9781332173013 - on the 'piano movers' problem: ii. general techniques for computing topological properties of ral algebraic manifolds (classic reprint) di schwartz, jacob t. (3 risultati)
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Paperback. Condizione: New. Print on Demand. This book details the mathematical foundations upon which pivot and non-pivot motions of a body can be calculated in a given configuration space. The work continues the discussion begun in the author's earlier publication, and presents general techniques for computing various topologi…cal properties of real algebraic manifolds, with an emphasis on identifying necessary and sufficient conditions for the existence of an uninhibited motion of one or more bodies in a designated space. The author shows that this problem can be handled by a refinement of methods pioneered by Tarski and Collins, leading to algorithms that are polynomial in the geometric complexity of the problem, for each fixed number of degrees of freedom, but exponential in the number of degrees of freedom. The author's method also provides a general (but not polynomial-time) procedure for calculating all the homology groups associated with an arbitrary real algebraic variety and other general topological properties. Various algorithmic issues concerning computations with algebraic numbers, which are required in the algorithms in this book, are also covered. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item.
