• Collect test cases

• Evaluate different algorithms for speed

• Evaluate different algorithms for different types of curve

• split GeoCubic into GeoCubic, GeoQuartic, ..., GeoImplicit as appropriate depending on investigations of algorithms

At the moment GeoCubic handles polynomials power x³y³ and lower

• Intersection of Lines and Implicits (already implemented for cubics and for vertical/horizontal lines and x³y³ and lower

• Extend Asymptote[ ] command to implicit polynomials

Self-contained project that can be done at the end if there's time / interest

• Extend to inequalities, eg x⁴ + y⁴ < 1