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

Reference No.	2023a006
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
Principal Investigator	Yuki Ishihara（Tokyo University of Science, Faculty of Science Division I, Department of Applied Mathematics・Assistant Professor）
Research Period	November 13,2023. ～ November 17,2023.
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
Abstract for Research Report	Symbolic Computation is a computational method that deals with various mathematical calculations symbolically. In contrast to numerical computation, symbolic computation is an error-free computation and is characterized by its ease of analyzing the mathematical structure behind a problem. This research aims to review the algorithms of symbolic computations in various fields and apply them to solve problems in the industry. 　In general, the evaluation of errors is extremely important in numerical computation. For example, an error will appear in the final result if a value is truncated in a calculation in the process. On the other hand, symbolic calculations do not produce errors since they are exact calculations. As an example, the square root of 2, √2, is often approximated by 1.41421356 in numerical computations, but in symbolic computations, x^2-2 is often used as the defining polynomial. 　Symbolic computation is a suitable method for solving mathematical problems, but on the other hand, it has the disadvantage of being computationally more expensive than numerical one. For example, it is known that the complexity of quantifier elimination (QE) is bi-exponential. Therefore, we conducted short-term joint research on QE in the IMI joint research project "Construction of efficient algorithms for quantifier elimination and their application to solving industrial problems" in 2022. In the course of this research, new issues emerged, such as the construction of a theory to apply QE to mathematical optimization theory and control theory. As a continuation of the research, this study will focus on various algorithms for symbolic computation, including QE. The expected results of this research are mainly the following three. (1) Review of the various algorithms for symbolic computation up to now and investigation of areas for improvement (2) Development of efficient algorithms that integrate symbolic and numerical computation (3) Application of the developed algorithms to 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）