吴文俊全集 数学机械化卷I
作者：吴文俊 著；高小山编订
出版时间：2019年版
内容摘要
本卷收录了吴文俊的Mathematics Mechanization:Mechanical Geometry Theorem-Proving，Mechanical Geometry Problem-Solving and Polynomial Equations-Solving一书。本书是围绕作者命名的“数学机械化”这一中心议题而陆续发表的一系列论文的综述。本书试图以构造性与算法化的方式来研究数学，使数学推理机械化以至于自动化，由此减轻繁琐的脑力劳动。全书分成三个部分：部分考虑数学机械化的发展历史，特别强调在古代中国的发展历史。第二部分给出求解多项式方程组所依据的基本原理与特征列方法。作为这一方法的基础，本书还论述了构造性代数几何中的若干问题。第三部分给出了特征列方法在几何定理证明与发现、机器人、天体力学、全局优化和计算机辅助设计等领域中的应用。
目录
Chapter 1 Polynomial Equations-Solving in Ancient Times， Mainly in Ancient China
1.1 A Brief Description of History of Ancient China and Mathematics Classics in Ancient China
1.2 Polynomial Equations-Solving in Ancient China
1.3 Polynomial Equations-Solving in Ancient Times beyond China and the Program of Descartes
Chapter 2 Historical Development of Geometry Theorem-Proving and Geometry Problem-Solving in Ancient Times
2.1 Geometry Theorem-Proving from Euclid to Hilbert
2.2 Geometry Theorem-Proving in the Computer Age
2.3 Geometry Problem-Solving and Geometry Theorem-Proving in Ancient China
Chapter 3 Algebraic Varieties as Zero-Sets and Characteristic-Set Method
3.1 Affine and Projective SpaceExtended Points and Speization
3.2 Algebraic Varieties and Zero-Sets
3.3 Polsets and Ascending SetsPartial Ordering
3.4 Characteristic Set of a Polset and Well-Ordering Principle
3.5 Zero-Decomposition Theorems
3.6 Variety-Decomposition Theorems
Chapter 4 Some Topics in Computer Algebra
4.1 Tuples of integers
4.2 Well-Arranged Basis of a Polynomial Ideal
4.3 Well-Behaved Basis of a Polynomial Idea l
4.4 Properties of Well-Behaved Basis and its Relationship with Groebner Basis
4.5 Factorization and GCD of Multivariate Polynomials over Arbitrary Extension Fields
Chapter 5 Some Topics in Computational Algebraic Geometry
5.1 Some Important Characters of Algebraic Varieties Complex and Real Varieties
5.2 Algebraic Correspondence and Chow Form
5.3 Chern Classes and Chern Numbers of an Irreducible Algebraic Variety with Arbitrary Singularities
5.4 A Projection Theorem on Quasi-Varieties
5.5 Extremal Properties of Real Polynomials
Chapter 6 Applications to Polynomial Equations-Solving
6.1 Basic Principles of Polynomial Equations-Solving: The Char-Set Method
6.2 A Hybrid Method of Polynomial Equations-Solving
6.3 Solving of Problems in Enumerative Geometry
6.4 Central Configurations in Planet Motions and Vortex Motions
6.5 Solving of Inverse Kinematic Equations in Robotics
Chapter 7 Appicaltions to Geometry Theorem-Proving
7.1 Basic Principles of Mechanical Geometry Theorem-Proving
7.2 Mechanical Proving of Geometry Theorems of Hilbertian Type
7.3 Mechanical Proving of Geometry Theorems involving Equalities Alone
7.4 Mechanical Proving of Geometry Theorems involving Inequalities
Chapter 8 Diverse Applications
8.1 Applications to Automated Discovering of Unknown Relations and Automated Determination of Geometric Loci
8.2 yApplications to Problems involving Inequalities， Optimization Problems， and Non-Linear Programming
8.3 Applications to 4-Bar Linkage Design
8.4 Applications to Surface-Fitting Problem in CAGD
8.5 Some Miscellaneous Complements and Extensions
Bibliography
Index
