Computer Algebra Methods in Tropical Geometry

Tropical geometry is a young field of mathematics which allows to study properties of objects from algebraic geometry with the aid of methods from discrete mathematics, like convex geometry and combinatorics. There are different ways to introduce tropical varieties and to derive the connection between these and their algebraic counterparts.We use a way, where the connection is concrete and where Grobner basis techniques can be used to to establish it in both directions.