The International Workshop on Mathematics Mechanization
Beijing, China, July 16-18, 1992

Proceedings Editors
Wen-Tsun Wu and Min-De Cheng

Preface of the Proceedings

In year 1990 the National Science Committee and the Chinese Academy of Sciences (or Academia Sinica) decided to establish a Research Center in the Institute of Systems Science of the Academy. The Center will aim at the study of Mathematics Mechanization} which is closely related to such disciplines vividly developed in recent years like Automated Reasoning, Symbolic Computation, Computer Algebra, et al. We adopted the name of Mathematics Mechanization for the Center which had its origin in works of Hao Wang, one of the pioneers in using computers to the research of mathematics, theorem-proving in particular. This International Workshop on Mathematics Mechanization will be the first one of a series of Workshops bearing the same title. They are aimed at the interchange of views and ideas about the development of related subjects for the sake of world-wide cooperations. The present first Workshop has its theme mainly restricted to algebraic equations solving, both in theories and in applications, for which the importance as well as difficulties have been widely well-acknowledged. More than ten mathematicians and computer scientists beyond China had accepted our invitations and contributed papers to be presented on the Workship. All these papers, as well as those by workers in China proper, have been collected in this Proceedings, to be distributed in the opening day of the Workshop. On behalf of the Center the undersigned would like to express our warm gratitudes to all the contributors, the principal sponsors of the Workshop, viz. the National Natural Science Foundation of China and the Academy, and besides, the International Academic Publishers who takes cares of the fast printing of this volume.

Wu Wen-tsun
Mathematics Mechanization Research Center

Table of Contents of the Proceedings

    Algebraic Equation Solving
  • An Algebraic System Based on the Characteristic Method, S.C. Chou and X.S Gao, 1
  • Reducing the Multivariate Polynomial System to Eigenvalue Problem, Guo-Cheng Feng and Shu-gong Zhang, 19
  • Recent Progress in Characteristic Set Computation: Complexity and Open Problems, G. Gallo and B. Mishra, 28
  • Grobner Basis Thehnique, Homogeneity and Solving Polynomial Equations, V.P. Gerdt, N.V. Khutornoy, A.Yu. Zharkov, 38
  • Solving Systems of Parametric Equations (abstract), D. Kapur, 52
  • The Multiplicity of a Solution of System of Algebraic Equations, H. Kobayashi and H. Suzuki, 53
  • Solving Polynomial Systems (abstarct), T.Y. Li, 65
  • A Set Equation with Applications, M. Otake, T. Mishima, Y. Manome, 66
  • On Solving the Yang-Baxter Equations, He Shi, 79
  • Some Improvements on Wu's Method for Solving Systems of Algebraic Equations, D.M. Wang, 89
  • On Char-Set Method and Linear-equations Method of Polynomial Equation Solving, Wen-Ts\"un Wu, 101
  • A Criterion of Dependency Between Algebraic Equations and its Applications, Lu Yang, Jing-Zhong Zhang, and Xiao-Rong Hou, 110

    Geometric Design

  • Local Parametrization of Space Curves at Singular Points, M.E. Alonso, T. Mora, G. Niesi, and M. Raimondo, 135
  • Generalized Hermite Interpolation and Approximation for Algebraic Varieties (abstarct), C. Bajaj, 167
  • On Projections in Geometric Design, C.M. Hoffmann, 168

    Space Mechanism Design

  • Kinematic Solution of A Stewart Platform, Yu-zhen Huang and Wen-da Wu, 181
  • Input-Output Equation for Mechanism and Inverse Solution of General 6R Manipulator, Chong-Gao Liang, 189

    Geometric Theorem Proving

  • A Geometric Theorem Prover based on Wu's Method, X.S. Gao, Y.L. Li, D.D. Lin, and X.S. Lu, 201
  • Mechanical Theorem-Proving on a PFM, Lian Li, 206
  • Some Results on Theorem Proving in Finite Geometry, Dong-Dai Lin and Zhuo-Jun Liu, 222
  • Mechanical Solution of a Group of Space Geometry Problems, Ding-Kang Wang, 236
  • A Prover for Parallel Numerical Verification of a Class of Constructive Geometry Theorems, Lu Yang, Jing-Zhong Zhang, and Chuan-Zhong Li, 244

    Differential Systems

  • Adomian's Decomposition Method for the Solutions of Generalized Duffing Equations and of Its Coupled Systems, Jin-Qing Fang and Wei-Guang Yao, 251
  • A Projection Theorem and its Application to Nonlinear Control Systems, Shu-Rong Li, 263
  • A Mechanical Method of Algebraic Structure of the General Solution to the System of Linear Operator Equations, Hong-Qing Zhang and Hong Feng, 274
  • A Mechanical Method to Construct the General Solution of a System of Partial Differential Equations, Hong-Qing Zhang and Fang-Xiang Wu, 280