arXiv subjects
Publications and source records attributed to D. V. Bogdanov.
With any integer convex polytope $P\subset\midR^n$ we associate a multivariate hypergeometric polynomial whose set of exponents is $\midZ^{n}\cap P.$ This polynomial is defined uniquely up to a constant multiple and satisfies a holonomic system of partial differential equations of Horn's type. We prove that the zero locus of any such polynomial is optimal in the sense of Forsberg-Passare-Tsikh.
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.