# Mathematics Mechanization and Applications

**Edited by**

- Dongming Wang, Laboratoire LEIBNIZ Institut IMAG, France
- Xiao-Shan Gao, Institute of Systems Science, Academica Sinica, China

**Mathematics Mechanization and Applications** provides a uniform presentation of major developments, carried out mostly in Wu's extended Chinese group, on algorithms and software tools for mechanizing algebraic equations solving and geometric theorem proving together with their applications to problems in science and engineering. It is distinguished by its uniform presentation with all-Chinese contributors and a 40-page list of references. There are 20 chapters written by experienced researchers. The book is divided into four parts: polynomial system solving, automated geometric reasoning, algebraic computation, and implementations and applications. Each chapter is devoted to surveying and expounding the main results achieved from one selected subject. The book contains surveys for diverse applications of the theories and methods to real world problems, ranging from the analysis of robotics and mechanisms to nonlinear programming and chemical equilibrium computation. Part of the theoretical and practical work reviewed in the book has been either unpublished or published only in Chinese journals or even only in the Chinese language. This book therefore provides Western readers working in symbolic and algebraic computation, geometric reasoning and modeling, algorithmic mathematics, robotics, CAGD, and other relevant areas with an easily accessible source of references for what the Chinese researchers have been doing under the banner of mathematics mechanization.

View full description### Audience

Researchers, practitioners and graduate students in symbolic and algebraic computation, geometric reasoning, authomated theorem proving, algorithmic mathematics, and computer-aided mathematical problem solving; researchers and university teachers in computer-aided instruction and education; and software developers, researchers and engineers in mechanics, computer-aided geometric design, geometric modeling, robotics, and computer vision.

### Book information

- Published: July 2000
- Imprint: ACADEMIC PRESS
- ISBN: 978-0-12-734760-8

### Reviews

"An outstanding feature of the book is the great variety and diversity of the material treated, together with the brevity, lucidity, and simplicity with which the leading ideas are presented. Another distinct, very appealing feature is the brief comparison of the philosophical ideas underlying the approaches undertaken by ancient Greek mathematicians and their contemporary Chinese pairs. The book is an indispensable reference to the workers actively engaged in symbolic computation, be it in mathematics, robotics, CAD, computer vision, non-linear optimization, theoretic physics, chemical equilibrium, celestial mechanics. It can also be strongly recommended to the "disengaged" mathematician who wishes to become familiar with an important and active research area.

--Zentralblatt MATH

### Table of Contents

Preface. List of Contributors. **Polynomial System Solving**: *W. Wu*, The Characteristic Set Method and Its Application. *D. Wang*, Some Algorithms for Zero Decomposition of Polynomial Systems. *S. Zhang, G. Feng*, The Eigenvalue Approach to Polynomial System. *S.Wang, K. Wu*, Solving the Yang-Baxter Equation by Wu's Method. **Automated Geometric Reasoning**: *S. Chou, D. Lin*, Wu's Method for Automated Geometry Theorem Proving and Discovering. *H. Li*, Mechanical Theorem Proving in Differential Geometry. *J. Zhang*, Points Elimination Methods for Geometric Problem Solving. *H. Li*, Clifford Algebra Approaches to Mechanical Geometry Theorem Proving. *X. Hou*, Proving by Examples. *X. Gao*, Search Methods Revisited. *J. Wu*, First-Order Polynomial Based Theorem Proving. **Algebraic Computation**: *Z. Li*, Greatest Common Right Divisors, Least Common Left Multiples, and Subresultants of Ore Polynomials. *L. Zhi*, Algebraic Factorization and GCD Computation. *X. Gao*, Conversion Between Implicit and Parametric Representations of Algebraic Varieties. **Implementations and Applications**: *Z. Lu, S. Ma*, Centers, Foci, and Limit Cycles for Polynomial Differential Systems. *Z. Li*, Exact Solitary Wave Solutions of Non-linear Evolution Equations. *H. Zhang, E. Fan*, Applications of Mechanical Methods to Partial Differential Equations. *Q. Liao*, Equation Solving in Robotics and Mechanisms. *G. Feng, H. Ren, Y. Zhou*, Blending Several Implicit Algebraic Surfaces. *S. Chou, X. Gao, Z. Liu, D-K Wang, D. Wang*, Geometric Theorem Provers and Algebraic Equation Solvers. References. Index.