MathematicalSoftwareAndFreeDocuments/04

数学ソフトウェアとフリードキュメント/04

MathematicalSoftwareAndFreeDocuments IV †

• 2007 March 26th (Mon） 13:00 -- 18:00
• Saitama University (Location)
• Faculty of Science-I, room 1337. (CAMPUS MAP)
• 255 Shimo-Okubo, Sakura-ku, Saitama City, Saitama 338-8570
• How to go to Saitama University
• Organizer: Noro, Masayuki (Kobe University) noro at math.kobe-u.ac.jp, Hamada, Tatsuyoshi (Fukuoka University) hamada at holst.sm.fukuoka-u.ac.jp

Program †

Abstract †

• The polyhedral homotopy continuation is known to be a powerful numerical method for approximating all isolated solutions of a system of polynomial equations. We mainly discuss a dynamic enumeration of all fine mixed cells, which is used in constructing a family of polyhedral homotopy functions, and provide some numerical results to demonstrate its effectiveness.

• I published an ISO Full BASIC language system, which is suitable for mathematics education, named "Decimal BASIC" aiming for sloughing off dialect BASIC's. I will state the aim of that.

• Algebraic topology is a powerful mathematical tool for the analysis of topological spaces and continuous maps. In particular, the homology functor translates topological information into algebraic data structures which can be effectively manipulated and analyzed by the computer in an algorithmic way. In this talk we introduce the software developped within the framework of the Computational Homology Project (CHomP; http://www.math.gatech.edu/~chomp/ ). This software can be used to effectively compute the homology groups of compact sets built of (hyper)cubes with respect to a uniform rectangular lattice in R^n, and it is also capable of computing the homomorphisms induced in homology by continuous maps between such spaces. The software already has several applications, and we will point out a few of them.

• CMCLab, written by N. Schmitt, is a computer graphics software to draw figures of constant mean curvature surfaces. I will give a short introduction for

• Geometric Constructor is one of the dynamic geometry softwares developed in Japan ( Dos version(1989), Windows version(1997), Java version(2000)). With some plug-in, it can be used as web-application with PukiWiki etc(GC Wiki, GC_BBS, etc.). Since 1990, it has been used in many secondary schools.

• JavaView is a mathematical visualization software developed by Konrad Polthier. Mathematica and Maple are frequently used in the study of surface theory. Combining JavaView with those standard packages results in an especially efficient tool for surface theory research. In this talk we introduce JavaView, particularly emphasizing how to visualize surfaces using JavaView in combination with Mathematica.

• Software Cabri Geometry is famous for dynamic geometry software of the two dimensions in the worldwide. The three dimensions versions Cabri 3D was released in 2005. Using Cabri 3D, you will quickly learn to construct, view and manipulate all sorts of objects in three dimensions: lines, polygons, planes, spheres, cones, (regular)polyhedra… You can build dynamic constructions, from the simplest to the most complex. You can measure objects, integrate numeric data and even replay the process by which you built your constructions. Here, I introduce part of the function through the drawing such as cutting the cube and truncated hexahedron.

Presentation files †

• "QWikS: A Tool for Helping Managers of Gatherings", Goto, Yuichi
• "PHoM -- software for solving polynomial systems using polyhedral homotopy continuation", Takeda, Akiko
  MathSoft-FreeDoc.pdf
• "On the Aim of Decimal BASIC", Shiraichi, Kazuo
  20070326Shiraishi.ppt
• "Computational Homology Project", Pilarczyk, Pawel
  chomp.pdf
• "Tutorial on CMCLab", Kobayashi, Shimpei
  saitama2007talk.pdf
• "Development and Educational Use of Geometric Constructor", Iijima, Yasuyuki
  20070326-iijima.pdf
• "Studying surfaces with JavaView and Mathematica", Fujimori, Shoichi
• "Introduction of the dynamic geometry software Cabri 3D", Komori, Tsuneo

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