Invariant Methods in Discrete and Computational Geometry : Proceedings of the Curaçao Conference, 13–17 June, 1994

Invariant, or coordinate-free methods provide a natural framework for many geometric questions. __Invariant Methods in Discrete and____Computational Geometry__ provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the Grassmann-Cayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. __Audience:__ Researchers studying mathematics, computers and robotics. Front Matter....Pages i-xiii The Power of Positive Thinking....Pages 1-36 Introduction to Chow Forms....Pages 37-58 Capelli’s Method of Variabili Ausiliarie , Superalgebras and Geometric Calculus....Pages 59-75 Letterplace Algebra and Symmetric Functions....Pages 77-91 A Tutorial on Grassmann-Cayley Algebra....Pages 93-106 Computational Symbolic Geometry....Pages 107-139 Invariant Theory and the Projective Plane....Pages 141-166 Automatic Proving of Geometric Theorems....Pages 167-196 The Resolving Bracket....Pages 197-222 Computation of the Invariants of a Point Set in P 3 from Its Projections in P 2 ....Pages 223-244 Geometric Algebra and Möbius Sphere Geometry as a Basis for Euclidean Invariant Theory....Pages 245-256 Invariants on G/U x G/U x G/U, G = SL(4,C)....Pages 257-277 On a Certain Complex Related to the Notion of Hyperdeterminant....Pages 279-288 On Cayley’s Projective Configurations an Algorithmic Study....Pages 289-299 On the Construction of Equifacetted 3-Spheres....Pages 301-312 Depths and Betti Numbers of Homology Manifolds....Pages 313-321 Back Matter....Pages 323-328 Invariant, or coordinate-free methods provide a natural framework for many geometric questions. Invariant Methods in Discrete and Computational Geometry provides a basic introduction to several aspects of invariant theory, including the supersymmetric algebra, the Grassmann-Cayler algebra, and Chow forms. It also presents a number of current research papers on invariant theory and its applications to problems in geometry, such as automated theorem proving and computer vision. Audience: Researchers studying mathematics, computers and robotics. Proceedings of the Curaçao Conference, 13--17 June, 1994