Graduate Computational Algebraic Geometry Seminar
Jan Verschelde
UIC
Polyhedral Methods for Space Curves Exploiting Symmetry Applied to the Cyclic n-roots Problem
Abstract: We present a polyhedral algorithm to manipulate positive dimensional
solution sets. Using facet normals to Newton polytopes as pretropisms,
we focus on the first two terms of a Puiseux series expansion.
The leading powers of the series are computed via the tropical
prevariety.
This polyhedral algorithm is well suited for exploitation of symmetry,
when it arises in systems of polynomials. Initial form systems with pretropisms in the same group orbit are solved only once, allowing for a systematic
filtration of redundant data.
Computations with cddlib, Gfan, PHCpack, and Sage
are illustrated on cyclic n-roots polynomial systems.
Thursday September 5, 2013 at 4:00 PM in SEO 1227