Mathematics mechanization and applications
著者
書誌事項
Mathematics mechanization and applications
Academic Press, c2000
大学図書館所蔵 全6件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 Part of the theoretical and practical work reviewed in the book has been either unpublished or published only in Chinese journals or even only in the Chinese language.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.
目次
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.
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