Real Numerical Algebraic Geometry: Finding All Real Solutions of a Polynomial System.

摘要

This project resulted in software and algorithms for computing the real solution of polynomial systems contained within complex curves and surfaces. The primary product was Bertini Real, a publicly available software package for these computations. Secondary products included four articles, all in progress. These articles document the algorithms developed during the reporting period, including (1) a complete algorithm in the case of complex surfaces with no restricitons on the type of surface; (2) a technical article on the theory underlying and algorithm for finding critical points; (3) an article on Bertini Real; and (4) an article on the real numerical irreducible decomposition.