Suppose I give a random 2 variable polynomial relation such as:
$$x^3+y^3=10$$
$$x^2 + 7yx^4 + x^2-15=0$$
Etc...
How do I determine how many individual pieces there are to the graph?
2026-04-12 23:41:41.1776037301
Connected component identification?
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Turns out this is a great question. So great, that it is one of the Hilbert questions. See this page for an intro on the subject. It's been solved in some settings, but some parts remain open. It's fun stuff.