for u being non zero Element of (TOP-REAL 3)
for O being Matrix of 3,REAL
for P being Element of (ProjectiveSpace (TOP-REAL 3))
for p being FinSequence of REAL st O = symmetric_3 (1,1,(- 1),0,0,0) & P = Dir u & u = p holds
( P in absolute iff SumAll (QuadraticForm (p,O,p)) = 0 )