Algorithmic and Quantitative Real Algebraic Geometry: DIMACS Workshop, Algorithmic and Quantitative Aspects of Real Algebraic, Geometry in Mathematics and Computer Science, March 12-16, 2001, DIMACS Center

Saugata Basu, Laureano González-Vega
American Mathematical Soc., 1. jan. 2003 - 219 sider
Algorithmic and quantitative aspects in real algebraic geometry are becoming increasingly important areas of research because of their roles in other areas of mathematics and computer science. The papers in this volume collectively span several different areas of current research. The articles are based on talks given at the DIMACS Workshop on ''Algorithmic and Quantitative Aspects of Real Algebraic Geometry''. Topics include deciding basic algebraic properties of real semi-algebraic sets, application of quantitative results in real algebraic geometry towards investigating the computational complexity of various problems, algorithmic and quantitative questions in real enumerative geometry, new approaches towards solving decision problems in semi-algebraic geometry, as well as computing algebraic certificates, and applications of real algebraic geometry to concrete problems arising in robotics and computer graphics. The book is intended for researchers interested in computational methods in algebra.

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Constructive approaches to representation theorems in finitely generated
Lower bounds and real algebraic geometry
The Viro method applied with quadratic transforms
How to show a set is not algebraic
Patterns of dependence among powers of polynomials
Efficient algorithms based on critical points method
Enumerative real algebraic geometry
Combinatorial roadmaps in configuration spaces of simple planar polygons
From discrete algorithms to real algebraic geometry

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