## 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 CenterAlgorithmic 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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### Indhold

Constructive approaches to representation theorems in finitely generated | 13 |

Lower bounds and real algebraic geometry | 35 |

The Viro method applied with quadratic transforms | 55 |

How to show a set is not algebraic | 77 |

Patterns of dependence among powers of polynomials | 101 |

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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Algorithmic and Quantitative Real Algebraic Geometry: DIMACS Workshop ... Saugata Basu Begrænset visning - 2003 |

### Almindelige termer og sætninger

algorithm alignment apply approach assume basic bodies called closed coefficients combinatorial compact complexity computation condition Conjecture connected components consider constructible contains convex coordinates corresponding critical points curve decision defined DEFINITION degree denote described dimension edge Editors elements embedding enumerative equations Euler example exists Figure finite fixed four functions geometry given gives graph hence Henneberg implies inequalities intersection Lemma linear lines lower bound Math Mathematics mechanism meeting method Note obtain optimal particular plane points polygon polynomial positive possible problem projective proof prove pseudo-triangulation question rational real algebraic set real solutions REMARK representation result roots satisfies Schubert semialgebraic set semidefinite programming shows simple singular smooth solutions solving space spheres step subset Suppose tangent Theorem topological transverse trees variables varieties vertex vertices visibility