Tropical geometry: Difference between revisions
no edit summary
(→Applications: improved wording) 

: <math>x \otimes y = x + y.</math>
So for example, the classical polynomial <math>x^3 + 2xy + y^4</math> would become <math>\min
Tropical geometry is a variant of [[algebraic geometry]] in which polynomial graphs resemble [[piecewise linear manifoldpiecewise linear]] meshes, and in which numbers belong to the [[tropical semiring]] instead of a field. Because classical and tropical geometry are closely related, results and methods can be converted between them. Algebraic varieties can be mapped to a tropical counterpart and, since this process still retains some geometric information about the original variety, it can be used to help prove and generalize classical results from algebraic geometry, such as the [[Brill–Noether theorem]], using the tools of tropical geometry.<ref>{{Cite weburl=https://www.quantamagazine.org/tinkertoymodelsproducenewgeometricinsights20180905/title=Tinkertoy Models Produce New Geometric Insightslast=Hartnettfirst=Kevinwebsite=[[Quanta Magazine]]accessdate=20181212}}</ref>
