  binary c=3: Gr(3,7)=12, lower bound 15, sigma=0 part 15, syzygetic <= 14
  binary c=2: Gr(3,8)=15, lower bound 18, sigma=0 part 18, syzygetic <= 16
  concise: lower bound 23, strata {6: 23, 5: 21, 4: 20, 3: 20};  pure: lower bound 42, sigma=0 part 42, strata sigma=1,2,3: {1: 40, 2: 40, 3: 36}
PASS (C) counts: in each of the three incidences every stratum other than the open one has dimension < the lower bound  [0.0s]
PASS (L) (dim H, dim S_1 H, syzygy kernel) = (7, 12, 9) (Z three collinear points), (8, 13, 11) (Z two points), (9, 14, 13) (I(p)_3)  [0.1s]
PASS (A0) concise F = XYZ(XY+XZ+YZ): h = 6, W = <x^3,y^3,z^3> in Ann(F)_3, H = [1, 3, 6, 7, 3, 1], local length 27, residual 6  [2.7s]
  binary, Z = three points (F = X^5+Y^5+(X+Y)^5): c = 3, dim Ann(F)_3 = 7, binary generator of Ann(F) besides z: [(-1) * y * (x - y) * x]
PASS (A1) binary, Z = three points (F = X^5+Y^5+(X+Y)^5): Ann(F)_3 = (z, g)_3 with g binary of degree 3  [2.7s]
  binary, Z = three points (F = X^5+Y^5+(X+Y)^5): trial 1 local length None
PASS (A1) binary, Z = three points (F = X^5+Y^5+(X+Y)^5): W = [2*x^2*z - x*y*z + 3*y^2*z - 2*y*z^2 - 5*z^3, -x^2*y + x*y^2 - 3*x^2*z - 3*x*y*z - 4*y^2*z + 3*x*z^2 + 5*y*z^2, -5*x^2*y + 5*x*y^2 - 4*x^2*z + x*y*z - 4*y^2*z - 3*x*z^2 - y*z^2 + 2*z^3], L = x + y - 2*z; local length 33 <= 41 (stable N = 9); Lemma 3.5 member: H = [1, 3, 6, 7, 3, 1], residual 12  [10.4s]
  binary, Z = double + simple point (F = X^4Y + Y^5): c = 3, dim Ann(F)_3 = 7, binary generator of Ann(F) besides z: [x * y^2]
PASS (A1) binary, Z = double + simple point (F = X^4Y + Y^5): Ann(F)_3 = (z, g)_3 with g binary of degree 3  [10.4s]
PASS (A1) binary, Z = double + simple point (F = X^4Y + Y^5): W = [-3*x*y^2 + 2*x^2*z + 2*x*y*z - 3*y^2*z - 2*x*z^2 + y*z^2 - z^3, x*y^2 + 4*x^2*z + 5*x*y*z - 5*y^2*z - 3*x*z^2 - 2*y*z^2 + 3*z^3, -5*x*y^2 - 2*x^2*z + 5*x*z^2 + 5*y*z^2 - z^3], L = 4*x - 2*y - z; local length 33 <= 41 (stable N = 9); Lemma 3.5 member: H = [1, 3, 6, 7, 3, 1], residual 12  [16.3s]
  binary, Z = triple point (F = X^3Y^2): c = 3, dim Ann(F)_3 = 7, binary generator of Ann(F) besides z: [y^3]
PASS (A1) binary, Z = triple point (F = X^3Y^2): Ann(F)_3 = (z, g)_3 with g binary of degree 3  [16.3s]
PASS (A1) binary, Z = triple point (F = X^3Y^2): W = [-x^2*z - 2*y^2*z + 2*x*z^2 - 3*y*z^2 - 3*z^3, -y^3 - 4*x^2*z + 3*x*y*z + y^2*z + 4*x*z^2 - 2*y*z^2 + 3*z^3, 5*y^3 - 3*x^2*z - 5*x*y*z + 4*y^2*z + x*z^2], L = x + 2*y + 4*z; local length 33 <= 41 (stable N = 9); Lemma 3.5 member: H = [1, 3, 6, 7, 3, 1], residual 12  [22.0s]
  binary, Z = two points (F = X^5+Y^5): c = 2, dim Ann(F)_3 = 8, binary generator of Ann(F) besides z: [y * x]
PASS (A1) binary, Z = two points (F = X^5+Y^5): Ann(F)_3 = (z, g)_3 with g binary of degree 2  [22.0s]
PASS (A1) binary, Z = two points (F = X^5+Y^5): W = [2*x^2*y - 5*x*y^2 + 4*x^2*z + 3*y^2*z + 2*x*z^2 + 5*y*z^2 + 3*z^3, 2*x^2*y - 2*x*y^2 - 4*x*y*z - 5*y^2*z - 4*x*z^2 - 5*y*z^2 + 5*z^3, 3*x^2*y - 2*x*y^2 - x^2*z - 5*x*y*z - 5*y^2*z + x*z^2 - 5*y*z^2 - 4*z^3], L = -2*x - 2*y + z; local length 31 <= 41 (stable N = 9); Lemma 3.5 member: H = [1, 3, 6, 7, 3, 1], residual 10  [27.0s]
  binary, Z = double point (F = X^4Y): c = 2, dim Ann(F)_3 = 8, binary generator of Ann(F) besides z: [y^2]
PASS (A1) binary, Z = double point (F = X^4Y): Ann(F)_3 = (z, g)_3 with g binary of degree 2  [27.1s]
PASS (A1) binary, Z = double point (F = X^4Y): W = [-3*x*y^2 - 5*y^3 + 5*x^2*z + 3*x*y*z - 3*y^2*z - x*z^2 + y*z^2, -3*x*y^2 + 4*y^3 + x^2*z + 5*x*y*z - 5*y^2*z - 4*x*z^2 - 3*y*z^2 - z^3, -x*y^2 + 3*y^3 - 5*x^2*z + 2*x*y*z - 5*y^2*z + 3*x*z^2 + 4*y*z^2], L = 2*x - 5*y - z; local length 31 <= 41 (stable N = 9); Lemma 3.5 member: H = [1, 3, 6, 7, 3, 1], residual 10  [31.5s]
PASS (A1) pure, F = X^5, W in I(p)_3: W = [-2*x^2*y - 5*x*y^2 - y^3 - x^2*z + 3*y^2*z + 2*x*z^2 - 4*y*z^2, 3*x^2*y + 3*x*y^2 + 2*y^3 - 4*x^2*z - 3*x*y*z - 3*y^2*z - x*z^2 - 3*y*z^2 - z^3, x*y^2 - 5*y^3 - 3*x^2*z + x*y*z - 5*y^2*z + x*z^2 + 4*y*z^2 - 4*z^3], L = x - 5*y - 2*z; local length 29 <= 41 (stable N = 9); Lemma 3.5 member: H = [1, 3, 6, 7, 3, 1], residual 8  [38.8s]
total time 38.8 s
ALL CHECKS PASSED
