Algebraic Curve "Topology"

MAPC has been used to compute the "topology" of an algebraic plane curve. In this case, finding the "topology" means decomposing the curve over some region of the plane into monotonic segments (in both coordinate directions), and finding the connectivity between the segments. This is done using a new algorithm implemented in MAPC, and is a key portion of our code for handling curves.

We provide some examples of the output from the MAPC code. Each of the following examples shows a single algebraic curve in a region of interest. The topology algorithm subdivides the curve into a number of segments, each of which is monotonic, and determines their connectivity. The pictures show the curve (in black), several points found on the curve (in red, exaggerated in size), and the connectivity between those points (connections between adjacent points given by the green lines).