
   gcd z      (expected 12 + 3*8 = 36): local length 36 (stable at N = 13)
  ok   gcd z      (expected 12 + 3*8 = 36)
   gcd z(y-z) (expected 12 + 10 + 16 = 38, G = (Y+Z)^5 so kappa(v1) = 6 at v1 = [Y+Z]): local length 38 (stable at N = 13)
  ok   gcd z(y-z) (expected 12 + 10 + 16 = 38, G = (Y+Z)^5 so kappa(v1) = 6 at v1 = [Y+Z])
   gcd z(y-z)(y+z), V = <Y^5,(Y+Z)^5>: local length 39 (stable at N = 13; expected 12 + 10 + 9 + 8 = 39)
  ok   gcd z(y-z)(y+z): 39
   gcd z(y-z)^2, V = <Y^5,(Y+Z)^4 Z>: local length 38 (stable at N = 13; expected 12 + 2*9 + 8 = 38)
  ok   gcd z(y-z)^2 with (Y+Z)^5 not in V: 38
   [info] gcd z^2, P'' = [y^2, z^2] : random complete intersections in I* have local length [40, 40, 40, 40]
   [info] gcd z^2, P'' = [y*z, y^2 - z^2] : random complete intersections in I* have local length [40, 40, 40, 40]
total time 1.4 s
ALL CHECKS PASSED
