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- W2184800845 abstract "We develop an incremental algorithm to compute the Newton polytope of the resultant, aka resultant polytope, or its projection along a given direction. Our algorithm exactly computes vertex- and halfspacerepresentations of the resultant polytope using an oracle producing resultant vertices in a given direction. It is output-sensitive as it uses one oracle call per vertex. We implement our algorithm using the experimental CGAL package triangulation. A variant of the algorithm computes successively tighter inner and outer approximations: when these polytopes have, respectively, 90% and 105% of the true volume, runtime is reduced up to 25 times. Compared to tropical geometry software, ours is faster up to dimensions 5 or 6, and competitive in higher dimensions. Compared to lrs, cdd, and polymake, the computation of convex hull is fastest along with polymake. The resultant is fundamental in algebraic elimination and in implicitizing parametric hypersurfaces: we compute the Newton polytope of surface equations in < 1sec, when there are < 100 terms in the parametric polynomials, which includes all common instances in geometric modeling. Our method computes instances of 5, 6 or 7-dimensional polytopes with 35K, 23K or 500 vertices, respectively, in < 2hr." @default.
- W2184800845 created "2016-06-24" @default.
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- W2184800845 date "2012-01-01" @default.
- W2184800845 modified "2023-09-27" @default.
- W2184800845 title "Exact and approximate algorithms for resultant polytopes" @default.
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