Computing tropical varieties over fields with valuation using classical standard basis techniques

Abstract

In this presentation, we discuss the application of classical Gröbner basis (or standard basis) techniques to algebraic problems in polynomial rings over fields with non-trivial valuation arising in tropical geometry. The key problem we will study is the computation of a tropical variety, given its ideal in the polynomial ring. All algorithms in this presentation have been implemented in the computer algebra system Singular and are available as part of the official distribution.