Wednesday, October 25, 2006 - 4:00pm - 7:00pm
- Algorithms for Algebraic Geometry in Magma
John Voight (University of Minnesota, Twin Cities)
We will demonstrate the use of algorithms for algebraic geometry implemented
in the computer algebra system Magma. These algorithms include the usual
commutative algebra functions which operate on schemes (defined by the
vanishing of polynomial equations in affine or projective space), including
efficient Groebner basis methods. Magma also contains many quite
specialized functions for working with familiar objects like plane curves.
- DEMiCs, Software for Dynamic Enumeration of all Mixed Cells
Enumeration of all mixed cells plays an essential role in the
polyhedral homotopy method; numerical method for solving polynomial systems.
Recently, we have developed a software, DEMiCs, which finds all mixed cells
using dynamic enumeration tree. It fairly surpasses the static enumeration in
computational time. This talk presents several techniques used in DEMiCs and
demonstrates its effectiveness.
- The Gambit System for Computing in Finite Games
Theodore Turocy (Texas A & M University)
Gambit is a collection of computer code for representing, building, and
manipulating finite games in extensive or strategic form. This session
will introduce the main components of Gambit. Gambit provides a
graphical user interface for manually creating, visualizing, and
game trees and payoff tables. Several programs for computing Nash
equilibria are provided, including specialized ones for two-player and
constant-sum games. Gambit's modular structure makes it possible to
plug in other analytical programs; this feature will be illustrated with
a program to compute Nash equilibria with PHCpack as a computational
backend. The underlying representation library facilitates programming
new computational methods, as well as the automation of the construction
of large games or of families of games, which will be demonstrated with
some examples using the binding of the Gambit library to the scripting
Yun Guan (University of Illinois, Chicago)
Tatsuyoshi Hamada (Fukuoka University)
Participants try the followings on their laptop in this tutorial.
1. Starting KNOPPIX/Math from DVD.
2. Saving data to a flash memory.
3. Installation of VMware(or Parallels)/knoppix/math.
4. Starting several mathematical software systems in the KNOPPIX/Math DVD.
Requirements for the laptop.
PC AT compatibles with a DVD drive or