Speeding up of symbolic computation and its application to solving industrial problems 2

Reference No.	2024a008
Type/Category	Grant for Young Researchers and Students-Short-term Joint Research
Title of Research Project	Speeding up of symbolic computation and its application to solving industrial problems 2
Principal Investigator	Yuki Ishihara（Tokyo University of Science, Faculty of Science Division I, Department of Applied Mathematics・Assistant Professor）
Research Period	November 11,2024. - November 15,2024.
Keyword(s) of Research Fields	Symbolic Computation (Computer Algebra), Groebner Basis, Quantifier Elimination, Mathematical Optimization, Real Algebraic Geometry, Primary Decomposition, Symbolic-Numeric Computation, Nonlinear Control Theory, Machine Learning, Algebraic Statistics
Abstract for Research Report	Symbolic Computation is a method of computing mathematical expressions symbolically and is one of the most powerful methods for analyzing mathematical structures. On the other hand, it is computationally more expensive than numerical computation, and many of them, such as the algorithms for the Groebner basis and quantifier elimination, have exponential complexity. As a continuation of the FY2023 Joint Research Project "Speeding up of symbolic computation and its application to solving industrial problems," this research aims to improve conventional symbolic computation methods in various fields and apply them to solving various industrial problems. 　In the FY2023 Joint Research Project, experts in various fields such as computer algebra, cryptography, statistics, optimization theory, machine learning, and control theory participated, discussing new problems and their solution methods from various perspectives. For example, a large number of symbolic computation problems and their solution pairs are required to learn symbolic computation with machine learning models, but naive computation requires a huge amount of time. This led to the discovery of a new problem: how to generate them efficiently. This is a point that would be difficult to conceive of only in the world of symbolic computation and is the result of joint research by specialists in different fields. In addition, through discussions led by Dr. Yuno on applications to control theory, we revealed the current status of practical control problems for which symbolic computation can be used. Also, the organizing committee members shared the use of "GaNRAC," software developed by Dr. Iwane for quantifier elimination calculations, and researched its application to industrial problems. 　In FY2024, one of the objectives is to continue interdisciplinary research to lead to breakthroughs. The expected results of this research are mainly the following two points. (1) Development of new algorithms for symbolic computation using machine learning, etc. (2) Application of symbolic computation algorithms to specific industrial problems.
Organizing Committee Members (Workshop) Participants (Short-term Joint Usage)	Yuki Ishihara（Tokyo University of Science, Faculty of Science Division I, Department of Applied Mathematics・Assistant Professor） Ryoya Fukasaku（Kyushu University, Faculty of Mathematics・Assistant Professor） Yasuhiko Ikematsu（Kyushu University, Institute of Mathematics for Industry・Assistant Professor） Yuta Kambe（Mitsubishi Electric Information Technology R&D Center・Research Associate） Hidenao Iwane（Reading Skill Test, Inc.・Employee） Masaru Ito（Nihon University, College of Science and Technology・Assistant Professor） Munehiro Kobayashi（Schilf Institute Co., Ltd.・Board Member） Tsuyoshi Yuno（Kyushu University, Faculty of Information Science and Electrical Engineering・Assistant Professor） Hiroshi Kera（Chiba University, Graduate School of Engineering・Assistant Professor） Tomoyuki Iori（Osaka University, Graduate School of Information Science and Technology・Assistant Professor）