Mathematics Mechanization

Title page
Preface
Part I Historical Developments
Chapter I 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 II Historical Development of Geometry Theorem-Proving and Geometry Problem-Sol ving 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
Part II Principles and Methods
Chapter III Algebraic Varieies as Zero-Sets and Characteristic-Set Method
§3.1 Affine and Projective Space Extended Points and Specialization
§3.2 Algebraic Varieties and Zero-Sets
§3.3 Polsets and Ascending Sets. Partial Ordering
§3.4 Characteristic Set of a Polset and the Well-Ordering Principle
§3.5 Zero-Decomposition Theorems
§3.6 Variety-Decomposition Theorems
Chapter IV 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 Ideal
§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 V 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
Part III Applications and Examples
Chapter VI 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 VII Applications 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 VIII Diverse Applications
§8.1 Applications to Automated Discovering of Unknown Relations and Automated Determination of Geometry Loci
§8.2 Applications to Problems Involving Inequalities, Optimization Problems, and NonLinear 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