Computing the Newton polygon of the implicit equation

Details Computing the Newton polygon of the implicit equation Computing the Newton polygon of the implicit equation

2008-11-03

arxiv.org/abs/0811.0103v1

Mathematics

Algebraic Geometry

21 pages, 9 figures

Scientific paper

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.

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