First, where does the degree 7 come from?

Second, if I wanted to see if ABx (the x-coordinate of A intersect B) equals ACx (the x-coordinate of A intersect C, where ABx = P/Q (a rational function of degree at most 7) and ACx = R/S ( a rational function of degree at most 7), then I can check if P*S = R*Q, where each side of the equation is polynomial of at most degree 14. So why is it not 15 points (degree of polynomial + 1)?

I hope you are still around.

Can you give a couple of key references for symmetric cubic forms in Projective Real Differential Geometry of Surfaces where i can find the geometric interpretation for the regular curves along which the cubic form vanish?

I hope this question makes sense for you.

Have in mind the quadratic case: second fundamental form and the asymptotic curves on a surface.

Thanks in advance,

Jorge

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