(1)-(4): types of Gamma with sigma_X = 1; random P of rank two and rank one; tail-map rank; members  [set_random_seed(1364411) at the start]
reduced {X,Y,Z,X+Y+Z}              length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
reduced, three collinear with X    length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
collinear reduced                  length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 1, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
double at X (dir Y) + 2 points     length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
curvilinear 3 on conic + point     length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
curv 3 tangent to Xq               length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=y): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
curv 3 on a line + point           length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
curv 3 on a line + point on it     length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 1, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
curv 4 on conic                    length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=y): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
curv 4 cusp-type                   length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=y): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
curv 4 on a line                   length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 1, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
two double points                  length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
fat point elsewhere + X            length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=y): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
CI (y^2,z^2) at X                  length 4, nu3 4, nu4 4, K5 6 | random P: rank beta 2, tail-map rank 18, member closed True H [1, 3, 6, 4, 4, 1, 1] | rank-one P (h=z): beta 1, tail-map 18, H [1, 3, 6, 4, 4, 1, 1]
   OK
(5) reduced Gamma: the sheared ray (y - a/30 x^2, z - b/30 x^2), exact colon test (I : L) not in I + L
   {X,Y,Z,X+Y+Z}              sheared ray: True; straight ray (y,z): False
   {X,Y,Z,X+Y+Z}              sheared ray: True; straight ray (y,z): False
   {X,X+Y,Y,Z}                sheared ray: True; straight ray (y,z): False
   {X,X+Y,Y,Z}                sheared ray: True; straight ray (y,z): False
   collinear {X,X+Y,Y,X+2Y}   sheared ray: True; straight ray (y,z): False
   collinear {X,X+Y,Y,X+2Y}   sheared ray: True; straight ray (y,z): False
   random                     sheared ray: True; straight ray (y,z): False
   random                     sheared ray: True; straight ray (y,z): False

ALL CHECKS PASSED
