ASCM’95

August 18-20, 1995,  Beijing, China,

Proceedings of ASCM'95

He Shi and Hidetsune Kobayashi (Eds.)

Scientists Incorporated

Tokyo, Japan.


PREFACE TO THE PROCEEDINGS

On January 21-22,1994,it was held in Tokyo, Japan, the Winter Workshop on Computer Algebra. Owning to the importance of the subject-related matter it was suggested at that time that such workshops should be extended to a regular series of symposia over the Asian area. Moreover, the main topics of such symposia should include, besides computer algebra, computational geometry and other related subjects. It was thus proposed that the symposia would bear the name Computer Mathematics, both reflecting the present status and promoting the development of mathematics to cope with the rapid pace of the computer era.

The proposal was soon realize. Thus, the first Asian symposium on Computer Mathematics, ASCM’95, was held on August 18-20, 1995 at Beijing, China. Sponsored by Mathematics Mechanization Research Center (MMRC) and Japanese Symposium on Symbolic and Algebraic Computations (JSSAC), ASCM is an international forum for the exchange lf ideas and techniques for studying mathematics by computer. Topics of the symposium include: symbolic computation mechanical theorem proving, computational geometry, combined symbolic-numeric method and software design. More than fourty mathematicians and computer scientists from Japan, Korea, France and China attended the Symposium and more than twenty papers were presented All these papers have been collected in this Proceedings. On behalf of MMRC the under-signed would like to thank the following corporations for the support of the symposium: the Natural Science Foundation lf China, Chinese Science and Technology Committee, Academia Sinica and the Institute of Systems Science of Academia Sinica.

                                                                     

Wu Wen-tsun

Chairman, ASCM95

Beijing,  August 1995

 

 

CONTENTS OF THE PROCEEDINGS

 

Preface………………………………………………………………………………………page I  

 

Friday, august 18

 

Separation of close roots by linear fraction transformation………………………………………1

Hidetsune Kobayashi, Hideo Suzuki and Yoshihiko SAKAI

 

Char-Set Method of Polynomial Equation-Solving and Its Applications………………………..11

Wu wen-tsun

 

The Genera of Algebraic Curves with Singularities……………………………………………..23

Liu Xian-fang

 

Automated Reasoning with Differential Forms…………………………………………………29

Li Hongbo

 

An Efficient Decomposition Algorithm for Geometry Theorem Proving without Factorization..33

Lu Yang, Jing-Zhong zhang and Xiao-Rong Hou

 

The Structure of Solutions to Algebraic System and Matrices in Eigenvalue Method………….43

Feng Guo-chen, Zhang Shu-gong and Liu Ying

 

 

Saturday, August 19

 

A Method for Solving Algebraic Systems Based on Subresultant PRS…………………………55

Dongming Wang

 

A Quantum Group with five parameters………………………………………………………...71

He Shi

 

Approximate GCD and PDE Approximation…………………………………………………….81

Hiroshi Kai and Matu-Tarow Noda

 

The Remainder Method for the First-Order Theorem Proving…………………………………91

Jinzhao Wu, Zhuo-jun Liu

 

Stabilizing Algebraic Algorithms…………………………………………………………………99

Kiyoshi Shirayanagi

 

An Hybrid Method for Proving Theorems in Elementary Geometry………………………….113

Stephane Fevre

 

Blending of Implicit Algebraic Surfaces………………………………………………………..125

Wu Tie-ru, Gao Wei-guo and Feng Guo-chen

 

Blending algebraic Surfaces of Lowest Degree………………………………………………..133

Zhou Yun-shi and Wu Tie-ru

 

 

Sunday, August 20

 

On the relation of Moduli for Simple K3 Singularities…………………………………………137

Tadashi Takahashi

 

The machine proof of five positions plane rigit body guidance mechanism synthesis…………145

Aiwen Guan, Huilin liu

 

The Eigenvalue Method for Computing high-dimensional Varieties……………………………153

Feng Guo-chen, Zhang Shu-gong and Zhang Chuan-lin

 

Wu Method And Solitons……………………………………………………………………….157

Li Zhibin

 

Approximate Kernel Space and Its Application to the Computation of Multivaiate Polynomial GCD165

Takuya Kitamoto

 

Deriving Some New Conditions on the Existence of Eight Limit Cycles for a Cubic System….175

Shilong Ma Shucheng Ning

 

One General Criterion for Stability……………………………………………………………...187

Zhuojun Liu

 

Author Index…………………………………………………………………………………….197