Computing Amoebas

DOI10.1080/10586458.2002.10504703zbMath1100.14048OpenAlexW4247126636MaRDI QIDQ5472047

Thorsten Theobald

Publication date: 14 June 2006

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/52814

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Real polynomials: location of zeros (26C10) Topology of real algebraic varieties (14P25)

Related Items

Amoebas of Cuspidal Strata for Classical Discriminant, Degenerations of amoebae and Berkovich spaces, Describing amoebas, Mahler measure for a quiver symphony, Computing the connected components of the complement to the amoeba of a polynomial in several complex variables, Amoeba-shaped polyhedral complex of an algebraic hypersurface, A survey on computational aspects of polynomial amoebas, On amoebas of algebraic sets of higher codimension, Metric estimates and membership complexity for Archimedean amoebae and tropical hypersurfaces, The Phaseless Rank of a Matrix, A nullstellensatz for amoebas, Tropical algebraic geometry in Maple: a preprocessing algorithm for finding common factors for multivariate polynomials with approximate coefficients, Lopsided approximation of amoebas, Zeros and amoebas of partition functions, Random polynomials with prescribed Newton polytope, Algorithmic Computation of Polynomial Amoebas, Approximating amoebas and coamoebas by sums of squares, Tropical varieties for exponential sums, Neurons on amoebae

Uses Software

• Macaulay2

Cites Work

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• The complexity of elementary algebra and geometry
• Solving systems of polynomial inequalities in subexponential time
• Real solving for positive dimensional systems.
• Real algebraic curves, the moment map and amoebas
• Laurent determinants and arrangements of hyperplane amoebas
• Computing the Equations of a Variety
• Algorithm 795