吴文俊全集 数学机械化 1PDF电子书下载

查看更多关于的内容

Chapter 1 Polynomial Equations-Solving in Ancient Times，Mainly in Ancient China 1

1.1 A Brief Description of History of Ancient China and Mathematics Classics in Ancient Chin 1

1.2 Polynomial Equations-Solving in Ancient China 9

1.3 Polynomial Equations-Solving in Ancient Times beyond China and the Program of Descartes 24

Chapter 2 Historical Development of Geometry Theorem-Proving and Geometry Problem-Solving in Ancient Times 31

2.1 Geometry Theorem-Proving from Euclid to Hilbert 31

2.2 Geometry Theorem-Proving in the Computer Age 43

2.3 Geometry Problem-Solving and Geometry Theorem-Proving in Ancient China 47

Chapter 3 Algebraic Varieties as Zero-Sets and Characteristic-Set Method 65

3.1 Affine and Projective Space Extended Points and Specialization 65

3.2 Algebraic Varieties and Zero-Sets 73

3.3 Polsets and Ascending Sets Partial Ordering 85

3.4 Characteristic Set of a Polset and Well-Ordering Principle 93

3.5 Zero-Decomposition Theorems 104

3.6 Variety-Decomposition Theorems 117

Chapter 4 Some Topics in Computer Algebra 130

4.1 Tuples of Integers 130

4.2 Well-Arranged Basis of a Polynomial Ideal 137

4.3 Well-Behaved Basis of a Polynomial Ideal 143

4.4 Properties of Well-Behaved Basis and its Relationship with Groebner Basis 151

4.5 Factorization and GCD of Multivariate Polynomials over Arbitrary Extension Fields 161

Chapter 5 Some Topics in Computational Algebraic Geometry 172

5.1 Some Important Characters of Algebraic Varieties Complex and Real Varieties 172

5.2 Algebraic Correspondence and Chow Form 186

5.3 Chern Classes and Chern Numbers of an Irreducible Algebraic Variety with Arbitrary Singularities 197

5.4 A Projection Theorem on Quasi-Varieties 205

5.5 Extremal Properties of Real Polynomials 214

Chapter 6 Applications to Polynomial Equations-Solving 227

6.1 Basic Principles of Polynomial Equations-Solving：The Char-Set Method 227

6.2 A Hybrid Method of Polynomial Equations-Solving 237

6.3 Solving of Problems in Enumerative Geometry 249

6.4 Central Configurations in Planet Motions and Vortex Motions 259

6.5 Solving of Inverse Kinematic Equations in Robotics 271

Chapter 7 Appicaltions to Geometry Theorem-Proving 283

7.1 Basic Principles of Mechanical Geometry Theorem-Proving 283

7.2 Mechanical Proving of Geometry Theorems of Hilbertian Type 294

7.3 Mechanical Proving of Geometry Theorems involving Equalities Alone 309

7.4 Mechanical Proving of Geometry Theorems involving Inequalities 320

Chapter 8 Diverse Applications 334

8.1 Applications to Automated Discovering of Unknown Relations and Automated Determination of Geometric Loci 334

8.2 Applications to Problems involving Inequalities，Optimization Problems，and Non-Linear Programming 346

8.3 Applications to 4-Bar Linkage Design 356

8.4 Applications to Surface-Fitting Problem in CAGD 364

8.5 Some Miscellaneous Complements and Extensions 373

Bibliography 395

Index 406

查看更多关于的内容