Polyhedral Methods for Space Curves Exploiting Symmetry
Applied to the Cyclic n-roots Problem
Jan Verschelde
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.
This is joint work with Danko Adrovic.
the 15th International Workshop on Computer Algebra in Scientific
Computing, CASC 2013, 9-13 September 2013, Berlin, Germany
slides of the talk