Analysis and Its Applications 12, no. 1 (1978): 38–46. ]]>

1. The number of interior points of the Newton polygon is the genus of the surface.

2. One can find a basis for the holomorphic 1-forms using the Newton polygon.

]]>I tried your algorithm for some simple examples, but it gave no out output, meaning it didn’t stop. Does it work only only for hexgonal circle configurations?

For example the following vertices-edge file produces no result:

21

4 1 2 3 4

7 0 3 4 5 6 7 8

7 0 3 4 17 18 19 20

7 0 1 2 5 9 13 17

7 0 1 2 8 12 16 20

4 1 3 6 9

4 1 5 7 10

4 1 6 8 11

4 1 4 7 12

4 3 5 10 13

4 6 9 11 14

4 7 10 12 15

4 4 8 11 16

4 3 9 14 17

4 10 13 15 18

4 11 14 16 19

4 4 12 15 20

4 2 3 13 18

4 2 14 17 19

4 2 15 18 20

4 2 4 16 19

Best :)

]]>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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