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- Creation of affine and projective curves together with the
ambient affine and projective planes
- Basic manoeuvres between affine and projective curves: projective
closure, affine patches and so on
- Basic scheme-type functions: e.g., irreducibility
- Specialised data types for distinct classes of curves such as
elliptic curves
- Linear systems of curves in the projective plane with assigned
basepoints
- Implicitization of parametric curves
- Parametrization of rational curves
- Global invariants of curves, such as genus and dimension
- Function field and divisor computations for plane curves (see below)
Next: Curves: Local Analysis
Up: General Algebraic Curves
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