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Tutorials

There are six tutorials in parallel; 1 morning and 2 afternoon sessions. You can attend the tutorials FREE of charge, without registration.

Lihong Zhi
Chinese Academy of Sciences, CHINA

Symbolic-numeric algorithms for computing validated results

Abstract: In the tutorial, we will introduce two kinds of problems for which validated results are computed via hybrid symbolic-numeric algorithms: 1) certification of lower bounds of polynomials or rational functions with or without constraints; 2) verification of solutions of polynomial systems. The proposed hybrid algorithms follow the basic principle pointed out by Siegfried M. Rump for computing validated results: First, a pure floating point algorithm is used to compute an approximate solution of good quality for a given problem. Second, a verification step using exact rational arithmetic or interval arithmetic is appended. If this step is successful, then certified lower bounds or verified error bounds are computed for the previously computed approximation.

[PDF: Tutorial Handout]


Mitsushi Fujimoto
Fukuoka University of Education, JAPAN

How to develop a mobile computer algebra system

Abstract: Historically, a lot of computer algebra systems were designed to have a command line interface, then GUI was added if required. AsirPad -- a computer algebra system with a handwriting interface on PDA developed by the author is one of them. Risa/Asir -- a CAS with a command line interface is the CAS engine of AsirPad, and AsirPad is created by covering it with GUI.
This method is suitable to develop an application based on an existing CAS for mobile devices such as tablets and smartphones.
In this tutorial, I would like to explain the details of this method.

[PDF: Tutorial Handout]


Francois Le Gall
University of Tokyo, JAPAN

Algebraic Complexity Theory and Matrix Multiplication

Abstract: This tutorial will give an overview of algebraic complexity theory focused on bilinear complexity, and describe several powerful techniques to analyze the complexity of computational problems from linear algebra, in particular matrix multiplication. The presentation of these techniques will follow the history of progress on constructing asymptotically fast algorithms for matrix multiplication, and include its most recent developments.

[PDF: Tutorial Handout]


Hirokazu Anai
Fujitsu Laboratories/Kyushu University, JAPAN

Effective quantifier elimination for industrial applications

Abstract: In this tutorial, we will give an overview of typical algorithms of quantifier elimination over the reals and illustrate their actual applications in industry. Some recent research results on computational efficiency improvement of quantifier elimination algorithms, in particular for solving practical industrial problems, will be also mentioned. Moreover, we will briefly explain valuable techniques and tips to effectively utilize quantifier elimination in practice.

[PDF: Tutorial Handout]


Hidefumi Ohsugi
Kwansei Gakuin University, JAPAN

Gröbner bases of toric ideals and their application

Abstract: The theory of Gröbner bases has a lot of application in many research areas, and is implemented in various mathematical software. Among their application, this tutorial will focus on basic and recent developments in the theory of Gröbner bases of toric ideals. In 1990's, several breakthroughs on toric ideals were done: Conti--Traverso algorithm for integer programming using Gröbner bases of toric ideals; Correspondence between regular triangulations of integral convex polytopes and Gröbner bases of toric ideals; Diaconis--Sturmfels algorithm for Markov chain Monte Carlo method in the examination of a statistical model using a set of generators of toric ideals.
In this tutorial, starting with introduction to Gröbner bases and toric ideals, we study some topics related with breakthroughs above.

[PDF: Tutorial Handout]


Hiroyuki Goto
Hosei University, JAPAN

An introduction to max-plus algebra

Abstract: This tutorial will focus on the basics of max-plus algebra along with relevant topics. Max-plus algebra is a discrete algebraic system in which the max and plus operations are defined as addition and multiplication in conventional algebra. Using this system, the behavior of a class of discrete event systems can be represented by simple linear equations, by which modeling, analysis, and control of the systems can be realized.

We will start with a simple project scheduling problem to understand the basic usage of max-plus algebra. The focus will then be oriented to its detailed definition and observe relevant properties in terms of graph theory, net theory, and so on. In the latter part, we will move on to modeling and formulation methods in control theory viewpoint. Several application examples as schedule solvers will be introduced, followed by several recent advances achieved by the presenter.

[PDF: Tutorial Handout]

[PPTX: Tutorial Handout]