Mathematics Mechanization Book

	Preface
Ch. I	Polynomial Equations-Solving in Ancient Times, Mainly in Ancient China	3
1.1	A Brief Description of History of Ancient China and Mathematics Classics in Ancient China	3
1.2	Polynomial Equations-Solving in Ancient China	12
1.3	Polynomial Equations-Solving in Ancient Times beyond China and the Program of Descartes	27
Ch. II	Historical Development of Geometry Theorem-Proving and Geometry Problem-Solving in Ancient Times	34
2.1	Geometry Theorem-Proving from Euclid to Hilbert	34
2.2	Geometry Theorem-Proving in the Computer Age	45
2.3	Geometry Problem-Solving and Geometry Theorem-Proving in Ancient China	50
Ch. III	Algebraic Varieies as Zero-Sets and Characteristic-Set Method	69
3.1	Affine and Projective Space Extended Points and Specialization	69
3.2	Algebraic Varieties and Zero Sets	78
3.3	Polsets and Ascending Sets. Partial Ordering	89
3.4	Characteristic Set of a Polset and the Well-Ordering Principle	98
3.5	Zero-Decomposition Theorems	109
3.6	Variety-Decomposition Theorems	121
Ch. IV	Some Topics in Computer Algebra	133
4.1	Tuples of Integers	133
4.2	Well-Arranged Basis of a Polynomial Ideal	139
4.3	Well-Behaved Basis of a Polynomial Ideal	146
4.4	Properties of Well-Behaved Basis and its Relationship with Groebner Basis	153
4.5	Factorization and GCD of Multivariate Polynomials over Arbitrary Extension Fields	163
Ch. V	Some Topics in Computational Algebraic Geometry	173
5.1	Some Important Characters of Algebraic Varieties Complex and Real Varieties	173
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
Ch. VI	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	250
6.4	Central Configurations in Planet Motions and Vortex Motions	259
6.5	Solving of Inverse Kinematic Equations in Robotics	271
Ch. VII	Applications 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	308
7.4	Mechanical Proving of Geometry Theorems Involving Inequalities	318
Ch. VIII	Diverse Applications	334
8.1	Applications to Automated Discovering of Unknown Relations and Automated Determination of Geometry Loci	334
8.2	Applications to Problems involving Inequalities, Optimization Problems, and NonLinear Programming	346
8.3	Applications to 4-Bar Linkage Design	355
8.4	Applications to Surface-Fitting Problem in CAGD	362
8.5	Some Miscellaneous Complements and Extensions	371
	Bibliography	392
	Index	403