--- matrix printed in gpolep.pdf ---
{'name': 'Eremenko printed [[z^2,1,z,0],[z+1,z^2,1,z]]', 'maxdeg': 4, 'gcddeg': 0, 'rankM': 5, 'dimU': 2, 'form': (Fraction(1, 1), Fraction(1, 1), Fraction(-1, 1)), 'disc': Fraction(5, 1), 'verdict': 'two real L', 'lead_on_U': [Fraction(1, 1), Fraction(0, 1)]}
--- complex-curve example v=(1+i z^2, z) ---
{'name': '[[1,z^2,z,0],[-z^2,1,0,z]]', 'maxdeg': 4, 'gcddeg': 0, 'rankM': 4, 'dimU': 2, 'form': (Fraction(1, 1), Fraction(0, 1), Fraction(1, 1)), 'disc': Fraction(-4, 1), 'verdict': 'NO real L', 'lead_on_U': [Fraction(0, 1), Fraction(0, 1)]}
--- sign variants of the printed matrix with NO real L ---
128 of 256 sign patterns (z^2,1,z ; 1,z,z^2,1,z) give no real L; examples:
   [[z^2,1,z,0],[z+1,-z^2,1,z]] -3
   [[z^2,1,z,0],[z+1,-z^2,1,-z]] -3
   [[z^2,1,z,0],[z+1,-z^2,-1,z]] -3/4
   [[z^2,1,z,0],[z+1,-z^2,-1,-z]] -3/4
   [[z^2,1,z,0],[-z+1,-z^2,1,z]] -3/4
   [[z^2,1,z,0],[-z+1,-z^2,1,-z]] -3/4
   [[z^2,1,z,0],[-z+1,-z^2,-1,z]] -3
   [[z^2,1,z,0],[-z+1,-z^2,-1,-z]] -3
  single sign change at position 0 [[-z^2,1,z,0],[z+1,z^2,1,z]] -> NO real L disc -3/4 maxdeg 4 rankM 5
  single sign change at position 1 [[z^2,-1,z,0],[z+1,z^2,1,z]] -> NO real L disc -3 maxdeg 4 rankM 5
  single sign change at position 2 [[z^2,1,-z,0],[z+1,z^2,1,z]] -> two real L disc 5/4 maxdeg 4 rankM 5
  single sign change at position 3 [[z^2,1,z,0],[z-1,z^2,1,z]] -> NO real L disc -3 maxdeg 4 rankM 5
  single sign change at position 4 [[z^2,1,z,0],[-z+1,z^2,1,z]] -> two real L disc 5/4 maxdeg 4 rankM 5
  single sign change at position 5 [[z^2,1,z,0],[z+1,-z^2,1,z]] -> NO real L disc -3 maxdeg 4 rankM 5
  single sign change at position 6 [[z^2,1,z,0],[z+1,z^2,-1,z]] -> two real L disc 5/4 maxdeg 4 rankM 5
  single sign change at position 7 [[z^2,1,z,0],[z+1,z^2,1,-z]] -> two real L disc 5 maxdeg 4 rankM 5
--- corrected example [[z^2,1,z,0],[z-1,z^2,1,z]] ---
{'name': 'corrected: [[z^2,1,z,0],[z-1,z^2,1,z]]', 'maxdeg': 4, 'gcddeg': 0, 'rankM': 5, 'dimU': 2, 'form': (Fraction(1, 1), Fraction(1, 1), Fraction(1, 1)), 'disc': Fraction(-3, 1), 'verdict': 'NO real L', 'lead_on_U': [Fraction(-1, 1), Fraction(0, 1)]}
   minors (I: coefficients low->high): {'12': [1, -1, 0, 0, 1], '13': [0, 1], '14': [0, 0, 0, 1], '23': [1, 0, 0, -1], '24': [0, 1], '34': [0, 0, 1]}
   ker M spanned by y = ['0', '-1', '0', '0', '1', '0']  Klein form value = 1 (non-zero => complex non-degenerate)
