
TL;DR
This paper studies almost-toric hypersurfaces, characterizes their Newton polytopes, and introduces an algorithm to compute their implicit equations efficiently.
Contribution
It provides a detailed description of the Newton polytope for almost-toric hypersurfaces and develops a novel algorithm for implicitization.
Findings
Newton polytope of almost-toric hypersurfaces characterized
Algorithm for implicit equation computation proposed
Enhanced understanding of hypersurface parameterizations
Abstract
An almost-toric hypersurface is parameterized by monomials multiplied by polynomials in one extra variable. We determine the Newton polytope of such a hypersurface, and apply this to give an algorithm for computing the implicit equation.
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