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

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

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 p...

Ausführliche Beschreibung

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Bibliographische Detailangaben
Hauptverfasser: Bates, Daniel J, Brake, Daniel A, Hao, Wenrui, Hauenstein, Jonathan D, Sommese, Andrew J, Wampler, Charles W
Format: Report
Sprache:eng
Schlagworte:
ALGEBRAIC GEOMETRY
ALGEBRAIC TOPOLOGY
ALGORITHMS
COMPUTER PROGRAMS
NUMERICAL ANALYSIS
Numerical Mathematics
PE61101E
POLYNOMIALS
WUAFRL100011Y0VW
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Beschreibung
Zusammenfassung: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. Sponsored in part by DARPA.