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 CenterSaugata Basu, Laureano González-Vega American Mathematical Soc., 2003年1月1日 - 219 頁 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. |
內容
| 1 | |
Constructive approaches to representation theorems in finitely generated | 13 |
Combinatorial characterizations of algebraic sets | 23 |
223 | 52 |
On the number of connected components of the relative closure of | 65 |
How to show a set is not algebraic | 77 |
Efficient algorithms based on critical points method | 123 |
Enumerative real algebraic geometry | 139 |
Combinatorial roadmaps in configuration spaces of simple planar polygons | 181 |
From discrete algorithms to real algebraic geometry | 207 |
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algebraic computation trees algorithm alignment event archimedean B₁ basic Betti numbers coefficients combinatorial common tangent lines compact condition Conjecture 5.1 connected components constructible functions convex hull coordinates critical points curve decision complexity defined Degree Bound denote dimension embedding enumerative geometry enumerative problems equations Euler characteristic example exists fewnomial finite given Grassmannian Gröbner bases Gröbner basis Henneberg homeomorphic homotopy implies inequalities integer intersection irreducible k-planes Laman graph Lemma linear lower bound Math Mathematics matrix method monomials number of connected number of real optimal Pfaffian planar plane Plücker coordinates polygon polynomial systems positive preprime proof quadratic rational normal curve Real Algebraic Geometry real algebraic set real numbers real solutions representation result Schubert calculus Schubert varieties semi-Pfaffian set semialgebraic set semidefinite programming singular solving space subset subspaces sum of squares Theorem topological transverse triangular set triangulation variables vertex vertices