Computer Algebra Seminar No.20 (計算代数セミナー, 第20回) at Kobe Univ.(神戸大学)

November 22 (Sat), 2003. 11月22日 (土曜日), 10:00 --- 15:30

場所: 神戸大学理学部 A棟2階より X209 教室. 土曜日は玄関の鍵がかかっているので, 土曜日到着の人は organizer に連絡を.

(前日[21日]午後は研究連絡日です. Afternoon of Nov 21 is for discussions.)

Nobuki Takayama (Kobe University) [高山信毅 (神戸大学)]
OpenXM digital formula book project [OpenXM ディジタル公式集プロジェクト] , 10:00-10:40

I will present a survey on the following topics.
  1. Y.Tamura's thesis on a digital formula book for generalized hypergeometric functions.
  2. Algorithmic methods to generate contiguity relations, Kummer type identities, and period relations of hypergeometric functions. These methods are used to generate formulas to store in the digital formula book.

Katsuyoshi Ohara (Kanazawa University) [小原功任 (金沢大学)]
An algorithmic method to generate period relations for hypergeometric functions [超幾何関数の周期関係式を生成するアルゴリズム] , 10:40-11:10

Period relations for hypergeometric functions are generalizations of the formula sin2(x) + cos2(x) = 1. About 10 years ago, Cho and Matsumoto gave a cohomological approach to derive period relations. We will present an algorithmic method to generate period relations for generalized hypergeometric functions based on Cho and Matsumoto's approach.

Raimundas Vidunas (Kyushu University) [ビヅナス ライマンダス (九州大学)]
Transformations of Gauss hypergeometric functions [ガウス超幾何関数の変換] , 11:25--12:25

In this talk a classification of algebraic transformations of Gauss hypergeometric functions will be given. Knowledge of these transformations can be important in computer algerba systems which aim to handle hypergeometric functions. Our classification scheme recovers the well-know classical transformations of degree 2, 3, 4, 6. It turns out that for special classes of Gauss hypergeometric functions there are more transformations. Examples of such hypergeometric functions are algebraic functions and elliptic integrals. We present these new transformations and algorithms for computing them.

Rouchdi Bahloul (Kobe Univ. and JSPS) [バルー ルッシュディ (神戸大学, JSPS)]
Bernstein-Sato polynomials via the Gr\"obner fan: an algorithmic construction. [ グレブナファンで調べるベルンシュタイン-佐藤 多項式 : そのアルゴリズム ] , 14:00--15:30

In 1987, C.Sabbah proved the existence of a non zero Bernstein-Sato polynomial associated with several analytic functions. In a recent work, I proposed a more elementary and constructive proof by using the notion of the Gr\"obner fan. In this talk, we shall recall how to construct such a Bernstein-Sato polynomial. In the algebraic case, and for two polynomials, this construction shall be completely algorithmic.

Past Lectures.

The computer algebra seminar is co-organized by
For more info see