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| MATHEMATICS MECHANIZATION AND APPLICATIONS
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Edited By
Dongming Wang, Laboratoire LEIBNIZ Institut IMAG, France
Xiao-Shan Gao, Institute of Systems Science, Academica Sinica, China
Description
Mathematics Mechanization and Applications provides a uniform presentation of major developments, carried out mostly
in Wu's extended Chinese group, on algorithms and software tools for mechanizing algebraic equations solving and geometric theorem proving
together with their applications to problems in science and engineering. It is distinguished by its uniform presentation with all-Chinese
contributors and a 40-page list of references. There are 20 chapters written by experienced researchers. The book is divided into four
parts: polynomial system solving, automated geometric reasoning, algebraic computation, and implementations and applications. Each chapter
is devoted to surveying and expounding the main results achieved from one selected subject. The book contains surveys for diverse applications
of the theories and methods to real world problems, ranging from the analysis of robotics and mechanisms to nonlinear programming and
chemical equilibrium computation. Part of the theoretical and practical work reviewed in the book has been either unpublished or published
only in Chinese journals or even only in the Chinese language. This book therefore provides Western readers working in symbolic and algebraic
computation, geometric reasoning and modeling, algorithmic mathematics, robotics, CAGD, and other relevant areas with an easily accessible
source of references for what the Chinese researchers have been doing under the banner of mathematics mechanization.
Audience
Researchers, practitioners and graduate students in symbolic and algebraic computation, geometric reasoning, authomated theorem proving,
algorithmic mathematics, and computer-aided mathematical problem solving; researchers and university teachers in computer-aided instruction
and education; and software developers, researchers and engineers in mechanics, computer-aided geometric design, geometric modeling,
robotics, and computer vision.
Contents
Preface. List of Contributors.
Polynomial System Solving
: W. Wu, The Characteristic Set Method and Its Application. D. Wang, Some Algorithms for Zero Decomposition of Polynomial Systems. S. Zhang, G. Feng, The Eigenvalue Approach to
Polynomial System. S.Wang, K. Wu, Solving the Yang-Baxter Equation by Wu's Method.
Automated Geometric Reasoning
: S. Chou, D. Lin, Wu's Method for Automated Geometry Theorem Proving and Discovering. H. Li, Mechanical Theorem Proving
in Differential Geometry. J. Zhang, Points Elimination Methods for Geometric Problem Solving. H. Li, Clifford Algebra
Approaches to Mechanical Geometry Theorem Proving. X. Hou, Proving by Examples. X. Gao, Search Methods Revisited. J.
Wu, First-Order Polynomial Based Theorem Proving.
Algebraic Computation
: Z. Li, Greatest Common Right
Divisors, Least Common Left Multiples, and Subresultants of Ore Polynomials. L. Zhi, Algebraic Factorization and GCD Computation. X. Gao, Conversion Between Implicit and Parametric Representations of Algebraic Varieties.
Implementations and Applications
: Z. Lu, S. Ma, Centers, Foci, and Limit Cycles for Polynomial Differential Systems. Z. Li, Exact Solitary Wave Solutions
of Non-linear Evolution Equations. H. Zhang, E. Fan, Applications of Mechanical Methods to Partial Differential Equations. Q.
Liao, Equation Solving in Robotics and Mechanisms. G. Feng, H. Ren, Y. Zhou, Blending Several Implicit Algebraic Surfaces. S. Chou, X. Gao, Z. Liu, D-K Wang, D. Wang, Geometric Theorem Provers and Algebraic Equation Solvers. References. Index.
| Bibliographic details |
Hardbound, 551 pages, publication date: JUL-2000
ISBN-13: 978-0-12-734760-8
ISBN-10: 0-12-734760-7
Imprint: ACADEMIC PRESS
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| Price and Ordering |
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USD 195
EUR 143
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Last update: 12 Jun 2009
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