m,p,n = 2 4 8  number of minors 15  max degree 8  gcd degree 0
rank M = 9 (need 9 )
dim U = 7 (expected 7 )
restricted quadric positive definite: True
pivots (floats): [2.4125812604878236, 1.0756806080743484, 4.509617591637614, 0.5352210512489185, 0.4095530788724561, 0.5964852850617159, 0.7185832322385592]
complex non-degeneracy: dim ker M = 6  Macaulay degree 4  rank mod p = 126  #monomials = 126
RESULT: in Q(m,m+p): True | rank M = n+1: True | PD certificate (no real solution, incl. degenerate): True | complex non-degenerate: True
ALL CHECKS PASSED
