Algorithmic computation of polynomial amoebas

TL;DR

This paper introduces algorithms for computing and visualizing polynomial amoebas, including methods for handling complex topologies and implementations in Matlab and Mathematica.

Contribution

It provides novel algorithms for computing and visualizing amoebas and their topologies, including a method for generating polynomials with maximally complex amoeba topologies.

Findings

Algorithms successfully compute and visualize amoebas and their contours.

Implementation in Matlab and Mathematica enables practical use.

Method for generating polynomials with complex amoeba topology demonstrated.

Abstract

We present algorithms for computation and visualization of amoebas, their contours, compactified amoebas and sections of three-dimensional amoebas by two-dimensional planes. We also provide method and an algorithm for the computation of~polynomials whose amoebas exhibit the most complicated topology among all polynomials with a fixed Newton polytope. The presented algorithms are implemented in computer algebra systems Matlab 8 and Mathematica 9.