Tropical Geometry

Tropical mathematics replaces + with min and × with +. A tropical polynomial f(x) = min(a₀, a₁+x, a₂+2x, …) is piecewise linear — its "tropical curve" is where two or more terms achieve the minimum simultaneously. Classical algebraic geometry degenerates into combinatorics.

Tropical zeros: x where two monomials tie for minimum

0.0
1.0
0.0
2.0
8.0