Algebraic Curves

Curves from algebraic geometry given as solution of a polynomial equation. This section lists numerically computed solutions. The number of unknowns may be arbitrary.

A planar algebraic curve is the solution set of a polynomial equation

F(x,y) = 0

where x and y are the unknowns. Planar examples are straight lines and cone sections.

The degree of the polynomial F is called the order of the algebraic curve. The order of a planar algebraic curve is the maximal number of intersection points with a straight line. If F is reducible into two factors F = GH then the algebraic curve F = 0 is the union of the two curves G = 0 and H = 0 and is called reducible.

References

  1. Egbert Brieskorn, Horst Knörrer: Plane Algebraic Curves, Birkhäuser Verlag, Basel-Boston (1986).
  2. R.J. Walker: Algebraic Curves, Springer Verlag, Berlin-New York (1978).

Technical Note

As a guide, polygons should be connected, no degenerate edges, no duplicate vertices.