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.

** **

Chairman, ASCM’95

**Beijing, **August 1995

** **

** **

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

** **

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

Dongming Wang

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

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

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