Abstracts of Japanese computer algebra meeting in Kyoto

s of Japanese Computer Algebra Meeting in Kyoto C o m m u n i c a t e d by Fuj io Kako D e p a r t m e n t of I n f o r m a t i o n and C o m p u t e r Science, N a r a W o m e n ' s U n i v e r s i t y N a r a 630, J A P A N ema ih kako@ics, n a r a w u . a c . j p This is a collection of abstracts of talks done at the 15th RIMS(Research Institute for Mathematical Sciences) Meeting of Computer Algebra and its Applications in Mathematical Research. The meeting took place on November 18-21, 1996. At the meeting, 31 talks were presented. Here, short abstracts of almost all talks are shown. If readers have an interest in in some of abstracts, please contact with authors directly or send your letter to Fujio Kako at the address above. Proceedings of the meeting will be soon published from RIMS as RIMS memoir 986 titled with Researches on Theory and' Applications of Computer Algebra . T e t r a d i a g r a m s for the root s y s t e m of t y p e E7 and its app l i ca t ion Jiro Sekiguchi sekiguti@sci.himeji-tech.acd:p Department of Mathematics, Faculty of Sciences Himeji Institute of Technology Himeji, 671-22, Japan Tetrahedral sets and extended tetrahedral sets are introduced. Both are subsets of the root system of type ET. We determine the ST-orbital structure of the totality of extended tetrahedral sets. This is a joint work with T. Tanabata. Facil i t ies for A p p r o x i m a t e Algebra ic C o m p u t a t i o n in G A L Tateaki Sasaki sasaki@math.tsukuba.ac.jp Institute of Mathematics, University of Tsukuba Tsukuba-shi, Ibaraki 305, Japan and Fujio Kako kako@ics.nara-wu.ac.jp Department of Computer Science, Nara Women's University, Nara-shi, Nara 630, Japan Recently, approximate algebraic computation using floating-point arithmetic for numeric coefficient operation is being studied by many researchers. The floatingpoint number is very useful but it suffers from roundoff and cancellation errors, and the latter is much more dangerous than the former. In order to monitor the occurrence and amount of cancellation error, we have proposed a new floating-point number which we call "effective floating-point number", or "efloat number" in short. Efloat arithmetic has been implemented in NSL, Nara Standard Lisp, and the experiments performed so far show that the efloat number is quite effective for monitoring the cancellation error. Several commands are explained which are equipped in GAL, an algebra system we developed, to handle polynomials and rational functions with efloat coefficients conveniently. Furthermore, we explain several basic approximate algebraic operations being implemented in GAL, such as factor separation of univariate polynomial, approximate multivariate polynomial GCD, and approximate multivariate polynomial factorization. These operations will be currently equipped only in GAL. An ex tens ion of the p lo t t i ng func t ions on R i s a / A s i r Yuji Kondoh kondoh@dc.takuma-ct.ac.jp Takuma National College of Technology, 551 Kohda, Takuma-cho, Mitoyo-gun, Kagawa 769-11, Japan Yoshihiko Miyoshi miyoshi@fa2.so-net.or.jp Saitama Women's Junior College, 2011 Kamihirose, Sayama-city, Saitama-Pref. 350-13 Japan and Tomokatsu Saito sa~to@mm.sophia.ac.jp Sophia University, 7-1 Kioi, Chiyoda-ku, Tokyo 102, Japan A problem of how to draw a figure of real zeros of a bivariate polynomial is old but not yet completely solved.