Solving polynomial systems

Tuesday, October 24, 2006 - 1:40pm - 2:30pm
Jan Verschelde (University of Illinois, Chicago)
PHCpack is a software package for Polynomial Homotopy Continuation to numerically solve polynomial systems. In the past five years, the package has been extended with tools to compute a numerical irreducible decomposition. Other features include deflation for isolated singularities and an equation-by-equation solver.
Most recently, PHCpack has been extended with a translation of the program MixedVol (by Tangan Gao, Tien-Yien Li, Mengnien Wu) to compute mixed volumes and define polyhedral homotopies more efficiently.
Monday, October 23, 2006 - 1:40pm - 2:30pm
Charles Wampler (General Motors Corporation)
It has been approximately twenty years since the initial germination of
numerical continuation as an approach to finding solution points of systems
of polynomial equations and ten years since its flowering into numerical
algebraic geometry, which facilitates description of solution sets of any
dimension and operations on these, such as intersection and fiber products.
We will attempt to step back from the torrent of recent developments to
sketch out the big picture of what a general software package for numerical
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