Computing the Newton polygon of the implicit equation

Autor:	Emiris, Ioannis Z., Konaxis, Christos, Palios, Leonidas
Rok vydání:	2008
Předmět:	Mathematics - Algebraic Geometry Mathematics - Combinatorics 14H50 (Primary) 14Q05 52B20 (Secondary)
Druh dokumentu:	Working Paper
Popis:	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. Comment: 21 pages, 9 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0811.0103 Zobrazit plný text záznamu View this record from Arxiv