(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
Abstract:
I will present a survey on the following topics.
Y.Tamura's thesis on a digital formula book for generalized hypergeometric functions.
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
Abstract:
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.
Abstract:
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
Abstract:
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.
---------------------------------------------------------------
The computer algebra seminar is co-organized by
M.Noro, noro@math.kobe-u.ac.jp
N.Takayama, takayama@math.kobe-u.ac.jp
K.Yokoyama, yokoyama@math.kyushu-u.ac.jp
For more info see http://www.math.kobe-u.ac.jp/seminar.html/compalg.html