Algorithmic Computation of Polynomial Amoebas
We present algorithms for computation and visualization of polynomial amoebas, their contours, compactified amoebas and sections 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 polynomials with a fixed Newton polytope. The presented algorithms are implemented in computer algebra systems Matlab 8 and Mathematica 9.
KeywordsAmoebas Newton polytope Optimal algebraic hypersurface The contour of an amoeba Hypergeometric functions
This research was supported by the state order of the Ministry of Education and Science of the Russian Federation for Siberian Federal University (task 1.1462.2014/K), by grant of the Government of the Russian Federation for investigations under the guidance of the leading scientists of the Siberian Federal University (contract No. 14.Y26.31.0006) and by the Russian Foundation for Basic Research, projects 15-31-20008-mol_a_ved and 16-41-240764-r_a.
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