=== (G) the P2 datum over Lambda + [Z] ===
=== (Tc) tangent pencil over Lambda + [Z] ===
  [ok] (Tc) R = Y^4 + Z^4: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-2*x^7 - 2*x^6*y - 3*x^5*y^2 - 2*x^4*y^3 + 3*x^2*y^5 + x*y^6 - 3*y^7 - x^5*y*z - x^4*y^2*z + x^3*y^3*z + 3*x^2*y^4*z - 3*x*y^5*z + y^6*z + 2*x^5*z^2 + 3*x^4*y*z^2 + x^2*y^3*z^2 + 3*x*y^4*z^2 + 3*y^5*z^2 + 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*x*y^3*z^3 - 2*y^4*z^3 - 2*x^3*z^4 + 2*x^2*y*z^4 - y^3*z^4 + 2*x*y*z^5 + y^2*z^5 + 3*y*z^6 + 3*z^7 - 7/360*x^6 + 2*x^5*y + x^2*y^4 - 3*x*y^5 + 2*y^6 + 3*x^5*z + x^4*y*z + x^3*y^2*z + 3*x^2*y^3*z - 2*y^5*z - x^4*z^2 + x^3*y*z^2 + 2*x^2*y^2*z^2 + x*y^3*z^2 - 3*y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 - x*y^2*z^3 - x*y*z^4 + 2*y^2*z^4 + 2*x*z^5 - y*z^5 + z^6 + 2*x^3*y^2 - x^2*y^3 + 3*x*y^4 + 3*y^5 - 2*x^4*z + 3*x^3*y*z - 2*x^2*y^2*z - 3*x*y^3*z + x^3*z^2 + 2*x*y^2*z^2 + 2*y^3*z^2 - 3*y^2*z^3 + 2*x*z^4 + y*z^4 + 3*z^5 + 2*x^2*y^2 - y^4 - 2*x^3*z + 3*x^2*y*z - 2*x*y^2*z - 3*y^3*z + x^2*z^2 + 2*x*y*z^2 + y^2*z^2 + x*z^3 - y*z^3 + z^4 + x^2*z - 3*x*y*z - 2*y^2*z + 3*x*z^2 - y*z^2, 2*x^7 + x^6*y - x^5*y^2 + 2*x^4*y^3 + x^3*y^4 - 2*x^2*y^5 - 3*x*y^6 + 3*y^7 - 3*x^6*z - 2*x^5*y*z + 3*x^4*y^2*z + 3*x^3*y^3*z - x^2*y^4*z + 3*x*y^5*z - 2*y^6*z - 3*x^5*z^2 + 2*x^4*y*z^2 - 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 + 3*x*y^4*z^2 + 2*y^5*z^2 + 3*x^3*y*z^3 - 2*x^2*y^2*z^3 - y^4*z^3 - 2*x^3*z^4 + 3*x^2*y*z^4 + y^3*z^4 + 3*x^2*z^5 + x*y*z^5 + x*z^6 - 3*y*z^6 + 3*z^7 - 13/180*x^6 - 2*x^4*y^2 - 3*x^3*y^3 + 2*x^2*y^4 + 2*x*y^5 + 3*y^6 + x^5*z + x^3*y^2*z + 3*x*y^4*z + 3*y^5*z + 2*x^4*z^2 - x^3*y*z^2 + 2*x^2*y^2*z^2 - x*y^3*z^2 - 3*y^4*z^2 - x^3*z^3 - 2*x^2*y*z^3 + 3*x*y^2*z^3 - 3*y^3*z^3 + x^2*z^4 + x*y*z^4 - y^2*z^4 - x*z^5 + 3*y*z^5 - 3*z^6 + x^3*y^2 - x^2*y^3 - x*y^4 + 3*x^4*z + 3*x^3*y*z + 2*x^2*y^2*z + x*y^3*z + y^4*z + 3*x^3*z^2 + 3*x^2*y*z^2 - 3*x*y^2*z^2 + 2*y^3*z^2 + 2*x^2*z^3 + 3*x*y*z^3 + 3*y*z^4 - 3*z^5 + x^2*y^2 - x*y^3 - 2*y^4 + 2*x^3*z - x^2*y*z + 2*x*y^2*z - 2*x^2*z^2 - x*y*z^2 + 2*y^2*z^2 - 3*x*z^3 - y*z^3 + 2*z^4 - 2*x^2*z + 2*x*y*z + 3*y^2*z + x*z^2 - 3*y*z^2, 3*x^7 - 2*x^6*y - 2*x^5*y^2 - x^4*y^3 - x^3*y^4 - 3*x^2*y^5 - x*y^6 - 3*y^7 - x^6*z - 3*x^5*y*z + 3*x^4*y^2*z + 2*x^3*y^3*z + x^2*y^4*z + 3*x*y^5*z - 2*y^6*z + x^5*z^2 - 2*x^4*y*z^2 + x^3*y^2*z^2 - 2*x^2*y^3*z^2 + x*y^4*z^2 + 3*y^5*z^2 - 2*x^4*z^3 + 2*x^3*y*z^3 + 3*x^2*y^2*z^3 - 2*x*y^3*z^3 + 3*y^4*z^3 + 3*x^3*z^4 - 2*x*y^2*z^4 - y^3*z^4 + 3*x^2*z^5 + x*y*z^5 + 2*y^2*z^5 + 2*x*z^6 - 3*y*z^6 - 3*z^7 + 1/180*x^6 - 3*x^5*y + x^3*y^3 + x^2*y^4 - 3*x*y^5 - 2*y^6 - 2*x^5*z + x^4*y*z - x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z - y^5*z + 3*x^4*z^2 + 2*x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*x*y^3*z^2 + y^4*z^2 + 2*x^3*z^3 + x^2*y*z^3 + x*y^2*z^3 + x*y*z^4 + 3*y^2*z^4 - 3*x*z^5 + y*z^5 + z^6 - 2*x^3*y^2 + x^2*y^3 + 3*x*y^4 + y^5 + 3*x^4*z - 2*x^3*y*z - x^2*y^2*z + 3*x*y^3*z - y^4*z - x^3*z^2 - x^2*y*z^2 + x*y^2*z^2 - 3*y^3*z^2 + 2*x*y*z^3 + 2*y^2*z^3 + x*z^4 + 2*y*z^4 + 3*x^2*y^2 - 2*x*y^3 - 3*x^3*z + x^2*y*z - 3*x*y^2*z - y^3*z + 2*x^2*z^2 - 2*x*y*z^2 - 3*y^2*z^2 + 2*x*z^3 + x^2*z - 2*x*y*z + 2*y^2*z + x*z^2 + 2*y*z^2]
  [ok] (Tc) R = X^2*Y^2 + Y^4: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [x^7 - x^6*y - 2*x^5*y^2 - 3*x^4*y^3 + 3*x^2*y^5 - x*y^6 + 2*x^6*z + 3*x^5*y*z - 2*x^4*y^2*z + 3*x^3*y^3*z - 2*x^2*y^4*z - 2*x*y^5*z - 2*y^6*z - x^4*y*z^2 + 3*x^3*y^2*z^2 + 3*x*y^4*z^2 - 2*x^4*z^3 + 2*x^3*y*z^3 - x^2*y^2*z^3 + 2*x*y^3*z^3 + 2*y^4*z^3 + 2*x^3*z^4 - 2*x^2*y*z^4 - x*y^2*z^4 - 3*x*y*z^5 + y^2*z^5 - 3*y*z^6 + z^7 - 1/20*x^6 - 3*x^4*y^2 + 2*x^3*y^3 - 3*x^2*y^4 - 3*x*y^5 - y^6 + 2*x^5*z + x^4*y*z - x^3*y^2*z - 3*x*y^4*z + 2*y^5*z - x^4*z^2 - 2*x^3*y*z^2 + 2*x^2*y^2*z^2 - x*y^3*z^2 - 2*x^3*z^3 + 3*x^2*y*z^3 - 3*x*y^2*z^3 + y^3*z^3 - 2*x^2*z^4 + x*y*z^4 + y^2*z^4 + 3*x*z^5 - 3*y*z^5 - 3*z^6 - x^3*y^2 + x^2*y^3 - 2*x*y^4 + 2*y^5 + 3*x^4*z + 2*x^3*y*z + x^2*y^2*z - 2*x*y^3*z - 3*y^4*z + 2*x^3*z^2 + x^2*y*z^2 - y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 - y^2*z^3 - 3*x*z^4 - y*z^4 - 2*z^5 + 6*x^2*y^2 - 2*x*y^3 - y^4 + x^3*z + 3*x^2*y*z + 3*x*y^2*z - 2*y^3*z - 2*y^2*z^2 + 3*x*z^3 - y*z^3 + z^4 + 2*x^2*z + 2*x*y*z + 3*y^2*z + 2*x*z^2 - y*z^2, -3*x^7 - x^6*y - x^5*y^2 + 2*x^4*y^3 - 2*x^3*y^4 + x^2*y^5 + x*y^6 + 2*y^7 + 3*x^6*z + 2*x^5*y*z + x^4*y^2*z + x^3*y^3*z + 2*x^2*y^4*z + x*y^5*z - 3*y^6*z - 3*x^5*z^2 - 3*x^4*y*z^2 - 3*x^3*y^2*z^2 - x^2*y^3*z^2 - 2*x*y^4*z^2 + y^5*z^2 - 2*x^4*z^3 + 3*x^3*y*z^3 - x^2*y^2*z^3 + 3*x*y^3*z^3 - 3*y^4*z^3 + 2*x^2*y*z^4 - 3*x*y^2*z^4 + 2*x^2*z^5 + 3*x*y*z^5 - 2*y^2*z^5 + 2*x*z^6 + 2*y*z^6 - z^7 + 1/180*x^6 + 2*x^4*y^2 + 2*x^3*y^3 - 3*x^2*y^4 + 3*y^6 + x^5*z + 2*x^4*y*z - x^3*y^2*z - 3*x^2*y^3*z + 2*x*y^4*z - y^5*z + x^4*z^2 + 3*x^3*y*z^2 + x^2*y^2*z^2 - x*y^3*z^2 + y^4*z^2 - x^3*z^3 + 2*x^2*y*z^3 - 2*x*y^2*z^3 + 3*x^2*z^4 + 3*x*y*z^4 - 3*y^2*z^4 - x*z^5 + y*z^5 - z^6 + 2*x^3*y^2 - x^2*y^3 + 2*x*y^4 - 2*y^5 + x^4*z + 2*x^3*y*z - 3*x^2*y^2*z + 3*x*y^3*z - y^4*z + 3*x^3*z^2 - x*y^2*z^2 - y^3*z^2 - 3*x^2*z^3 + 2*x*y*z^3 - y^2*z^3 + 3*x*z^4 + 2*y*z^4 - z^5 - 6*x^2*y^2 + x*y^3 + y^4 + 2*x*y^2*z + 3*y^3*z + x^2*z^2 - 2*x*y*z^2 - 2*y^2*z^2 + 3*y*z^3 - z^4 - 2*x^2*z - 3*y^2*z + 2*x*z^2 + y*z^2, -3*x^7 + 2*x^6*y + 3*x^5*y^2 - 3*x^4*y^3 - 3*x^3*y^4 - 2*x^2*y^5 - 2*x*y^6 + 3*y^7 + x^6*z - 3*x^5*y*z + x^4*y^2*z + 2*x^3*y^3*z + x^2*y^4*z + x*y^5*z + 3*y^6*z + 3*x^5*z^2 - 2*x^4*y*z^2 - 2*x^3*y^2*z^2 - 3*x^2*y^3*z^2 - 2*x*y^4*z^2 - y^5*z^2 - 3*x^4*z^3 + 2*x^3*y*z^3 - x^2*y^2*z^3 + 3*x*y^3*z^3 - 3*y^4*z^3 + 3*x^3*z^4 - 3*x^2*y*z^4 + x*y^2*z^4 - 3*y^3*z^4 - 3*x^2*z^5 + 3*x*y*z^5 + x*z^6 + 7/120*x^6 + x^5*y - 3*x^3*y^3 - 2*x^2*y^4 - x*y^5 - 2*y^6 - 3*x^5*z + 2*x^4*y*z + 3*x^3*y^2*z - 2*x^2*y^3*z - 3*x*y^4*z + 3*y^5*z + 3*x^4*z^2 - 2*x^3*y*z^2 - x^2*y^2*z^2 - 2*x*y^3*z^2 + 2*x^3*z^3 - x^2*y*z^3 - 3*x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 - 2*x*z^5 + y*z^5 - 3*z^6 + 2*x^3*y^2 + 3*x*y^4 + 2*y^5 + 2*x^4*z - x^2*y^2*z + 2*x*y^3*z + 3*y^4*z - x^2*y*z^2 - 3*y^3*z^2 + 3*x^2*z^3 - x*y*z^3 + y^2*z^3 + 2*x*z^4 + 3*y*z^4 + 2*z^5 + 18*x^2*y^2 + x*y^3 - 3*y^4 + x^3*z + 2*x^2*y*z - y^3*z - 3*x^2*z^2 - x*y*z^2 - 2*y^2*z^2 + x*z^3 - 2*y*z^3 - 3*x^2*z - 3*y^2*z - y*z^2]
  [ok] (Tc) R = X^2*Y^2 + Y^4 + Z^4: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-x^6*y + x^4*y^3 - 2*x^3*y^4 + 3*x^2*y^5 + 2*y^7 - 2*x^5*y*z + 3*x^4*y^2*z + 3*x^3*y^3*z + x^2*y^4*z - x*y^5*z - 3*y^6*z + 3*x^5*z^2 + 2*x^4*y*z^2 - 2*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - 3*x*y^4*z^2 - y^5*z^2 + 3*x^4*z^3 - 2*x^3*y*z^3 + 3*x^2*y^2*z^3 + 3*y^4*z^3 + 3*x^3*z^4 - x^2*y*z^4 - x*y^2*z^4 + 2*y^3*z^4 + 3*x^2*z^5 - 2*x*y*z^5 + 2*y^2*z^5 - 3*x*z^6 + 3*y*z^6 - 1/45*x^6 - 3*x^5*y - 2*x^4*y^2 - x^3*y^3 + 2*x^2*y^4 + 2*x*y^5 + 2*y^6 + 3*x^5*z + 3*x^3*y^2*z + 3*x^2*y^3*z - x*y^4*z + x^4*z^2 - x^3*y*z^2 - x^2*y^2*z^2 + 3*x*y^3*z^2 + y^4*z^2 + 2*x^3*z^3 - 2*x^2*y*z^3 + y^3*z^3 - x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 - 2*x*z^5 + y*z^5 + 3*z^6 + 2*x^3*y^2 + 2*x^2*y^3 - 2*y^5 + 2*x^4*z - x^3*y*z - 2*x^2*y^2*z + 3*x*y^3*z + 3*y^4*z + x^3*z^2 - 2*x^2*y*z^2 - 2*y^3*z^2 - x^2*z^3 + x*y*z^3 + 3*y^2*z^3 + x*z^4 - 3*y*z^4 - 2*z^5 + 18*x^2*y^2 + 3*x*y^3 - 3*y^4 + x^3*z - 3*x^2*y*z + x*y^2*z - 3*y^3*z - 2*x^2*z^2 - x*y*z^2 - x*z^3 + 2*y*z^3 - 3*x^2*z - x*y*z + y^2*z + x*z^2, -2*x^6*y + x^5*y^2 + x^4*y^3 - 3*x^3*y^4 - x^2*y^5 - x*y^6 - 2*x^6*z + 3*x^5*y*z + 3*x^4*y^2*z - 2*x^3*y^3*z + 2*x^2*y^4*z - 3*x*y^5*z + 2*y^6*z - 3*x^5*z^2 - 2*x^4*y*z^2 - x^3*y^2*z^2 + x^2*y^3*z^2 - y^5*z^2 - 3*x^4*z^3 - x^3*y*z^3 - 2*x^2*y^2*z^3 - 3*y^4*z^3 - x^3*z^4 + 2*x^2*y*z^4 + y^3*z^4 - 2*x*y*z^5 - y^2*z^5 + 2*x*z^6 - 2*y*z^6 - 2*z^7 - 17/180*x^6 - x^5*y + 2*x^4*y^2 + 2*x^2*y^4 + 2*x*y^5 + 2*y^6 + 2*x^5*z - 2*x^4*y*z + 3*x^3*y^2*z - x^2*y^3*z - 2*y^5*z - x^4*z^2 - x^3*y*z^2 + x^2*y^2*z^2 + x*y^3*z^2 + 3*y^4*z^2 + 2*x^3*z^3 - 3*y^3*z^3 - x^2*z^4 + 2*x*y*z^4 - x*z^5 + 2*y*z^5 - 3*z^6 - 2*x*y^4 + y^5 - 2*x^4*z - 2*x^3*y*z + x^2*y^2*z - 3*x*y^3*z - 3*y^4*z - 2*x*y^2*z^2 + 3*y^3*z^2 - x*y*z^3 + 2*y^2*z^3 + 3*y*z^4 - 3*z^5 - 12*x^2*y^2 - x*y^3 + x^3*z + x^2*y*z + 2*x*y^2*z + 2*y^3*z - 2*x^2*z^2 + 3*x*y*z^2 - y^2*z^2 + 2*x*z^3 - 3*y*z^3 + 2*z^4 - 3*x^2*z - x*y*z - y^2*z + 3*y*z^2, -2*x^7 + 2*x^6*y + 3*x^5*y^2 - x^4*y^3 + 2*x^3*y^4 - x^2*y^5 + 2*x*y^6 + y^7 - 3*x^6*z - 3*x^5*y*z + 2*x^4*y^2*z - 2*x^3*y^3*z + 3*x^2*y^4*z - 3*x*y^5*z - 2*y^6*z - 3*x^4*y*z^2 + 2*x^3*y^2*z^2 - x^2*y^3*z^2 - 2*x*y^4*z^2 + 3*y^5*z^2 + 3*x^4*z^3 - 3*x^3*y*z^3 + 3*x^2*y^2*z^3 - 3*x*y^3*z^3 + x^3*z^4 + x^2*y*z^4 + x*y^2*z^4 + 2*y^3*z^4 - 2*x^2*z^5 + x*y*z^5 + 2*x*z^6 + 3*y*z^6 + 3*z^7 - 1/36*x^6 - 3*x^5*y + 2*x^4*y^2 - 3*x*y^5 - 2*y^6 - 3*x^5*z - x^4*y*z - 2*x^3*y^2*z + x^2*y^3*z + x*y^4*z + 2*y^5*z - 3*x^4*z^2 + 2*x^3*y*z^2 - 2*x^2*y^2*z^2 + 2*x*y^3*z^2 + 2*y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 + 3*x*y^2*z^3 + y^3*z^3 - 2*x*y*z^4 + 2*x*z^5 - z^6 + 2*x^3*y^2 + x^2*y^3 - 3*x*y^4 - y^5 - x^4*z - x^3*y*z - 2*x^2*y^2*z + x*y^3*z - 2*y^4*z + 3*x^3*z^2 - x^2*y*z^2 - x*y^2*z^2 + 2*x^2*z^3 + x*y*z^3 + 2*y^2*z^3 + x*z^4 - y*z^4 + z^5 - 12*x^2*y^2 - 3*x*y^3 + 3*y^4 - 3*x^2*y*z - x*y^2*z - x^2*z^2 + 2*x*y*z^2 - 2*y^2*z^2 + x*z^3 - 3*y*z^3 - z^4 - 2*x^2*z + 2*x*y*z - y^2*z - 2*x*z^2 - 2*y*z^2]
  [ok] (Tc) R = X*Y^3: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [3*x^7 - x^6*y + 3*x^5*y^2 + 2*x^3*y^4 - 3*x^2*y^5 + 2*x*y^6 + 2*y^7 + x^6*z + 2*x^5*y*z + x^4*y^2*z + 3*x^3*y^3*z - 3*x*y^5*z + x^4*y*z^2 + x^3*y^2*z^2 - 2*x^2*y^3*z^2 - y^5*z^2 - 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*y^4*z^3 - x^3*z^4 + x^2*y*z^4 - 2*x*y^2*z^4 + y^3*z^4 + 3*x^2*z^5 + 3*x*y*z^5 - y^2*z^5 + 3*x*z^6 - 3*y*z^6 - z^7 + 1/72*x^6 - 3*x^5*y + 2*x^4*y^2 + 2*x^2*y^4 + x*y^5 - 2*y^6 + 2*x^5*z - 3*x^4*y*z + x^2*y^3*z - x*y^4*z + 3*y^5*z - 3*x^4*z^2 - 3*x^3*y*z^2 + x^2*y^2*z^2 + x*y^3*z^2 + 3*y^4*z^2 + x^3*z^3 - 3*y^3*z^3 + x^2*z^4 - 2*x*y*z^4 - y^2*z^4 + 2*x*z^5 - 3*y*z^5 + 2*x^2*y^3 + 2*x*y^4 - 3*x^4*z + 3*x^3*y*z + 2*x^2*y^2*z - x*y^3*z - 3*y^4*z - 3*x^3*z^2 + x^2*y*z^2 - x*y^2*z^2 + 2*y^3*z^2 + 3*x^2*z^3 + 2*x*y*z^3 - 3*y^2*z^3 + x*z^4 + 2*y*z^4 + 2*z^5 - 3*x^2*y^2 + 3*x^3*z - 2*x^2*y*z - 2*y^3*z + 3*x^2*z^2 + x*y*z^2 + 3*y^2*z^2 + 2*x*z^3 + 3*y*z^3 - 3*z^4 + 2*x^2*z + 2*x*y*z - y^2*z + x*z^2 - y*z^2, x^7 + 3*x^6*y + x^5*y^2 + x^3*y^4 - 3*x^2*y^5 - x*y^6 + 3*x^6*z + x^5*y*z + 2*x^4*y^2*z - 2*x^3*y^3*z - 2*x^2*y^4*z - x*y^5*z + 3*y^6*z + 3*x^5*z^2 - x^4*y*z^2 - 3*x^3*y^2*z^2 + x*y^4*z^2 - y^5*z^2 + 3*x^3*y*z^3 - 2*x^2*y^2*z^3 - 3*x*y^3*z^3 + 2*y^4*z^3 + 2*x^3*z^4 - 3*x^2*y*z^4 + x*y^2*z^4 - 2*y^3*z^4 - 2*x^2*z^5 - 2*x*y*z^5 + 3*y^2*z^5 - 2*y*z^6 - z^7 + 5/72*x^6 + x^5*y + x^4*y^2 - 2*x^3*y^3 - 2*x^2*y^4 - x*y^5 + 2*y^6 + 3*x^4*y*z - x^3*y^2*z + 2*x^2*y^3*z + 3*x*y^4*z + 3*y^5*z + 3*x^4*z^2 - 2*x^3*y*z^2 - x^2*y^2*z^2 + 3*x^3*z^3 + x*y^2*z^3 + y^3*z^3 - 3*x^2*z^4 + 2*x*y*z^4 - 2*y^2*z^4 - x*z^5 - y*z^5 + 3*z^6 - 2*x^3*y^2 + 3*x^2*y^3 + 3*x*y^4 + 2*y^5 + 2*x^4*z + 2*x^3*y*z + 2*x^2*y^2*z - 3*x*y^3*z - 3*y^4*z - x^3*z^2 + 2*x^2*y*z^2 - 3*x*y^2*z^2 + y^3*z^2 - 2*x^2*z^3 - 2*x*y*z^3 + 3*y^2*z^3 - y*z^4 - 3*x^2*y^2 - y^4 + x^3*z - 3*x*y^2*z - 2*y^3*z + 3*x^2*z^2 - 2*x*y*z^2 + 3*y^2*z^2 + x*z^3 - y*z^3 + 3*z^4 + 3*x^2*z + 2*y^2*z - 2*y*z^2, -3*x^7 - 3*x^6*y + 3*x^5*y^2 + 3*x^4*y^3 - x^3*y^4 + x^2*y^5 - x*y^6 - 3*y^7 - x^6*z - 3*x^5*y*z - 2*x^3*y^3*z - x^2*y^4*z + x*y^5*z - y^6*z + 3*x^5*z^2 + 3*x^4*y*z^2 + 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 - 3*x*y^4*z^2 - 3*y^5*z^2 - 2*x^4*z^3 - 2*x^3*y*z^3 + 3*x^2*y^2*z^3 - 2*x*y^3*z^3 - y^4*z^3 - x^3*z^4 - 2*x*y^2*z^4 + y^3*z^4 + x^2*z^5 - x*y*z^5 - 2*y^2*z^5 - y*z^6 - z^7 + 11/180*x^6 - 3*x^5*y + 2*x^3*y^3 - 3*x^2*y^4 + 2*x*y^5 - y^6 + x^5*z - 2*x^4*y*z - x^3*y^2*z + 3*x^2*y^3*z + x*y^4*z + 2*y^5*z - x^4*z^2 - x^2*y^2*z^2 + 2*x*y^3*z^2 - 2*y^4*z^2 + 2*x^3*z^3 - x^2*y*z^3 - 2*x*y^2*z^3 - 2*y^3*z^3 - x^2*z^4 - 3*y^2*z^4 + 2*z^6 + 3*x^3*y^2 + 2*x^2*y^3 - 3*x*y^4 - y^5 + 2*x^3*y*z - 3*x^2*y^2*z + 2*x*y^3*z - 3*y^4*z + x^3*z^2 + x^2*y*z^2 - 3*x*y^2*z^2 + 3*y^3*z^2 + 2*x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 - 2*x*z^4 - 3*y*z^4 + z^5 + 2*x^2*y^2 - 3*y^4 - x^3*z + 3*x^2*y*z + 2*x*y^2*z + 3*y^3*z - 2*x^2*z^2 - 2*x*y*z^2 - y^2*z^2 + z^4 - x^2*z + 3*y^2*z - 2*x*z^2 - 2*y*z^2]
  [ok] (Tc) R = X*Y^3 + Z^4: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-3*x^7 - x^6*y + 3*x^5*y^2 - x^4*y^3 - 2*x^3*y^4 - 3*x^2*y^5 + 3*x*y^6 - 2*y^7 + 2*x^6*z - 3*x^5*y*z + x^2*y^4*z + 2*x*y^5*z - 3*x^4*y*z^2 - x*y^4*z^2 + 2*y^5*z^2 + x^4*z^3 + 2*x^3*y*z^3 - 3*x^2*y^2*z^3 + 2*x*y^3*z^3 + x^3*z^4 + 2*x^2*y*z^4 - 3*x*y^2*z^4 + 2*y^3*z^4 + 2*x^2*z^5 - 2*x*y*z^5 - 3*y^2*z^5 - 2*x*z^6 + 2*y*z^6 + 2*z^7 - 1/90*x^6 - 2*x^5*y + x^4*y^2 - 2*x^3*y^3 + x^2*y^4 - 3*x*y^5 + 3*y^6 + 3*x^5*z - x^3*y^2*z + 3*x^2*y^3*z - x*y^4*z + y^5*z + x^4*z^2 - x^3*y*z^2 - 3*x^2*y^2*z^2 + x*y^3*z^2 + 3*y^4*z^2 + 3*x^3*z^3 + 2*x^2*y*z^3 - 3*x*y^2*z^3 + 3*y^3*z^3 - 2*x^2*z^4 + 2*x*y*z^4 + 2*y^2*z^4 + x*z^5 - 2*y*z^5 - 3*z^6 - 3*x^3*y^2 + 3*x^2*y^3 - 2*x*y^4 - y^5 - 3*x^4*z - 3*x^3*y*z + x^2*y^2*z - x*y^3*z + 2*y^4*z + x^3*z^2 - x^2*y*z^2 - 3*x*y^2*z^2 - y^3*z^2 - x^2*z^3 + 2*x*y*z^3 - x*z^4 - 3*y*z^4 - 2*z^5 - 2*x^2*y^2 + 12*x*y^3 - y^4 + 2*x^3*z + x^2*y*z + 2*x*y^2*z + 3*y^3*z - 2*x^2*z^2 - 3*x*y*z^2 + 2*y^2*z^2 + x*z^3 - y*z^3 - 3*z^4 - x^2*z + 2*x*y*z + 2*y^2*z + 3*y*z^2, x^7 - 2*x^5*y^2 + x^4*y^3 + x^3*y^4 - x*y^6 - 2*y^7 + 3*x^5*y*z - 2*x^4*y^2*z + 3*x^3*y^3*z - x^2*y^4*z - x*y^5*z + 2*y^6*z - 3*x^5*z^2 + 3*x^4*y*z^2 + 3*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - 3*y^5*z^2 - 2*x^3*y*z^3 - 3*x^2*y^2*z^3 + 3*y^4*z^3 + 2*x^3*z^4 + x^2*y*z^4 - x*y^2*z^4 + 3*y^3*z^4 + x^2*z^5 + x*y*z^5 + 3*y^2*z^5 - 2*x*z^6 + 2*y*z^6 + z^7 - 5/144*x^6 + x^5*y + x^2*y^4 - 2*x*y^5 - 3*y^6 + 3*x^5*z - 3*x^4*y*z + 3*x^3*y^2*z + 3*x^2*y^3*z - 3*x*y^4*z + y^5*z + 2*x^4*z^2 - x^2*y^2*z^2 - x*y^3*z^2 - 3*y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 + 2*x*y^2*z^3 - 3*y^3*z^3 + 2*x^2*z^4 - 2*x*y*z^4 - y^2*z^4 - x*z^5 + 3*y*z^5 - 2*z^6 - 3*x^3*y^2 - 2*x^2*y^3 + 3*x*y^4 + 2*y^5 - 3*x^4*z + 3*x^3*y*z - 3*x^2*y^2*z + 3*x*y^3*z - y^4*z + 3*x^2*y*z^2 + 3*x*y^2*z^2 - 2*y^3*z^2 - x^2*z^3 + 3*x*y*z^3 + 2*y^2*z^3 - 3*x*z^4 - y*z^4 - z^5 + 2*x^2*y^2 + 2*y^4 + 2*x^3*z + 3*x^2*y*z + 2*x*y^2*z + y^3*z - 3*y^2*z^2 + 2*x*z^3 + 3*y*z^3 - 3*x*y*z + x*z^2 + 3*y*z^2, -x^7 - 2*x^6*y + x^5*y^2 - x^4*y^3 + 3*x^3*y^4 + x*y^6 - y^7 - 2*x^6*z + 2*x^5*y*z + x^3*y^3*z - 3*x^2*y^4*z - 2*y^6*z - 3*x^4*y*z^2 - x^3*y^2*z^2 - 3*x^2*y^3*z^2 - 2*x*y^4*z^2 + 2*y^5*z^2 + 2*x^4*z^3 - x^3*y*z^3 - 2*x^2*y^2*z^3 + y^4*z^3 - 3*x^3*z^4 - x^2*y*z^4 - 2*x*y^2*z^4 + 2*y^2*z^5 - 3*x*z^6 + y*z^6 + z^7 + 1/144*x^6 + 2*x^5*y - 2*x^4*y^2 + 2*x^2*y^4 - x*y^5 - 2*y^6 + 3*x^5*z - 2*x^3*y^2*z - 3*x^2*y^3*z - x*y^4*z + 3*y^5*z + x^4*z^2 + 2*x^3*y*z^2 - 3*x^2*y^2*z^2 + 3*x*y^3*z^2 - y^4*z^2 - 2*x^3*z^3 - 3*x^2*y*z^3 - x*y^2*z^3 - 3*y^3*z^3 - x^2*z^4 + x*y*z^4 + 3*y^2*z^4 + x*z^5 + 2*y*z^5 + 2*z^6 + x^3*y^2 + 3*x*y^4 - 2*y^5 - x^4*z + 2*x^3*y*z - x^2*y^2*z - 3*x^3*z^2 + 3*x^2*y*z^2 + 2*x*y^2*z^2 - y^3*z^2 - x^2*z^3 - x*y*z^3 - 2*y^2*z^3 + 3*x*z^4 - 2*y*z^4 - 3*z^5 - x^2*y^2 + 4*x*y^3 - 3*y^4 - 3*x^2*y*z + 3*x*y^2*z - y^3*z + 3*x^2*z^2 - 3*x*y*z^2 + 3*y^2*z^2 - 2*x*z^3 + 2*y*z^3 - z^4 - 3*x^2*z - x*y*z - 2*y^2*z + 2*x*z^2 + y*z^2]
  [ok] (Tc) R = X^2*Y^2 + Z^4: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-3*x^6*y - 3*x^4*y^3 + 2*x^3*y^4 + x^2*y^5 + 2*x*y^6 - 3*y^7 - x^6*z - 2*x^5*y*z - 2*x^4*y^2*z + x^3*y^3*z - 3*x^2*y^4*z + 2*y^6*z - x^5*z^2 - 3*x^4*y*z^2 - 2*x^3*y^2*z^2 + 2*x^2*y^3*z^2 + x*y^4*z^2 + 3*y^5*z^2 + 2*x^4*z^3 + 3*x^3*y*z^3 + x^2*y^2*z^3 + 3*x*y^3*z^3 + 2*y^4*z^3 + 2*x^3*z^4 + 2*x^2*y*z^4 + 2*x*y^2*z^4 + 2*y^3*z^4 - x^2*z^5 - 3*x*y*z^5 + 2*x*z^6 - y*z^6 + 3*z^7 + 1/120*x^6 - x^5*y + x^4*y^2 + 3*x^3*y^3 + 3*x^2*y^4 + x*y^5 + y^6 - x^5*z - 2*x^4*y*z + 2*x^3*y^2*z + 2*y^5*z + 3*x^4*z^2 - 3*x^3*y*z^2 - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 - 2*y^4*z^2 - 2*x^3*z^3 + 2*x^2*y*z^3 - 2*x*y^2*z^3 - 3*y^3*z^3 + x*y*z^4 - 3*y^2*z^4 + 3*x*z^5 - y*z^5 - 2*x^3*y^2 + x^2*y^3 + y^5 - 3*x^4*z - 3*x^3*y*z + 2*x^2*y^2*z - x*y^3*z - 3*y^4*z + 3*x^3*z^2 - x^2*y*z^2 - 3*x*y^2*z^2 - 2*y^3*z^2 - 3*x^2*z^3 + x*y*z^3 - 3*y^2*z^3 - 3*x*z^4 + 3*y*z^4 - 2*z^5 + x*y^3 + 3*y^4 - 2*x^3*z + 3*x^2*y*z - 2*x*y^2*z + 3*y^3*z - 2*x^2*z^2 - x*y*z^2 + 3*y^2*z^2 - x*z^3 + y*z^3 + 2*x*y*z + 2*x*z^2, -x^7 + 2*x^6*y + 2*x^5*y^2 - 3*x^4*y^3 - x^3*y^4 + x*y^6 + 3*y^7 - x^6*z - 3*x^5*y*z - x^4*y^2*z - 3*x^3*y^3*z - 2*x^2*y^4*z + 3*y^6*z + x^5*z^2 + 3*x^4*y*z^2 + 2*x^3*y^2*z^2 - 2*x*y^4*z^2 - 2*y^5*z^2 + x^4*z^3 - 3*x^3*y*z^3 + 3*x^2*y^2*z^3 - 2*y^4*z^3 - x^3*z^4 - x^2*y*z^4 + x*y^2*z^4 - 3*y^3*z^4 + 3*x^2*z^5 + x*y*z^5 + 2*y^2*z^5 - x*z^6 - y*z^6 + z^7 - 7/240*x^6 - 2*x^5*y - 2*x^4*y^2 - 2*x^3*y^3 - 2*x^2*y^4 - x*y^5 + 2*y^6 - x^5*z + x^4*y*z + x^2*y^3*z + 2*x*y^4*z + 2*y^5*z - 3*x^3*y*z^2 - x^2*y^2*z^2 + 2*x*y^3*z^2 - y^4*z^2 - x^3*z^3 + x^2*y*z^3 - 3*x*y^2*z^3 - y^3*z^3 + 3*x^2*z^4 + 2*x*y*z^4 + y^2*z^4 - 3*x*z^5 + 2*y*z^5 - 3*z^6 + x^3*y^2 + 3*x^2*y^3 - 2*x*y^4 + y^5 + 2*x^4*z + 2*x^3*y*z + 3*x^2*y^2*z + x*y^3*z - 3*y^4*z - x^3*z^2 + x^2*y*z^2 - 3*x*y^2*z^2 + 3*y^3*z^2 - x^2*z^3 - 2*x*y*z^3 - 3*y^2*z^3 + x*z^4 - y*z^4 + z^5 + 12*x^2*y^2 - 3*y^4 - 2*x^3*z + 2*x^2*y*z - y^3*z + x^2*z^2 + 2*x*y*z^2 + 2*y^2*z^2 + 3*x*z^3 - 2*z^4 + 2*x^2*z + x*y*z - 3*y^2*z + 2*x*z^2 + 3*y*z^2, 3*x^7 - 2*x^4*y^3 + 3*x^3*y^4 - x^2*y^5 - 2*x*y^6 - y^7 + x^6*z - 2*x^5*y*z + 3*x^4*y^2*z - 3*x^3*y^3*z + x*y^5*z + y^6*z - 2*x^4*y*z^2 + 3*x^3*y^2*z^2 - x^2*y^3*z^2 + x*y^4*z^2 + x^4*z^3 + 3*x^3*y*z^3 - x^2*y^2*z^3 - 2*x*y^3*z^3 + 2*y^4*z^3 - 3*x^3*z^4 - 3*x^2*y*z^4 - x*y^2*z^4 - 3*x^2*z^5 - 2*x*y*z^5 + y^2*z^5 + 3*x*z^6 - 2*y*z^6 - z^7 - 13/720*x^6 - 3*x^5*y - 2*x^4*y^2 - 3*x^3*y^3 + 3*x^2*y^4 - x*y^5 - y^6 - 2*x^5*z - x^4*y*z - 3*x^3*y^2*z - x^2*y^3*z + 3*x*y^4*z + 2*y^5*z - 2*x^3*y*z^2 - 3*y^4*z^2 + x^3*z^3 + x^2*y*z^3 + 2*y^3*z^3 - 3*y^2*z^4 + x*z^5 - 3*y*z^5 - 2*z^6 - 3*x^3*y^2 - x^2*y^3 - 2*x*y^4 + 3*y^5 - x^4*z + 3*x^3*y*z + 2*x^2*y^2*z - 3*x*y^3*z + 2*y^4*z - x^3*z^2 - x*y^2*z^2 - 2*y^3*z^2 + 3*x^2*z^3 + 3*x*y*z^3 + x*z^4 - y*z^4 - z^5 + 18*x^2*y^2 - x^3*z + x^2*y*z + 2*x*y*z^2 + 3*y*z^3 - 3*z^4 + x*y*z + 2*y^2*z - x*z^2 + 2*y*z^2]
=== (Sx) pure secant, point embedded at [X], active datum ===
  [ok] (Sx) D4=<X^4,Y^4,X^3Z>: QT(u=-3*x - y - z), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [2*x^7 + x^6*y + 2*x^5*y^2 + x^4*y^3 + 2*x^3*y^4 - x^2*y^5 + x*y^6 + 3*x^5*y*z - 2*x^3*y^3*z + 2*x*y^5*z + 3*y^6*z + 3*x^4*y*z^2 + x^2*y^3*z^2 - x*y^4*z^2 - 3*y^5*z^2 + x^4*z^3 - 3*x^3*y*z^3 - 2*x^2*y^2*z^3 - x*y^3*z^3 - 3*y^4*z^3 + 3*x^3*z^4 + x*y^2*z^4 - y^3*z^4 + 3*x^2*z^5 - x*y*z^5 + 3*y^2*z^5 - x*z^6 - 2*z^7 + 1/5*x^6 - 3*x^5*y - 2*x^4*y^2 - x^3*y^3 + x*y^5 - 2*y^6 - x^5*z - 3*x^3*y^2*z - 3*x^2*y^3*z + 2*x*y^4*z + 2*y^5*z + 2*x^2*y^2*z^2 + 3*x*y^3*z^2 + 2*x^3*z^3 + 2*x^2*y*z^3 - 2*x*y^2*z^3 - x^2*z^4 + x*y*z^4 + 3*x*z^5 - y*z^5 - 3*z^6 - 1/30*x^5 - x^4*y - 2*x^3*y^2 - 3*x^2*y^3 + 3*x*y^4 - 1/7290*y^5 - x^4*z - 3*x^3*y*z - 2*x*y^3*z + x^3*z^2 + 2*x^2*y*z^2 + 2*x*y^2*z^2 - 3*y^3*z^2 + 2*x^2*z^3 - 2*x*y*z^3 - 2*y^2*z^3 + 2*x*z^4 + y*z^4 - 2*z^5 + 3*x^3*y + 3*x^2*y^2 - 2*x*y^3 + 2*x^2*y*z + x*y^2*z + 3*y^3*z - 2*x^2*z^2 - x*y*z^2 - y^2*z^2 + 3*x*z^3 + 2*y*z^3 - 2*z^4 + 2*x*y*z + 3*x*z^2 + 2*y*z^2 + 3*z^3, -2*x^4*y^3 + x^3*y^4 + 3*x^2*y^5 - 3*y^7 + 2*x^6*z + 2*x^5*y*z + 3*x^4*y^2*z - 3*x^3*y^3*z + x^2*y^4*z - y^6*z - 2*x^5*z^2 + 3*x^4*y*z^2 - x^2*y^3*z^2 + 2*x*y^4*z^2 + 2*y^5*z^2 - x^4*z^3 + 3*x^3*y*z^3 + 3*x*y^3*z^3 - 3*x^3*z^4 - 2*x^2*y*z^4 + 2*x^2*z^5 - 3*x*y*z^5 - 3*y^2*z^5 + 2*x*z^6 - 3*y*z^6 - z^7 + 1/90*x^6 + 3*x^5*y - x^4*y^2 + 3*x^3*y^3 + 2*x^2*y^4 + x*y^5 + 3*y^6 - 3*x^4*y*z - x^3*y^2*z + 3*x^2*y^3*z + 2*x*y^4*z + y^5*z - x^4*z^2 - 2*x^3*y*z^2 - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 - 3*y^4*z^2 + 3*x^3*z^3 + 3*x^2*y*z^3 - 2*x*y^2*z^3 - 2*x^2*z^4 + 2*x*y*z^4 + y^2*z^4 + 2*x*z^5 + 3*y*z^5 + z^6 + 1/30*x^5 - x^4*y - x^3*y^2 - x^2*y^3 - 2*x*y^4 + 1/7290*y^5 - 3*x^4*z + x^3*y*z - 3*x^2*y^2*z + 2*x*y^3*z + y^4*z - 3*x^3*z^2 - 3*x^2*y*z^2 - x*y^2*z^2 + 3*y^3*z^2 - 3*x^2*z^3 + 2*y^2*z^3 - 2*x*z^4 - y*z^4 + 2*z^5 + 2*x^3*y - x^2*y^2 + x*y^3 + x^2*y*z + 3*x*y^2*z - 3*y^3*z - 3*x^2*z^2 + 3*x*y*z^2 - 2*y^2*z^2 + x*z^3 + y*z^3 + z^4 - 2*x*y*z + y^2*z - 3*x*z^2 - y*z^2 - 2*z^3, -3*x^7 - 2*x^6*y + 2*x^4*y^3 + 3*x^3*y^4 + 3*x^2*y^5 - x*y^6 - y^7 + 2*x^6*z + 3*x^5*y*z - x^3*y^3*z - x^2*y^4*z - 2*x*y^5*z - y^6*z + x^5*z^2 - 2*x^4*y*z^2 + 3*x^3*y^2*z^2 + 3*x^2*y^3*z^2 + 2*x*y^4*z^2 - 2*y^5*z^2 + 2*x^4*z^3 + x*y^3*z^3 + 3*y^4*z^3 + x^3*z^4 - x*y^2*z^4 + 3*y^3*z^4 - x*y*z^5 + 3*y^2*z^5 + x*z^6 - y*z^6 + 67/720*x^6 + 3*x^5*y + 2*x^4*y^2 - x^3*y^3 + 3*y^6 - 3*x^5*z + 3*x^4*y*z - x^2*y^3*z - x*y^4*z + 2*y^5*z + 3*x^4*z^2 - 2*x^3*y*z^2 - 3*y^4*z^2 + 2*x^3*z^3 + 2*x^2*y*z^3 - 2*x*y^2*z^3 - y^3*z^3 - 2*x^2*z^4 - 3*x*y*z^4 - y^2*z^4 + 2*x*z^5 + 3*y*z^5 + 2*z^6 - 1/120*x^5 + 2*x^4*y - 3*x^3*y^2 - x^2*y^3 + 3*x*y^4 - 1/29160*y^5 + x^4*z - 2*x^3*y*z - x^2*y^2*z + x*y^3*z + 3*y^4*z + 3*x^3*z^2 + x^2*y*z^2 - 3*x*y^2*z^2 + 2*y^3*z^2 - x^2*z^3 - 3*x*y*z^3 + 2*x*z^4 + y*z^4 + 2*z^5 - x^3*y + 2*x^2*y^2 - 3*x*y^3 - 3*x^2*y*z - 3*x*y^2*z - 2*x^2*z^2 + 3*y^2*z^2 + 3*x*z^3 + 3*y*z^3 + 3*x*y*z - y^2*z - 3*x*z^2 + y*z^2 + z^3]
=== (Tx) tangent pencil, point embedded at [X] ===
  [ok] (Tx) R = Y^4 + X^3*Z: QT(u=x + y), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [3*x^7 - 3*x^6*y + 3*x^5*y^2 - x^4*y^3 + x^3*y^4 + 2*x^2*y^5 - 3*x*y^6 - 2*y^7 + x^6*z + x^5*y*z + x^4*y^2*z + 2*x^3*y^3*z - x*y^5*z + 3*y^6*z - 3*x^4*y*z^2 + 3*x^3*y^2*z^2 - x^2*y^3*z^2 + x*y^4*z^2 - 2*y^5*z^2 + 3*x^4*z^3 + x^3*y*z^3 + x^2*y^2*z^3 - 3*x*y^3*z^3 + y^4*z^3 + 2*x^3*z^4 + 3*y^3*z^4 + 2*x^2*z^5 - x*y*z^5 + 3*y^2*z^5 - 2*x*z^6 - 3*y*z^6 - 2*z^7 - 1/20*x^6 - 2*x^5*y - x^4*y^2 - 3*x^3*y^3 - 2*x*y^5 - 2*y^6 - 3*x^4*y*z - 3*x^3*y^2*z - 2*x^2*y^3*z + x*y^4*z - y^5*z + x^4*z^2 + 3*x^3*y*z^2 + 3*x^2*y^2*z^2 + x*y^3*z^2 - 3*y^4*z^2 - 2*x^2*y*z^3 - x*y^2*z^3 + 3*y^3*z^3 + x^2*z^4 - x*y*z^4 + y^2*z^4 + 2*x*z^5 - 3*y*z^5 - 2*z^6 + 2*x^2*y^3 + 2*x*y^4 + 2*y^5 + 2*x^4*z + x^3*y*z - 3*x^2*y^2*z - x*y^3*z + y^4*z + 3*x^3*z^2 - x^2*y*z^2 - 2*x*y^2*z^2 - y^3*z^2 - 2*x^2*z^3 - x*y*z^3 - 3*x*z^4 + y*z^4 - z^5 + 3*x^2*y^2 - 2*x*y^3 + 1/2*y^4 - 2*x^3*z - 2*x^2*y*z - 3*x*y^2*z + 3*y^3*z + x^2*z^2 - x*y*z^2 + 3*y^2*z^2 + 2*x*z^3 + 2*y^2*z + 2*y*z^2, x^7 - x^6*y + 2*x^4*y^3 - 2*x^3*y^4 + 2*x^2*y^5 + x*y^6 - y^7 - 3*x^6*z + 2*x^5*y*z - 3*x^4*y^2*z - 3*x^2*y^4*z + 3*x*y^5*z - y^6*z - x^5*z^2 - 3*x^4*y*z^2 + 2*x^3*y^2*z^2 - x^2*y^3*z^2 + y^5*z^2 + 2*x^3*y*z^3 - 2*x*y^3*z^3 + 2*y^4*z^3 + 3*x^3*z^4 + 2*x^2*y*z^4 + 3*x*y^2*z^4 + 2*y^3*z^4 - x^2*z^5 + y^2*z^5 - 2*y*z^6 + 3*z^7 - 149/720*x^6 + 2*x^5*y - x^4*y^2 - x^3*y^3 + 3*x^2*y^4 + x*y^5 + 2*x^4*y*z - 2*y^5*z - 3*x^4*z^2 - 3*x^3*y*z^2 + 2*x^2*y^2*z^2 + x*y^3*z^2 + 3*y^4*z^2 - 2*x^2*y*z^3 - 3*x*y^2*z^3 + y^3*z^3 + x^2*z^4 + 2*x*y*z^4 + y^2*z^4 - x*z^5 - 2*y*z^5 - 3*z^6 - 2/45*x^5 - 2/9*x^4*y - x^3*y^2 + x^2*y^3 - 3*x*y^4 + 2*y^5 - 3*x^4*z + 2*x^3*y*z - 2*x^2*y^2*z + x*y^3*z + 3*y^4*z - x^3*z^2 - x^2*y*z^2 + 3*x*y^2*z^2 + y^3*z^2 + x^2*z^3 - 2*x*y*z^3 - 2*x*z^4 + 3*y*z^4 - z^5 - 2*x^2*y^2 + 2*x*y^3 + 3/4*y^4 - 3*x^3*z + 2*x^2*y*z - 3*x*y^2*z + 3*y^3*z - 2*x^2*z^2 + x*y*z^2 - 2*y^2*z^2 - 3*x*z^3 - y*z^3 - 2*z^4 + x*y*z + 3*x*z^2 - y*z^2 - 3*z^3, x^7 + x^6*y + x^5*y^2 - 2*x^4*y^3 + 2*x^3*y^4 + 3*x^2*y^5 - 2*x*y^6 + 2*y^7 - x^6*z + 2*x^5*y*z + 2*x^4*y^2*z + x^2*y^4*z + 2*x*y^5*z + 3*y^6*z - 3*x^5*z^2 + 3*x^4*y*z^2 - 3*x^3*y^2*z^2 + 2*x*y^4*z^2 + y^5*z^2 - 3*x^4*z^3 - 3*x^3*y*z^3 - 2*x^2*y^2*z^3 - 2*x*y^3*z^3 - y^4*z^3 + 2*x*y^2*z^4 + 3*y^3*z^4 + 3*x^2*z^5 - x*y*z^5 - 3*y^2*z^5 - 2*x*z^6 - 2*y*z^6 - z^7 - 17/360*x^6 + x^4*y^2 - x^3*y^3 + 3*x^2*y^4 + 3*x*y^5 + 3*y^6 + 2*x^5*z + x^4*y*z + 3*x^2*y^3*z + 2*x*y^4*z - 3*y^5*z - 2*x^4*z^2 + 2*x^3*y*z^2 - 3*x^2*y^2*z^2 + x*y^3*z^2 + 3*y^4*z^2 + 2*x^2*y*z^3 + 2*x*y^2*z^3 - 3*x^2*z^4 + 3*x*y*z^4 - y^2*z^4 - 3*z^6 - 1/45*x^5 - 1/9*x^4*y - 3*x^3*y^2 - x^2*y^3 - x*y^4 - 2*y^5 + 2*x^4*z - 3*x^3*y*z - 2*x^2*y^2*z - 2*x*y^3*z - 2*x^3*z^2 + x^2*y*z^2 - 2*x*y^2*z^2 - y^3*z^2 + x^2*z^3 + 2*x*y*z^3 - 3*y^2*z^3 - 2*x*z^4 - y*z^4 + 2*z^5 + 2*x^2*y^2 + 3*x*y^3 + 3/4*y^4 - 3*x^3*z - 2*x^2*y*z - 3*x*y^2*z + 2*y^3*z - 3*x^2*z^2 - x*y*z^2 + 2*y^2*z^2 + x*z^3 + 3*y*z^3 + z^4 + 2*x*y*z + y^2*z + 2*x*z^2 - y*z^2]
  [ok] (Tx) R = X^2*Y^2 + Y^4: QT(u=3*x + 3*y - 3*z), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-2*x^7 - 3*x^6*y + x^5*y^2 - 3*x^3*y^4 + 2*x^2*y^5 + 3*x*y^6 - x^6*z - x^5*y*z - x^4*y^2*z - 2*x^3*y^3*z - 2*x*y^5*z + y^6*z + 3*x^5*z^2 + 3*x^4*y*z^2 + 2*x^3*y^2*z^2 - x^2*y^3*z^2 - 2*x*y^4*z^2 - 3*x^4*z^3 + x^3*y*z^3 + 2*x^2*y^2*z^3 - x*y^3*z^3 - y^4*z^3 - x^3*z^4 + x^2*y*z^4 - 3*x*y^2*z^4 - 2*y^3*z^4 + 3*x^2*z^5 - 2*x*y*z^5 - 2*y^2*z^5 + 3*x*z^6 + 3*y*z^6 + 2*z^7 + 1/10*x^6 + 2*x^5*y - 3*x^4*y^2 - x^3*y^3 + x^2*y^4 - x*y^5 + y^6 + 3*x^5*z + 3*x^4*y*z + x^3*y^2*z - 3*x*y^4*z + 3*y^5*z + x^4*z^2 + x^3*y*z^2 + x^2*y^2*z^2 - 3*x*y^3*z^2 - 3*y^4*z^2 + x^3*z^3 - 3*x^2*y*z^3 + 2*x^2*z^4 + 3*x*y*z^4 + y^2*z^4 - x*z^5 + y*z^5 + z^6 + 1/30*x^5 + 1/6*x^4*y + x^3*y^2 + x^2*y^3 + 3*x*y^4 + 2*y^5 - 3*x^4*z + x^3*y*z + 2*x^2*y^2*z - y^4*z - 2*x^3*z^2 + x^2*y*z^2 - 2*x*y^2*z^2 + y^3*z^2 - 2*x^2*z^3 + 3*x*y*z^3 + y^2*z^3 + x*z^4 - 2*y*z^4 - 3*z^5 - 18*x^2*y^2 + 3*y^4 + x^3*z + 3*x^2*y*z + 3*y^3*z + 2*x^2*z^2 - 3*x*y*z^2 + 3*y^2*z^2 - 3*x*z^3 + y*z^3 + z^4 - 2*x*y*z - 2*y^2*z + 3*x*z^2 + 2*y*z^2 - z^3, -x^7 - x^6*y + 3*x^5*y^2 - x^4*y^3 - x^3*y^4 + x^2*y^5 - 2*x*y^6 - 3*y^7 - 3*x^6*z - 3*x^4*y^2*z + 2*y^6*z - 2*x^4*y*z^2 - 3*x^3*y^2*z^2 + 3*x^2*y^3*z^2 - 3*x*y^4*z^2 - 3*y^5*z^2 + 3*x^4*z^3 - 3*x^3*y*z^3 - x^2*y^2*z^3 - 2*x*y^3*z^3 - y^4*z^3 + 3*x^3*z^4 + 3*x^2*y*z^4 - 2*x*y^2*z^4 + y^3*z^4 + x^2*z^5 - 2*x*y*z^5 + 2*y^2*z^5 + 2*x*z^6 - 2*y*z^6 + 2*z^7 - 79/720*x^6 - x^5*y - 2*x^4*y^2 + x^3*y^3 - x^2*y^4 + 2*x*y^5 + 2*y^6 + 2*x^4*y*z - 2*x^3*y^2*z - 2*x^2*y^3*z + 3*y^5*z - 3*x^4*z^2 - x^3*y*z^2 - 2*x*y^3*z^2 + y^4*z^2 - 3*x^3*z^3 - 2*x*y^2*z^3 + 3*y^3*z^3 - 3*x^2*z^4 - 3*x*y*z^4 + y^2*z^4 + 2*x*z^5 + y*z^5 + 3*z^6 + 1/45*x^5 + 1/9*x^4*y - x^3*y^2 - x^2*y^3 - 2*x*y^4 - 3*y^5 - 3*x^4*z + 3*x^3*y*z - 2*x^2*y^2*z + x*y^3*z + 3*y^4*z + 3*x^3*z^2 + 3*x^2*y*z^2 + 3*x*y^2*z^2 + y^3*z^2 - x^2*z^3 + y^2*z^3 - x*z^4 - 3*y*z^4 + 2*z^5 + 12*x^2*y^2 - 2*y^4 - x^3*z + 2*x*y^2*z - 2*y^3*z - x^2*z^2 - 2*x*y*z^2 + 2*x*z^3 + 2*y*z^3 + 3*z^4 + x*y*z + y^2*z + 2*x*z^2 - 3*y*z^2 - 2*z^3, 3*x^7 - x^6*y + x^5*y^2 - 2*x^4*y^3 - 2*x^3*y^4 - x^2*y^5 - 3*y^7 - x^6*z - 2*x^4*y^2*z + x^3*y^3*z - x^2*y^4*z + x*y^5*z + 3*y^6*z - 2*x^4*y*z^2 - x^3*y^2*z^2 + 2*x^2*y^3*z^2 + 2*x*y^4*z^2 - 2*y^5*z^2 - x^4*z^3 - x^3*y*z^3 - 2*x^2*y^2*z^3 - 3*x*y^3*z^3 - y^4*z^3 + 3*x^3*z^4 - 2*x^2*y*z^4 + 3*x*y^2*z^4 + 3*y^3*z^4 + x^2*z^5 + y^2*z^5 + x*z^6 - 2*y*z^6 + z^7 - 7/72*x^6 + 2*x^5*y + 3*x^4*y^2 - 2*x^3*y^3 - 3*x^2*y^4 - x*y^5 - y^6 + 3*x^5*z - 3*x^4*y*z - x^3*y^2*z - 3*x^2*y^3*z + 3*x*y^4*z + 2*y^5*z - 3*x^4*z^2 + x^3*y*z^2 + 2*x^2*y^2*z^2 - x*y^3*z^2 + 2*y^4*z^2 + 3*x^3*z^3 + 3*x^2*y*z^3 - 3*x*y^2*z^3 - x^2*z^4 + 2*x*y*z^4 + 2*y^2*z^4 + x*z^5 + y*z^5 + 2*z^6 - 1/45*x^5 - 1/9*x^4*y + 2*x^2*y^3 + 3*x*y^4 - 2*y^5 + x^2*y^2*z - x*y^3*z + 3*y^4*z + 2*x^3*z^2 + 2*x^2*y*z^2 - 2*x*y^2*z^2 - 3*y^3*z^2 + x^2*z^3 + x*y*z^3 + 3*y^2*z^3 + 2*y*z^4 + 3*z^5 + 12*x^2*y^2 + 2*x*y^3 - 2*y^4 - 2*x^3*z - x^2*y*z - 3*y^3*z + x^2*z^2 + x*y*z^2 + y^2*z^2 + x*z^3 - 3*y*z^3 + 3*z^4 - 2*x*y*z + 2*y^2*z - 2*x*z^2 + 3*y*z^2 - 2*z^3]
  [ok] (Tx) R = X^2*Y^2 + Y^4 + X^3*Z: QT(u=-3*x - 2*y + 2*z), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-2*x^7 + x^6*y - 3*x^4*y^3 - x^3*y^4 - 2*y^7 - 3*x^6*z + 3*x^5*y*z + 3*x^4*y^2*z + 3*x^3*y^3*z - 2*x^2*y^4*z - 3*x*y^5*z + 2*y^6*z + 2*x^5*z^2 + 2*x^4*y*z^2 + 2*x^3*y^2*z^2 - 3*x*y^4*z^2 + y^5*z^2 + 3*x^4*z^3 - x^3*y*z^3 - x*y^3*z^3 - 3*y^4*z^3 + 3*x^3*z^4 + 2*x^2*y*z^4 - 2*x*y^2*z^4 + 3*y^3*z^4 - 2*x^2*z^5 + x*y*z^5 + 2*y^2*z^5 + x*z^6 + 3*y*z^6 - 3*z^7 - 17/60*x^6 - x^5*y - 2*x^4*y^2 - 3*x^3*y^3 + x^2*y^4 + x*y^5 + 2*y^6 - 2*x^3*y^2*z + 2*y^5*z - 2*x^4*z^2 - 3*x^3*y*z^2 + 3*x^2*y^2*z^2 + x*y^3*z^2 + y^4*z^2 + 3*x^3*z^3 - 2*x^2*y*z^3 - 3*x*y^2*z^3 - 3*y^3*z^3 + 2*x^2*z^4 + 2*x*y*z^4 - 3*y^2*z^4 + 2*x*z^5 + 2*y*z^5 + z^6 - 1/40*x^5 - 1/12*x^4*y + 3*x^3*y^2 - x^2*y^3 - 3*x*y^4 - 3*y^5 - 3*x^4*z + x^3*y*z - 2*x^2*y^2*z + 2*y^4*z - 2*x^2*y*z^2 - 3*x*y^2*z^2 - y^3*z^2 + x^2*z^3 - 2*y^2*z^3 - x*z^4 + 2*y*z^4 + 2*z^5 - 45/2*x^2*y^2 - x*y^3 + 3*y^4 + 3*x^3*z - 2*x^2*y*z - 3*x*y^2*z + 3*y^3*z - 2*x*y*z^2 + 3*y^2*z^2 + x*z^3 + 2*y*z^3 - 2*z^4 - 3*x*y*z + 3*y^2*z + 3*y*z^2, -x^7 + 2*x^6*y - x^5*y^2 + x^4*y^3 + 3*x^2*y^5 - x*y^6 + y^7 - 3*x^5*y*z + 3*x^4*y^2*z - 3*x^3*y^3*z - 3*x*y^5*z - y^6*z + 2*x^5*z^2 + x^4*y*z^2 - 3*x^2*y^3*z^2 - 3*x*y^4*z^2 + y^5*z^2 - x^4*z^3 + 2*x*y^3*z^3 - y^4*z^3 - 2*x^3*z^4 - x^2*y*z^4 - 3*x*y^2*z^4 + y^3*z^4 + 2*x^2*z^5 - 3*y^2*z^5 - 3*x*z^6 + y*z^6 - 2*z^7 - 11/45*x^6 - 2*x^5*y - 2*x^4*y^2 + 3*x^3*y^3 + 2*x^2*y^4 - 2*x^5*z + 3*x^4*y*z + 3*x^2*y^3*z - x*y^4*z - x^4*z^2 + x^2*y^2*z^2 - 3*y^4*z^2 + x^3*z^3 - 3*y^3*z^3 + 3*x^2*z^4 + x*y*z^4 + 3*y^2*z^4 - 3*x*z^5 - y*z^5 - 2*z^6 - 1/24*x^5 - 5/36*x^4*y + 3*x^3*y^2 + 2*x^2*y^3 - 3*y^5 + 3*x^4*z - 2*x^3*y*z + x^2*y^2*z + 3*x*y^3*z - 2*x^2*y*z^2 + y^3*z^2 - x^2*z^3 - 2*x*y*z^3 + 3*y^2*z^3 + x*z^4 - 3*y*z^4 - 2*z^5 - 33/2*x^2*y^2 - 3*x*y^3 + 2*y^4 + 3*x^3*z + 2*x^2*y*z + 2*x*y^2*z - 3*y^3*z + x^2*z^2 - 3*x*y*z^2 + 3*y^2*z^2 - 2*x*z^3 - 3*y*z^3 - z^4 - x*y*z - 2*x*z^2 - y*z^2 - z^3, -2*x^7 + x^6*y - 3*x^5*y^2 + 2*x^4*y^3 - 2*x^3*y^4 - 2*x^2*y^5 - x*y^6 + 3*y^7 - 3*x^6*z - x^5*y*z + 3*x^4*y^2*z + x^2*y^4*z - 2*x*y^5*z + y^6*z - 3*x^5*z^2 + 2*x^4*y*z^2 + 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 - 2*x*y^4*z^2 + 3*y^5*z^2 + x^4*z^3 - x^3*y*z^3 + 2*x^2*y^2*z^3 - 2*x*y^3*z^3 + y^4*z^3 + 2*x^3*z^4 - 2*x^2*y*z^4 + 3*x*y^2*z^4 - 2*y^3*z^4 + 2*x^2*z^5 - 2*x*y*z^5 + 3*y^2*z^5 + 2*y*z^6 + z^7 + 37/120*x^6 + x^5*y + 2*x^4*y^2 + 3*x^3*y^3 - 2*x^2*y^4 + 3*x*y^5 - 2*x^5*z + 2*x^4*y*z + x^3*y^2*z + 3*x^2*y^3*z - 3*x*y^4*z + 3*y^5*z - 2*x^2*y^2*z^2 + 2*y^4*z^2 + 2*x^3*z^3 + 2*x^2*y*z^3 + 2*x*y^2*z^3 - 2*y^3*z^3 + x^2*z^4 + y^2*z^4 + x*z^5 + 2*y*z^5 - 2*z^6 - 1/60*x^5 - 1/18*x^4*y + x^2*y^3 - 3*x*y^4 + 3*y^5 - 3*x^4*z - x^3*y*z - 3*x^2*y^2*z + 2*y^4*z + 3*x^3*z^2 + x^2*y*z^2 + 3*x*y^2*z^2 - 3*y^3*z^2 + 3*x^2*z^3 + 3*x*y*z^3 + 3*y^2*z^3 - y*z^4 - z^5 + 3/2*x^2*y^2 + 2*x*y^3 - y^4 + 3*x^3*z - x^2*y*z - x*y^2*z - 2*y^3*z + 3*x^2*z^2 - 3*x*y*z^2 - 2*y^2*z^2 + 3*y*z^3 - 2*z^4 - 2*y^2*z - x*z^2]
  [ok] (Tx) R = X*Y^3: QT(u=2*x + 3*y + 2*z), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [x^7 + 3*x^6*y - 2*x^5*y^2 + x^4*y^3 + 3*x^2*y^5 + x*y^6 + 2*y^7 - 2*x^6*z + 3*x^5*y*z + x^4*y^2*z + 2*x^3*y^3*z - 3*x^2*y^4*z - 2*x*y^5*z + y^6*z - 3*x^5*z^2 + 3*x^4*y*z^2 + x^3*y^2*z^2 + x^2*y^3*z^2 - 3*y^5*z^2 - x^4*z^3 + 2*x^3*y*z^3 + 3*x^2*y^2*z^3 - 2*x*y^3*z^3 + 3*y^4*z^3 + x^3*z^4 + x^2*y*z^4 - 3*x*y^2*z^4 + x^2*z^5 + 3*x*y*z^5 + x*z^6 + 2*y*z^6 - 3*z^7 - 19/720*x^6 + 2*x^4*y^2 + x^2*y^4 - 2*x^4*y*z + 3*x^3*y^2*z + 2*x*y^4*z - y^5*z + 3*x^4*z^2 - x^3*y*z^2 + 2*x^2*y^2*z^2 + 2*y^4*z^2 + 3*x^3*z^3 + 2*x^2*y*z^3 + x*y^2*z^3 + 2*x^2*z^4 + 2*y^2*z^4 + x*z^5 - 2*y*z^5 - 3*z^6 + 1/60*x^5 + 1/8*x^4*y - 3*x^3*y^2 - 3*x*y^4 - y^5 + 3*x^4*z - 3*x^3*y*z + 3*x^2*y^2*z + 2*y^4*z + x^3*z^2 + 2*x^2*y*z^2 + x*y^2*z^2 - 2*y^3*z^2 + x^2*z^3 - 2*x*y*z^3 + 3*y^2*z^3 + 3*y*z^4 - z^5 + x^2*y^2 + y^4 + 3*x^3*z + x^2*y*z + x*y^2*z + y^3*z + 2*x^2*z^2 + 3*x*y*z^2 - x*z^3 + 3*y*z^3 + 3*z^4 - 3*x*y*z - 3*y^2*z - 3*y*z^2 - 2*z^3, 2*x^7 + x^6*y - 2*x^5*y^2 - 2*x^4*y^3 - 3*x^3*y^4 - 2*x^2*y^5 - 2*x*y^6 + 3*y^7 + 3*x^6*z - 2*x^5*y*z + 3*x^4*y^2*z - x^3*y^3*z - 3*x^2*y^4*z + x*y^5*z - 2*x^5*z^2 + 2*x^4*y*z^2 - 3*x^3*y^2*z^2 - 3*x*y^4*z^2 + 2*y^5*z^2 - 2*x^4*z^3 - x^3*y*z^3 - x^2*y^2*z^3 + 2*y^4*z^3 - x^3*z^4 + 3*x^2*y*z^4 - 2*x*y^2*z^4 + 3*y^3*z^4 - 3*x*y*z^5 + 3*y^2*z^5 + x*z^6 - 3*y*z^6 - 3*z^7 + 8/45*x^6 + 2*x^5*y + x^4*y^2 - x^3*y^3 - x^2*y^4 + x*y^5 + y^6 - 3*x^5*z + x^4*y*z + 3*x^3*y^2*z + x^2*y^3*z + 2*x*y^4*z + y^5*z - x^4*z^2 - 3*x^3*y*z^2 + x^2*y^2*z^2 + 3*x*y^3*z^2 - 2*y^4*z^2 - 2*x*y^2*z^3 - 3*y^3*z^3 - 2*x^2*z^4 + 3*x*y*z^4 + y^2*z^4 - 3*x*z^5 + 3*y*z^5 + 3*z^6 + 2/45*x^5 + 1/3*x^4*y - 3*x^3*y^2 - 2*x^2*y^3 - 2*x*y^4 + 3*y^5 + 2*x^4*z + 2*x^3*y*z - 3*x^2*y^2*z - x*y^3*z - 2*y^4*z + 2*x^2*y*z^2 - y^3*z^2 - 3*x^2*z^3 - x*y*z^3 + 3*y^2*z^3 - x*z^4 - 2*y*z^4 + 2*z^5 - 2*x^2*y^2 - y^4 + 3*x^3*z + 2*x^2*y*z - x*y^2*z + y^3*z - 2*x^2*z^2 + 2*y^2*z^2 + 3*x*z^3 + 2*y*z^3 + 3*z^4 - 2*x*y*z - 2*y^2*z + 2*x*z^2 - y*z^2 - 3*z^3, -x^7 + x^6*y + x^5*y^2 - 3*x*y^6 - x^5*y*z + 2*x^4*y^2*z + 2*x^2*y^4*z - 2*x*y^5*z + 3*y^6*z + x^5*z^2 - 3*x^4*y*z^2 + 2*x^3*y^2*z^2 + 3*x^2*y^3*z^2 + x*y^4*z^2 + y^5*z^2 - 2*x^3*y*z^3 - 2*x^2*y^2*z^3 - x*y^3*z^3 + y^4*z^3 + 3*x^3*z^4 + 2*x^2*y*z^4 - 3*x*y^2*z^4 - 2*x^2*z^5 + x*y*z^5 - 3*y^2*z^5 + x*z^6 + 2*y*z^6 - 2*z^7 - 37/180*x^6 - 2*x^5*y - 3*x^4*y^2 - 2*x^3*y^3 - 3*x^2*y^4 + 2*x*y^5 - y^6 - 2*x^4*y*z - 2*x^3*y^2*z - 3*x*y^4*z + 2*y^5*z + x^3*y*z^2 - x^2*y^2*z^2 - 2*y^4*z^2 - 3*x^3*z^3 + x^2*y*z^3 + x*y^2*z^3 - 3*y^3*z^3 - 3*x*y*z^4 - 3*y^2*z^4 + 3*x*z^5 - 3*y*z^5 - 2*z^6 - 1/45*x^5 - 1/6*x^4*y + x^3*y^2 + 2*x^2*y^3 - 2*x*y^4 - y^5 - x^4*z + x*y^3*z - 3*y^4*z + x^3*z^2 - 3*y^3*z^2 - 2*x*y*z^3 + 3*y^2*z^3 - x*z^4 + y*z^4 - 3*z^5 - 3*x^2*y^2 + y^4 - 2*x^3*z - x^2*y*z + 3*y^3*z + 2*x*y*z^2 - y^2*z^2 + 3*x*z^3 - 2*y*z^3 - 2*z^4 - 2*x*y*z + y^2*z - 2*x*z^2]
  [ok] (Tx) R = X*Y^3 + X^3*Z: QT(u=-2*x + 2*y), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-3*x^7 - 2*x^5*y^2 + 3*x^3*y^4 - 2*x*y^6 + 3*y^7 + x^6*z - x^4*y^2*z + x^3*y^3*z + 3*x^2*y^4*z + 3*x^5*z^2 - 3*x^4*y*z^2 + 2*x^2*y^3*z^2 + 3*x*y^4*z^2 - 3*y^5*z^2 + 3*x^4*z^3 - x^3*y*z^3 - x*y^3*z^3 + y^4*z^3 - x^3*z^4 + 3*x*y^2*z^4 - x^2*z^5 + x*y*z^5 + x*z^6 + 3*z^7 + 13/180*x^6 - 2*x^5*y - x^4*y^2 - x^3*y^3 - x^2*y^4 - 3*x*y^5 - y^6 + x^5*z - x^4*y*z + x^3*y^2*z + 2*x^2*y^3*z - 3*x*y^4*z + y^5*z - x^4*z^2 - x^3*y*z^2 + 2*x^2*y^2*z^2 + 2*x*y^3*z^2 + 2*y^4*z^2 - 2*x^3*z^3 - 3*x^2*y*z^3 - x*y^2*z^3 - y^3*z^3 + 3*x^2*z^4 - x*y*z^4 - y^2*z^4 + 3*y*z^5 + 2*z^6 - 1/180*x^5 + 1/36*x^4*y + x^3*y^2 - 2*x^2*y^3 + x*y^4 - 3*x^4*z + 2*x^3*y*z + 3*x^2*y^2*z - 2*x*y^3*z - 3*x^3*z^2 - x^2*y*z^2 - x*y^2*z^2 - y^3*z^2 + x^2*z^3 - 2*x*y*z^3 - y^2*z^3 + 3*x*z^4 - 2*y*z^4 - 2*z^5 + 2*x^2*y^2 - 3*y^4 - x^2*y*z + 2*x*y^2*z + 3*y^3*z + 3*x^2*z^2 - 3*x*y*z^2 - 3*y^2*z^2 - 2*y*z^3 - 2*x*y*z + y^2*z - 3*x*z^2 - 2*y*z^2, x^7 + 3*x^6*y + 2*x^5*y^2 + x^3*y^4 + 2*x^2*y^5 + 2*x*y^6 + y^7 - 3*x^6*z + 2*x^5*y*z - 3*x^4*y^2*z - 2*x^3*y^3*z + 3*x^2*y^4*z + x*y^5*z + y^6*z - 3*x^4*y*z^2 - 2*x^3*y^2*z^2 - 2*x^2*y^3*z^2 + 3*y^5*z^2 + x^3*y*z^3 - 2*x^2*y^2*z^3 - 3*x*y^3*z^3 - 3*x^3*z^4 - 2*x^2*y*z^4 - y^3*z^4 + 2*x^2*z^5 - 3*x*y*z^5 - y^2*z^5 + 3*y*z^6 - z^7 - 43/720*x^6 - x^5*y - 3*x^4*y^2 + 2*x^2*y^4 + 3*y^6 + x^5*z + 3*x^4*y*z + 2*x^3*y^2*z - x^2*y^3*z + 2*x*y^4*z - y^5*z - 3*x^4*z^2 - 3*x^3*y*z^2 - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 + y^4*z^2 + 2*x^3*z^3 - x^2*y*z^3 + 2*x*y^2*z^3 - y^3*z^3 - 3*x^2*z^4 + x*y*z^4 - y^2*z^4 + 2*x*z^5 - 3*y*z^5 + 2*z^6 - 1/180*x^5 + 1/36*x^4*y + 3*x^3*y^2 - x^2*y^3 + 2*x*y^4 + 3*x^4*z - 3*x^3*y*z - x^2*y^2*z - 2*y^4*z + 3*x^3*z^2 - x^2*y*z^2 - 3*y^3*z^2 - x^2*z^3 - x*y*z^3 - 2*y^2*z^3 + 2*x*z^4 - 2*y*z^4 + 2*z^5 - x^2*y^2 - 3*x*y^3 + y^4 + 3*x^3*z - 3*x^2*y*z - x*y^2*z + y^3*z + x^2*z^2 + x*y*z^2 - 3*y^2*z^2 + 3*x*z^3 + 2*y*z^3 - 2*z^4 + x*y*z + 3*y^2*z + y*z^2 + 3*z^3, -2*x^7 + x^6*y + x^5*y^2 - x^4*y^3 - 2*x^3*y^4 - 2*x^2*y^5 - x*y^6 + 2*x^6*z + x^5*y*z - 3*x^4*y^2*z + 3*x^3*y^3*z - 2*x^2*y^4*z + 3*x*y^5*z - 2*y^6*z - 2*x^5*z^2 + 2*x^4*y*z^2 - 2*x^3*y^2*z^2 + 3*x*y^4*z^2 + 2*y^5*z^2 + x^3*y*z^3 + x^2*y^2*z^3 + 2*x*y^3*z^3 - 3*y^4*z^3 + 2*x^2*y*z^4 - 3*x*y^2*z^4 - y^3*z^4 - 3*x^2*z^5 + y^2*z^5 - 3*x*z^6 + 2*y*z^6 + 3*z^7 - 167/720*x^6 + 2*x^5*y - 3*x^4*y^2 - 3*x^3*y^3 + 3*x^2*y^4 + 2*x*y^5 + 2*y^6 + 2*x^5*z + 2*x^3*y^2*z + 2*x^2*y^3*z - 2*x*y^4*z - 2*y^5*z + x^3*y*z^2 + 2*x*y^3*z^2 - 2*x^3*z^3 - x^2*y*z^3 + x*y^2*z^3 - 3*x^2*z^4 + 3*x*y*z^4 - 3*y^2*z^4 - x*z^5 + 2*y*z^5 + 3*z^6 - 1/90*x^5 + 1/18*x^4*y - 2*x^3*y^2 + x^2*y^3 + 3*x*y^4 + 2*y^5 + x^4*z + 2*x^3*y*z - 2*x^2*y^2*z + x*y^3*z - 2*y^4*z + 3*x^3*z^2 - x*y^2*z^2 - x^2*z^3 + 2*x*y*z^3 - 2*y^2*z^3 - 2*x*z^4 - 3*z^5 + x^2*y^2 - 3*x*y^3 + y^4 + 3*x^3*z - 3*x*y^2*z + 3*y^3*z - x^2*z^2 - x*y*z^2 - 3*x*z^3 - 3*z^4 + x*y*z - 3*y^2*z - x*z^2 + 2*y*z^2]
  [ok] (Tx) R = X^2*Y^2 + X^3*Z: QT(u=x - 3*y - z), triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [-3*x^7 - x^5*y^2 + 2*x^3*y^4 + 3*x^2*y^5 - 3*x*y^6 - 3*y^7 - 2*x^6*z + 3*x^5*y*z - 2*x^4*y^2*z + x^3*y^3*z + 3*x^2*y^4*z + x*y^5*z - 2*y^6*z + 2*x^5*z^2 + x^4*y*z^2 + x^3*y^2*z^2 - 3*x^2*y^3*z^2 - x*y^4*z^2 - y^5*z^2 + x^4*z^3 - 3*x^3*y*z^3 - 2*x^2*y^2*z^3 + 3*x*y^3*z^3 + y^4*z^3 - 2*x^3*z^4 + 3*x^2*y*z^4 - x*y^2*z^4 + 3*y^3*z^4 + 2*x^2*z^5 + 2*x*y*z^5 + x*z^6 + 3*y*z^6 - 1/15*x^6 - 2*x^4*y^2 + 2*x^2*y^4 + 2*x*y^5 - 3*y^6 - x^4*y*z - x^3*y^2*z + x^2*y^3*z + 3*x^4*z^2 + 2*x^3*y*z^2 + 3*x^2*y^2*z^2 - x*y^3*z^2 + 2*y^4*z^2 - 2*x^2*y*z^3 + 2*y^3*z^3 - 3*x^2*z^4 - 3*x*y*z^4 - 3*y^2*z^4 - x*z^5 + 3*y*z^5 + 2*z^6 - 1/24*x^5 + 5/8*x^4*y + 2*x^2*y^3 + x*y^4 - 3*y^5 - x^4*z - x^3*y*z - 3*x^2*y^2*z - 3*y^4*z - 2*x^3*z^2 - 2*x^2*y*z^2 - x*y^2*z^2 + y^3*z^2 - 2*x*y*z^3 - 2*y^2*z^3 + 2*x*z^4 + y*z^4 - 3*z^5 - 3*x^2*y^2 + 3*y^4 + 2*x^3*z + 2*x^2*y*z + x*y^2*z + 3*x^2*z^2 + 3*x*y*z^2 + y^2*z^2 + 3*x*z^3 - y*z^3 + z^4 - 3*x*y*z + 3*y^2*z + y*z^2 + 2*z^3, x^7 + 2*x^6*y - x^5*y^2 + 3*x^4*y^3 - x^3*y^4 + 2*x^2*y^5 + y^7 + 3*x^6*z - 3*x^5*y*z + 3*x^4*y^2*z - 3*x^2*y^4*z - 2*x*y^5*z - 2*y^6*z + 2*x^5*z^2 + 3*x^4*y*z^2 + 3*x^3*y^2*z^2 + 3*x^2*y^3*z^2 + x*y^4*z^2 - 3*x^4*z^3 - 2*x^3*y*z^3 + x^2*y^2*z^3 + 3*x*y^3*z^3 + y^4*z^3 + 3*x^3*z^4 + 2*x^2*y*z^4 + 2*x*y^2*z^4 - x^2*z^5 - 2*x*y*z^5 - y^2*z^5 - 3*x*z^6 + y*z^6 + z^7 + 13/360*x^6 - 3*x^5*y + 3*x^4*y^2 + 3*x^3*y^3 + 3*x*y^5 - 2*y^6 + x^5*z + x^3*y^2*z + x^2*y^3*z - 3*x*y^4*z - y^5*z + 2*x^4*z^2 - x^3*y*z^2 - 3*x^2*y^2*z^2 - 2*x*y^3*z^2 - 3*y^4*z^2 + 3*x^3*z^3 + 3*x^2*y*z^3 - x*y^2*z^3 + 2*y^3*z^3 + 2*x^2*z^4 + x*y*z^4 - 3*y^2*z^4 - 2*x*z^5 + 3*y*z^5 - 1/360*x^5 + 1/24*x^4*y - 2*x^3*y^2 - x^2*y^3 + 2*x*y^4 + y^5 - 2*x^4*z + x^3*y*z + 2*x^2*y^2*z + 2*x*y^3*z - 2*y^4*z - x^3*z^2 + x*y^2*z^2 + 2*y^3*z^2 + 2*x^2*z^3 + 3*x*y*z^3 + y^2*z^3 - x*z^4 + y*z^4 + 3*x^2*y^2 - 2*x*y^3 - 2*x^3*z + 3*x^2*y*z - 3*x*y^2*z - x*y*z^2 + 2*y^2*z^2 + x*z^3 + 2*y*z^3 + z^4 + x*y*z + 2*y^2*z + x*z^2 - 3*y*z^2 + 2*z^3, -2*x^7 - 3*x^6*y - x^5*y^2 - 2*x^4*y^3 + x^3*y^4 + 3*x*y^6 + y^7 - 3*x^6*z - 3*x^3*y^3*z + 2*x^2*y^4*z - 3*x*y^5*z + 2*y^6*z + x^5*z^2 + 2*x^4*y*z^2 - x^2*y^3*z^2 - x*y^4*z^2 - 2*y^5*z^2 - x^4*z^3 - 3*x^3*y*z^3 + x^2*y^2*z^3 + 3*x*y^3*z^3 - x^2*y*z^4 - 3*y^3*z^4 + 2*x*y*z^5 + 3*y^2*z^5 + 2*x*z^6 + 3*y*z^6 - z^7 - 7/120*x^6 + 2*x^4*y^2 - 3*x^3*y^3 + 3*x*y^5 + 3*x^5*z - x^4*y*z + x^3*y^2*z - x^2*y^3*z - x*y^4*z - y^5*z - 3*x^4*z^2 - 2*x^3*y*z^2 + 3*x^2*y^2*z^2 + x*y^3*z^2 - 3*y^4*z^2 + 3*x*y^2*z^3 - 2*y^3*z^3 + 2*x^2*z^4 - 3*x*y*z^4 - y*z^5 + 2*z^6 - 1/60*x^5 + 1/4*x^4*y - 2*x^3*y^2 - 2*x^2*y^3 - x*y^4 + x^4*z - 3*x^3*y*z + 2*x^2*y^2*z + 3*x*y^3*z - 2*y^4*z + x^3*z^2 - x^2*y*z^2 - 3*x*y^2*z^2 + 2*y^3*z^2 + x^2*z^3 + x*y*z^3 - 3*y^2*z^3 - 3*x*z^4 + 3*y*z^4 + 2*z^5 - 2*x*y^3 - 3*y^4 - x^2*y*z + 2*x*y^2*z + 3*y^3*z + x*y*z^2 - y^2*z^2 - x*z^3 - 3*y*z^3 - 3*z^4 - 3*y^2*z + x*z^2 + 2*y*z^2]
=== (Ty) tangent pencil, point embedded at [Y], R = rho X^2Y^2 + Y^3Z ===
  [ok] (Ty) R = Y^3*Z: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [3*x^7 + 2*x^6*y + 2*x^5*y^2 + x^4*y^3 + x^3*y^4 + 3*x*y^6 + 3*y^7 - 2*x^6*z + 2*x^5*y*z + 2*x^4*y^2*z + 3*x^3*y^3*z + 2*x*y^5*z + 3*y^6*z - 2*x^5*z^2 + 3*x^4*y*z^2 - 2*x^3*y^2*z^2 - 3*x^2*y^3*z^2 - 3*y^5*z^2 + x^4*z^3 + 3*x^3*y*z^3 + 2*x^2*y^2*z^3 + 3*x*y^3*z^3 - 2*y^4*z^3 - 2*x^3*z^4 - x^2*y*z^4 + y^3*z^4 + x^2*z^5 - 3*x*y*z^5 + y^2*z^5 - 2*x*z^6 - 2*y*z^6 + 3*z^7 - 11/720*x^6 + 2*x^5*y - x^4*y^2 + x^3*y^3 - 3*x^2*y^4 + y^6 + 3*x^4*y*z + x^3*y^2*z - x*y^4*z + x^2*y^2*z^2 - y^4*z^2 - 3*x^3*z^3 - x^2*y*z^3 - 3*x*y^2*z^3 - 2*x^2*z^4 - x*y*z^4 + 3*y^2*z^4 + 3*y*z^5 - z^6 + 2*x^3*y^2 - x^2*y^3 + 2*x*y^4 - y^5 + 3*x^3*y*z + 3*x^2*y^2*z - 2*x*y^3*z - y^4*z - 3*x^3*z^2 - 2*x^2*y*z^2 + 2*x*y^2*z^2 + 2*y^3*z^2 - x^2*z^3 + 3*x*y*z^3 - 2*x*z^4 + y*z^4 + 3*z^5 - 3*x^2*y^2 + 3*x*y^3 - 2*y^4 - 2*x^3*z + x^2*y*z + x*y^2*z - 2*x^2*z^2 + 2*y^2*z^2 - x*z^3 - 3*z^4 - x^2*z - 3*x*y*z - 2*x*z^2 - 2*y*z^2 + 3*z^3, -x^7 + x^6*y - 2*x^5*y^2 - 2*x^4*y^3 - 3*x^3*y^4 + 2*x*y^6 + 2*y^7 + x^6*z - 3*x^5*y*z - 3*x^4*y^2*z + x^3*y^3*z + 2*x^2*y^4*z - 3*y^6*z - x^5*z^2 - 3*x^4*y*z^2 + 2*x^3*y^2*z^2 + x^2*y^3*z^2 - 2*x^4*z^3 - x^3*y*z^3 + 2*x^2*y^2*z^3 - x*y^3*z^3 - y^4*z^3 - 3*x^3*z^4 + 2*x*y^2*z^4 - y^3*z^4 + x^2*z^5 - x*y*z^5 - y^2*z^5 + x*z^6 + 3*y*z^6 + 3*z^7 - 1/144*x^6 + x^5*y + 2*x^4*y^2 + x^3*y^3 + 3*x^2*y^4 + y^6 - x^5*z + x^4*y*z - x^3*y^2*z + 3*x^2*y^3*z - x*y^4*z - y^5*z + 2*x^4*z^2 + 3*x^3*y*z^2 - x^2*y^2*z^2 + 3*x*y^3*z^2 - 3*y^4*z^2 + 3*x^2*y*z^3 + 3*x*y^2*z^3 + x^2*z^4 + x*y*z^4 - 3*y^2*z^4 + 2*x*z^5 - 2*y*z^5 - 2*z^6 - x^3*y^2 - 2*x^2*y^3 + x*y^4 - 3*y^5 - x^4*z + x^3*y*z + 2*x^2*y^2*z + 2*x*y^3*z - 3*y^4*z + 2*x^3*z^2 - 2*x*y^2*z^2 + x^2*z^3 + 3*x*y*z^3 - 3*y^2*z^3 + x*z^4 + 2*y*z^4 - z^5 + 2*x^2*y^2 + y^4 + x^3*z + 2*x^2*y*z - 3*x*y^2*z + 3*x^2*z^2 - 2*x*y*z^2 - 2*y^2*z^2 + x*z^3 + 3*y*z^3 + 3*z^4 + 3*x^2*z - x*y*z + x*z^2 - 2*y*z^2 - 3*z^3, 2*x^7 + 3*x^6*y + x^5*y^2 + x^4*y^3 + 2*x^3*y^4 - 2*x^2*y^5 + x*y^6 - 2*y^7 + 2*x^6*z + 3*x^5*y*z - 3*x^4*y^2*z - 2*x^2*y^4*z - x*y^5*z - 3*y^6*z - x^5*z^2 - x^3*y^2*z^2 + x^2*y^3*z^2 - y^5*z^2 - 2*x^4*z^3 - 3*x^2*y^2*z^3 + 3*x*y^3*z^3 + 2*y^4*z^3 + 2*x^2*y*z^4 - 3*x*y^2*z^4 - x^2*z^5 + 2*y^2*z^5 + 2*x*z^6 + 3*y*z^6 + z^7 - 1/120*x^6 - x^5*y - x^4*y^2 - x^3*y^3 - x^2*y^4 - 3*y^6 + x^5*z + 2*x^4*y*z + 3*x^3*y^2*z + x^2*y^3*z - 2*x*y^4*z - 2*y^5*z + 2*x^4*z^2 - x^3*y*z^2 - 2*x^2*y^2*z^2 + x*y^3*z^2 - 2*y^4*z^2 + 3*x^2*y*z^3 - 2*x*y^2*z^3 + 2*x^2*z^4 + 3*x*y*z^4 + 3*x*z^5 - 3*z^6 - 3*x^3*y^2 + 3*x^2*y^3 + 2*x*y^4 + 2*y^5 - x^4*z - 2*x^3*y*z + 2*x^2*y^2*z - 2*x^3*z^2 - 2*x*y^2*z^2 - 3*y^3*z^2 + 3*x^2*z^3 - 3*x*y*z^3 + 3*y^2*z^3 + 3*x*z^4 + 2*y*z^4 - 2*z^5 - 3*x^2*y^2 + x*y^3 + 3*x^2*z^2 + 3*x*y*z^2 - 2*y^2*z^2 + 3*x*z^3 + 3*z^4 + x^2*z - 2*x*z^2 - 3*y*z^2 - 2*z^3]
  [ok] (Ty) R = X^2*Y^2 + Y^3*Z: S6.2, triple in Ann, local length ds = 41, stabilization = 41, in [21,41]
      triple: [3*x^7 - 2*x^6*y + 3*x^5*y^2 + 3*x^4*y^3 - x^3*y^4 - 2*x^2*y^5 - 3*x*y^6 + 2*x^6*z + x^5*y*z - x^4*y^2*z - 2*x^3*y^3*z + x^2*y^4*z - 3*x*y^5*z + 2*y^6*z - x^3*y^2*z^2 + 2*x^2*y^3*z^2 + x*y^4*z^2 - 2*y^5*z^2 + x^4*z^3 + 2*x^3*y*z^3 + 2*x^2*y^2*z^3 + 2*x*y^3*z^3 - 2*y^4*z^3 - 2*x^3*z^4 + x^2*y*z^4 + 2*x*y^2*z^4 + y^3*z^4 - 2*x*y*z^5 + 3*x*z^6 + 2*y*z^6 - z^7 + 11/360*x^6 + 3*x^4*y^2 - x^2*y^4 - 3*x*y^5 + y^6 - x^5*z + x^4*y*z + 3*x^3*y^2*z + 2*x*y^4*z - 3*x^4*z^2 - x^3*y*z^2 - 3*x^2*y^2*z^2 - 3*x*y^3*z^2 + 2*y^4*z^2 - 3*x^2*y*z^3 + 2*x*y^2*z^3 + 2*y^3*z^3 + 3*x^2*z^4 + 2*x*y*z^4 + 3*y^2*z^4 + x*z^5 + 3*y*z^5 + 3*z^6 - x^3*y^2 + x*y^4 - 2*y^5 + 2*x^4*z - 3*x^2*y^2*z + 2*x*y^3*z - y^4*z + 2*x^3*z^2 + 2*x^2*y*z^2 - y^3*z^2 - x^2*z^3 - x*y*z^3 + 3*y^2*z^3 + x*z^4 + y*z^4 - 3*z^5 - 9/2*x^2*y^2 - y^4 + x^3*z - 2*x^2*y*z - x*y^2*z + 3*y^3*z - x*y*z^2 - 3*y^2*z^2 - x^2*z - x*y*z - 2*x*z^2 + 2*y*z^2 - 3*z^3, 3*x^7 - 2*x^6*y - 3*x^5*y^2 - 3*x^4*y^3 - 2*x^3*y^4 - 2*x^2*y^5 + 2*x*y^6 - 3*y^7 + 3*x^6*z + 3*x^5*y*z + 3*x^4*y^2*z + 3*x^3*y^3*z - 2*x*y^5*z + 2*y^6*z - x^5*z^2 - x^4*y*z^2 - 3*x^3*y^2*z^2 + 2*x^2*y^3*z^2 - y^5*z^2 + 3*x^4*z^3 + x^3*y*z^3 - x^2*y^2*z^3 - x*y^3*z^3 - 2*y^4*z^3 + x^3*z^4 - x^2*y*z^4 + 2*x*y^2*z^4 - y^3*z^4 - 3*x^2*z^5 + 3*x*y*z^5 + 3*y^2*z^5 - 3*x*z^6 - y*z^6 - 3*z^7 - 1/20*x^6 + 2*x^5*y + 2*x^4*y^2 + 3*x^3*y^3 - 3*x^2*y^4 + x*y^5 - 2*y^6 + 2*x^5*z + 3*x^4*y*z - 3*x^3*y^2*z - 3*x^2*y^3*z - 3*x*y^4*z - y^5*z + x^4*z^2 - x^3*y*z^2 + 3*x^2*y^2*z^2 - 3*y^4*z^2 - x^3*z^3 + x^2*y*z^3 + x*y^2*z^3 - 3*y^3*z^3 - x^2*z^4 + x*y*z^4 + 3*y^2*z^4 - x^3*y^2 + 2*x^2*y^3 + 3*x*y^4 + y^5 - 2*x^4*z + 2*x^3*y*z - 2*x^2*y^2*z + 2*x*y^3*z + y^4*z - x^2*y*z^2 + 3*x*y^2*z^2 - 2*y^3*z^2 + 2*x^2*z^3 + 2*y^2*z^3 + 3*x*z^4 + 3/2*x^2*y^2 + 3*x*y^3 + y^4 - 3*x^3*z + 3*x^2*y*z - 3*x*y^2*z - y^3*z + 2*x*y*z^2 - 2*y^2*z^2 - 2*z^4 - 3*x^2*z - 2*x*y*z + x*z^2 + 3*y*z^2, 2*x^7 + 3*x^6*y + x^4*y^3 + x^3*y^4 - 3*x^2*y^5 + x*y^6 + 2*y^7 - 2*x^6*z - x^4*y^2*z + 2*x^3*y^3*z - 3*x^2*y^4*z - x*y^5*z + 2*y^6*z + 2*x^5*z^2 + 3*x^4*y*z^2 + 3*x^3*y^2*z^2 - 3*x^2*y^3*z^2 - 3*x*y^4*z^2 + 2*y^5*z^2 - 3*x^4*z^3 - x^3*y*z^3 - x^2*y^2*z^3 - 3*x*y^3*z^3 - y^4*z^3 - 2*x^3*z^4 - x^2*y*z^4 - 2*y^3*z^4 + 2*x*y*z^5 - 2*x*z^6 + y*z^6 + 2*z^7 - 7/360*x^6 - 2*x^5*y - 3*x^4*y^2 - 3*x^3*y^3 - x^2*y^4 - 3*x*y^5 - y^6 - 3*x^3*y^2*z - x*y^4*z - 3*y^5*z + x^4*z^2 + x^2*y^2*z^2 + y^4*z^2 - 3*x^2*y*z^3 + 3*x*y^2*z^3 + 3*y^3*z^3 + 3*x^2*z^4 + 2*x*y*z^4 - y^2*z^4 + x*z^5 - y*z^5 - z^6 - x^3*y^2 - x^2*y^3 + 3*x*y^4 + y^5 - 3*x^3*y*z + x^2*y^2*z - 2*y^4*z + 2*x^3*z^2 - x^2*y*z^2 + x*y^2*z^2 + 2*x^2*z^3 - 3*y^2*z^3 + 2*x*z^4 - y*z^4 - 3*z^5 + 3/2*x^2*y^2 - x*y^3 - 2*y^4 - x^3*z + 3*x^2*y*z + 3*x*y^2*z - y^3*z - x^2*z^2 + x*y*z^2 + y^2*z^2 - 3*x*z^3 + y*z^3 - z^4 - x^2*z - 3*x*y*z - 3*y*z^2 + 2*z^3]
certified values: {'Tc Y^4 + Z^4': 41, 'Tc X^2*Y^2 + Y^4': 41, 'Tc X^2*Y^2 + Y^4 + Z^4': 41, 'Tc X*Y^3': 41, 'Tc X*Y^3 + Z^4': 41, 'Tc X^2*Y^2 + Z^4': 41, 'Sx': 41, 'Tx Y^4 + X^3*Z': 41, 'Tx X^2*Y^2 + Y^4': 41, 'Tx X^2*Y^2 + Y^4 + X^3*Z': 41, 'Tx X*Y^3': 41, 'Tx X*Y^3 + X^3*Z': 41, 'Tx X^2*Y^2 + X^3*Z': 41, 'Ty Y^3*Z': 41, 'Ty X^2*Y^2 + Y^3*Z': 41}
  [ok] all 15 certified values lie in [21, 41]
=== not certified here (information only): graded data and their H ===
  [info] (G) D5=<X^5,X^4Y+Z^5>  H = [1, 3, 6, 5, 3, 2, 1]
  [info] (Tc) R = Z^4  H = [1, 3, 6, 5, 3, 2, 1]
  [info] (Tc) R = Y^4  H = [1, 3, 6, 5, 3, 2, 1]
  [info] (Tc) R = X^2*Y^2  H = [1, 3, 6, 5, 3, 2, 1]
  [info] (Tx) R = X^3*Z  H = [1, 3, 6, 5, 3, 2, 1]
  [info] (Tx) R = Y^4  H = [1, 3, 6, 5, 3, 2, 1]
  [info] (Tx) R = X^2*Y^2  H = [1, 3, 6, 5, 3, 2, 1]
16 checks, 0 failed
ALL CHECKS PASSED
