===== b=1: v=(1+i z^2, z) : b = 1 (m,p) = (2,2)
  v_j = x_j + i y_j with x = [[1], [0, 1]]  y = [[0, 0, 1], []]
  rank of the 4b x (b+1)^2 system: 4  dim K_v = 0 (expected (b-1)^2 = 0 )
  K_v = {0}: NO real L.   CERTIFIED
===== b=2: v=(i z, 1+i z^4, 1+z^2+i z^3) : b = 2 (m,p) = (2,4)
  v_j = x_j + i y_j with x = [[], [1], [1, 0, 1]]  y = [[0, 1], [0, 0, 0, 0, 1], [0, 0, 0, 1]]
  rank of the 4b x (b+1)^2 system: 8  dim K_v = 1 (expected (b-1)^2 = 1 )
  K_v spanned by H0 with Re = [['4', '0', '0'], ['0', '2', '0'], ['0', '0', '-2']]  Im = [['0', '-1', '1'], ['1', '0', '1'], ['-1', '-1', '0']]
  v^* H0 v = c z^{4b} with c = 2 ; inertia of H0 (pos,neg,zero) = (2, 1, 0)
  rank H0 = 3 -> NO real L.   CERTIFIED
===== b=3: random small integers, seed 2029 : b = 3 (m,p) = (2,6)
  v_j = x_j + i y_j with x = [[1, 1, -1, -1, 1, 2, 2], [-1, 0, 0, 2, 1, 1, 1], [1, 2, -1, 0, -2, 2, -2], [1, -1, -1, -2, 2, -1, -2]]  y = [[2, -2, 1, 0, 0, 2, 2], [0, 2, -2, -2, -2, -1, -1], [0, 1, 1, 0, 1, 0, 1], [-1, -2, 1, -2, 1, -2, 1]]
  rank of the 4b x (b+1)^2 system: 12  dim K_v = 4 (expected (b-1)^2 = 4 )
  number of real cubic generators (Re/Im of 3x3 minors): 16
   degree 3 : Macaulay rank mod p = 16 of 20
   degree 4 : Macaulay rank mod p = 34 of 35
   degree 5 : Macaulay rank mod p = 56 of 56
  => no nonzero complex t with rank H(t) <= 2: NO real L.   CERTIFIED
ALL CERTIFIED
