| dc.description.abstract | The main topic of this thesis is the tropical semiring. We discuss tropical
addition and multiplication and what the graphs of polynomials, defined using
this type of addition and multiplication, look like. We will discuss the notion
of a tropical amoeba and how Voronoi diagrams relate to this notion. We will
also consider power diagrams, a type of generalization of the Voronoi diagram,
and look at their relation to tropical amoebas. We will show that every tropical
polynomial defines a power diagram and, even better, also a Voronoi diagram.
We will also approach tropical geometry from the view of algebraic geometry.
We discuss the notion of an amoeba in algebraic geometry and consider the spine
of this amoeba. Finally we will show how the spine of an amoeba relates to the
tropical amoeba | |
