  ok   (v-a) sample 0: actual algebra closed with HF [1, 3, 6, 5, 4, 1, 1] (embedded point at [X] on the line z = 0, a = -3/2)
  ok   (v-a) sample 0: family closed over QQ(t), top pivot minor 76, fibre at 0 = M, fibre at 1/3 closed HF [1, 3, 6, 5, 4, 1, 1]; base scheme at 1/3: [[z], [y, x - 3*z]] (the line z = 0 and one reduced point off it: True)
  ok   (v-b) sample 0: actual algebra closed with HF [1, 3, 6, 5, 4, 1, 1] (a = 0, c = 3)
  ok   (v-b) sample 0: family closed over QQ(t), top pivot minor -35, fibre at 0 = M, fibre at 1/3 closed HF [1, 3, 6, 5, 4, 1, 1] with a = 1/3 != 0
  ok   (v-a) sample 1: actual algebra closed with HF [1, 3, 6, 5, 4, 1, 1] (embedded point at [X] on the line z = 0, a = 1/2)
  ok   (v-a) sample 1: family closed over QQ(t), top pivot minor -66, fibre at 0 = M, fibre at 1/3 closed HF [1, 3, 6, 5, 4, 1, 1]; base scheme at 1/3: [[z], [y, x - 3*z]] (the line z = 0 and one reduced point off it: True)
  ok   (v-b) sample 1: actual algebra closed with HF [1, 3, 6, 5, 4, 1, 1] (a = 0, c = -3)
  ok   (v-b) sample 1: family closed over QQ(t), top pivot minor 738, fibre at 0 = M, fibre at 1/3 closed HF [1, 3, 6, 5, 4, 1, 1] with a = 1/3 != 0
  ok   (v-a) sample 2: actual algebra closed with HF [1, 3, 6, 5, 4, 1, 1] (embedded point at [X] on the line z = 0, a = 4/3)
  ok   (v-a) sample 2: family closed over QQ(t), top pivot minor -20, fibre at 0 = M, fibre at 1/3 closed HF [1, 3, 6, 5, 4, 1, 1]; base scheme at 1/3: [[z], [y, x - 3*z]] (the line z = 0 and one reduced point off it: True)
  ok   (v-b) sample 2: actual algebra closed with HF [1, 3, 6, 5, 4, 1, 1] (a = 0, c = 1/3)
  ok   (v-b) sample 2: family closed over QQ(t), top pivot minor 18, fibre at 0 = M, fibre at 1/3 closed HF [1, 3, 6, 5, 4, 1, 1] with a = 1/3 != 0
  ok   (v-a) sample 3: actual algebra closed with HF [1, 3, 6, 5, 4, 1, 1] (embedded point at [X] on the line z = 0, a = -2)
  ok   (v-a) sample 3: family closed over QQ(t), top pivot minor -90, fibre at 0 = M, fibre at 1/3 closed HF [1, 3, 6, 5, 4, 1, 1]; base scheme at 1/3: [[z], [y, x - 3*z]] (the line z = 0 and one reduced point off it: True)
  ok   (v-b) sample 3: actual algebra closed with HF [1, 3, 6, 5, 4, 1, 1] (a = 0, c = 3)
  ok   (v-b) sample 3: family closed over QQ(t), top pivot minor -156, fibre at 0 = M, fibre at 1/3 closed HF [1, 3, 6, 5, 4, 1, 1] with a = 1/3 != 0
  ok   accepted: (v-a) 4 of 4, (v-b) 4 of 4
checks: 17
ALL CHECKS PASSED
