Tropical Geometry
Table of Contents
Study of polynomials and their geometric properties under tropical addition and tropical multiplication.
Tropical addition can be defined to be either maximum or mimumum of two number: \[ x\oplus y := \min\{x,y\} \] and the tropical multiplication is just ordinary addition: \[ x \otimes y := x + y. \]
It is like calculating the degrees of polynomials.
1. Tropical Hypersurface
A tropical curve, or more generally hypersurface, is defined to be the the set of boundaries on which the tropical polynomial is non-differentiable.