Mathematics Mechanization(精)

The present book is a collection of essays centred around the subject of mathematical mechanization. It tries to deal with mathematics in a constructive and algorithmic manner so that reasoning becomes mechanical, automated and less labourious. This book is divided into three parts. Part I concerns historical developments of mathematics mechanization, especially in ancient China. Part II describes the underlying principles of polynomial equations-solving, with polynomial coefficients in fields restricted to the case of characteristic O. Based on the general principle, some methods of solving such arbitrary polynomial systems may be found. This part also goes back to classical Chinese mathematics as well as treating modern works in this field. Finally, Part III contains applications and examples. Audience This volume will be of interest to research and applied mathematicians, computer scientists and historians in mathematics.

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-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
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

The present book is actually a collection of essays by the author since 1977 centered around the subject which has been baptized mathematics mechanization. The subject tries to deal with mathematics in a constructive and algorithmic man- ner so that the reasonings become mechanical, automated, and as much as possible to be intelligence-lacking, with the result of lessening the painstaking heavy brain- labor. The desire of getting mathematics mechanized or more generally of getting all kinds of reasonings automated, may be traced..