PASS (F) secant X^5+Y^5: 2 point(s) with P^4 in S_1 o F; dim S_2 o F = 2, dim Ann(F)_3 = 8  [0.2s]
PASS (F) tangent X^4Y: 1 point(s) with P^4 in S_1 o F; dim S_2 o F = 2, dim Ann(F)_3 = 8  [0.2s]
PASS (F) rank three X^5+Y^5+(X+Y)^5: 0 point(s) with P^4 in S_1 o F; dim S_2 o F = 3, dim Ann(F)_3 = 7  [0.2s]
PASS (A) secant F = X^5+Y^5: Ann(F)_3 = J_3 (dim 8); w1 = 2*x^2*y + 4*x*y^2 + x^2*z + 2*y^2*z + 2*x*z^2 + 5*y*z^2 + z^3, w2 = x^2*y + 5*x*y^2 + 4*x^2*z + 7*x*y*z - 3*x*z^2 + 3*y*z^2 + 4*z^3 coprime; H = [1, 3, 6, 8, 2, 1]; local length 40 < 42 (stable N = 10); residual 19, H = [1, 3, 6, 8, 1]  [11.2s]
PASS (A) tangent F = X^4Y: Ann(F)_3 = J_3 (dim 8); w1 = x*y^2 - 2*y^3 - 3*x^2*z + x*y*z - 5*y^2*z - 2*x*z^2 - y*z^2 + 5*z^3, w2 = 3*x*y^2 - 2*y^3 - 2*x^2*z + 5*x*y*z + 7*y^2*z - 3*x*z^2 + 4*y*z^2 - 4*z^3 coprime; H = [1, 3, 6, 8, 2, 1]; local length 40 < 42 (stable N = 10); residual 19, H = [1, 3, 6, 8, 1]  [21.7s]
  anchor lengths: 40 40
PASS (A3) Ann(F)_3 contains exactly one binary cubic g = -x^2*y + x*y^2  [21.7s]
PASS (A3) W = <g+z^3, z l^2> coprime in Ann(F)_3, graded module H = (1,3,6,8,2,1), local length of (w1,w2,q) = 36 = 36  [21.9s]
PASS (S1) actual rank-three binary members with random tails: (f1,f2,f3) of orders 3,3,4 local length 36 in 6 of 6 samples  [249.1s]
PASS (S2) F = X^5: M = M' + <G,G'> with M' closed, H(M') = (1,3,6,6,2,1), in 4 of 4 samples  [249.6s]
total time 249.6 s
ALL CHECKS PASSED
