The degree of a tropical basis
Michael Joswig, Benjamin Schr\"oter
TL;DR
This paper provides an explicit upper bound for the degree of tropical bases of homogeneous polynomial ideals and discusses properties of tropical varieties, highlighting differences from Gr"obner bases.
Contribution
It introduces a new explicit upper bound for tropical basis degrees and explores the structure of tropical varieties with illustrative examples.
Findings
Established an explicit degree bound for tropical bases.
Analyzed differences between Gr"obner and tropical bases.
Discussed properties of tropical varieties and their f-vectors.
Abstract
We give an explicit upper bound for the degree of a tropical basis of a homogeneous polynomial ideal. As an application f-vectors of tropical varieties are discussed. Various examples illustrate differences between Gr\"obner and tropical bases.
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