# Quadratic tropical varieties

This page is still under heavy construction. Expect massive updates.

In light of the two leading candidates for the title of "tropical variety", we need to distinguish two competing (cooperating?) notions of tropical conics: 1) bend loci defined by quadratic tropical polynomials; and 2) congruence varieties defined by quadratic tropical equations.

# Quadratic bend varieties

The bendy option for tropical conics is the bend locus of a quadratic tropical polynomial. Focusing on plane conics, these are the bend loci of polynomials of the form

(INSERT EXAMPLES OF EVERY TYPE, ALONG WITH AARON'S CONDITIONS FOR EACH TYPE)

# Quadratic congruence varieties

The congruence option for tropical conics is the congruence variety of a quadratic tropical equation, i.e., an equation of the form

(INSERT A BUNCH OF EXAMPLES)