RandomCurveOfGenus9WithPencilOfDegree8 -- construction of genus 9 curves together with degree 8 maps to P^1

Using the method of Unirationality of the Hurwitz space H_{9,8} we construct a plane curve C of degree 8 and genus 9 together with a map f: C -> P^1.

Constructions

• randomPlanePoints -- Find random plane points.
• randomCurveOfGenus9WithPencilOfDegree8 -- construct such curve

Verifications

• distinctPoints -- Does the ideal defines an plane curve with ordinars double points?
• ordinaryDoublePoints -- Does the ideal defines an plane curve with ordinars double points?
• simpleRamification -- Does the pencil defines a map to P^1 with simple ramification?
• verifyAllAssertionsOfThePaper -- Print the commands needed to verify all assertions