Computer Algebra Seminar No.19 (計算代数セミナー, 第19回) at Kyushu Univ.(九州大学)

November 5 (Wed), 2003. 11月5日 (水), 13:00 --- 17:30

(セミナー終了後、懇親会を行う予定です.)

An Application of Elimination Ideal for a Defining Equation of Singularity , 13:00-14:00

Abstract:
We can obtain non-degeneracy conditions of singularities by using Gr\"obner basis. We can treat divisions of polynomials that have parameter coefficients and indeterminate exponents by using pseudo-remainders. In classification of singularities using hierarchy, the defining equations are polynomials with parameter coefficients and indeterminate exponents.
In general, the forms of Gr\"obner bases of ideals generated by such polynomials depend on the values of parameters, and those calculations are not easy. We will see that a stratification problem of coefficients and exponents of a set of polynomials is naturally raised to classify singularities. We will give a partial answer to this problem.

Volker Weispfenning (Passau University)
Canonical Comprehensive Groebner Bases (Tentative), 14:10--15:40

Hirokazu Anai (FUJITSU Laboratories)
Quantifier Elimination for Real Algebraic Constraints , 15:50--16:40

Abstract:
The wide range of problems in science and engineering can be reduced to that of solving real algebraic constraints. Hence, making progress in solving real algebraic constraints has a significant impact on those areas. Quantifier elimination (QE) provides exact solutions for real algebraic constraints and makes it possible to deal with the constraints parametrically. These are significant advantages of QE in solving such constraints and lead to a way of resolving difficult problems (e.g. nonconvex cases) that are hard to solve with numerical methods. Thus, QE has been applied to various kinds of problems in science and engineering. Though the actual applicability of QE has been fairly limited due to the practical complexity of the implemented QE methods, some of these methods have been able to solve the problems of interesting size in application fields by virtue of the enormous increase in computational power and theoretical work. In this talk, we show the successful applications of some QE methods to industrial problems with concrete examples from system and control theory. Then, we present some promising directions to achieve efficiency of the methods solving real algebraic constraints by combining the QE based approach with the numerical approach.

Hitoshi Yanami (FUJITSU Laboratories)
SyNRAC: Maple 上の代数制約問題解決ツールボックス , 16:40--17:30

Abstract:

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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