2008/11/03 by Ioannis Z. Emiris, Emiris, Ioannis Z., Christos Konaxis +3
Computer Science · Engineering · Mathematics · #14H50 (Primary) 14Q05 #52B20 (Secondary) #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Mathematics and Applications #Polynomial and algebraic computation #math.AG #math.CO #msc:14H50 #msc:14Q05 #msc:52B20
paper · pdf · doi:10.48550/arxiv.0811.0103
21 pages, 9 figures
arxiv created 2008/11/03 · openalex publication_date 2008/11/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider polynomially and rationally parameterized curves, where the polynomials in the parameterization have fixed supports and generic coefficients. We apply sparse (or toric) elimination theory in order to determine the vertex representation of its implicit polygon, i.e. of the implicit equation's Newton polygon. In particular, we consider mixed subdivisions of the input Newton polygons and regular triangulations of point sets defined by Cayley's trick. We distinguish polynomial and rational parameterizations, where the latter may have the same or different denominators; the implicit polygon is shown to have, respectively, up to 4, 5, or 6 vertices.