2019/05/20 by Lionel Lang, Boris Shapiro, Lang, Lionel +3
Computer Science · Engineering · #14P15 #14T05 #32A60 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1905.08056
openalex publication_date 2019/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we investigate the maximal number of intersection points of a line with the contour of hypersurface amoebas in ℝn. We define the latter number to be the ℝ-degree of the contour. We also investigate the ℝ-degree of related sets such as the boundary of amoebas and the amoeba of the real part of hypersurfaces defined over ℝ. For all these objects, we provide bounds for the respective ℝ-degrees.