Author: Eiko
Time: 2025-04-05 05:02:42 - 2025-04-05 05:02:42 (UTC)
Introduction To Tropical Geometry
Tropical Numbers
The tropical semiring, depending on convention, is defined as
where is the maximum and is classical addition,
where is the minimum and is classical addition,
We will follow the second convention.
Tropical Polynomials
The tropical monomials are understood as a classical function . To distinguish tropical numbers and classical numbers, we suggest sometimes we use to denote a tropical number , and make a convention that
- If either an expression involves , or a bracket contained number , we understand the entire expression as tropical, e.g. and .
A tropical polynomial is understood as a tropical sum of tropical monomials.
which evaluates as the function
which is