Algorithmic Computation of Polynomial Amoebas

Abstract

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