Algorithmic Computation of Polynomial Amoebas

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9890)

Abstract

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.

Keywords

Amoebas Newton polytope Optimal algebraic hypersurface The contour of an amoeba Hypergeometric functions 

Notes

Acknowledgements

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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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • D. V. Bogdanov
    • 1
  • A. A. Kytmanov
    • 2
  • T. M. Sadykov
    • 1
  1. 1.Plekhanov Russian UniversityMoscowRussia
  2. 2.Siberian Federal UniversityKrasnoyarskRussia

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