Algèbre - Algebra

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Algebra, Number Theory and Geometry

A Computer Algebra System for Polynomial Computations

Intuitive, C-like programming language

commutative computer algebra

is a versatile tool for the algorithmic treatment of polytopes and polyhedra. It offers access to a wide variety of algorithms and packages within a common framework. Moreover, polymake is flexible and continuously expanding. It is highly adaptable to individual needs. In particular, polymake has a C/C++ interface which allows the user to combine the wealth of available methods with his/her own implementations.

is a visualization tool developed at the Laboratory for Computation and Visualization in Mechanics, formerly at the University of Maryland and currently at the Ecole Polytechnique Federal de Lausanne. The unifying themes in VBM are to use visualization and special projections of the bifurcation diagram to facilitate efficient computation of the solution set, organize and allow easy access to the large data sets that arise, and most of all to generate mathematical understanding of the features and properties of the solution set.

is a computer algebra system, especially for number theoretic purpose

The need to "solve" (i.e. simplify or find solutions to) systems of polynomials arises in many areas of science and engineering: for example geometric modelling, robotics, chemical engineering, scheduling and electronics. There are various generic algorithms implemented in commercial algebra systems such as AXIOM, Maple, Mathematica etc. for solving these problems, but in many cases their very generality makes them too inefficient for use on the size of problems encountered in industry. The aim of the FRISCO project is to investigate and develop technologies which can be used to deliver highly efficient, versatile polynomial solvers to industrial users.

a new software system devoted to supporting research in algebraic geometry and commutative algebra. We hope you will download it, try it out, and give us useful feedback as we continue the development of the program.

GAP is a free system for computational discrete algebra.

for the Numerical Treatment of ODEs

Notes from Ed Eikenberg's talk on November 9, 2000

Let n be a positive integer. Does there exist a right triangle with rational sides whose area is n? If so, then n is called a congruent number. For example, the familiar 3-4-5 right triangle has area 6, so n=6 is a congruent number. But what about other values of n, like n=5 or n=157?

Un polynôme irréductible P(x) de degré n sur un corps fini p est primitif, si son ordre est égal à pn-1.

Cet outil permet de rechercher des polynômes primitifs sur corps primaires p, où p est un nombre premier.

Il y a 4 groupes d'ordre 28.

calculs sur des groupes finis de permutation, basé sur le logiciel GAP4

To determine linear integer dependence among numerical constants and to determine the minimal polynomial of an approximate algebraic number

This page, written at the suggestion of the Director of Research at the USNA, Prof. Reza Malek-Madani, describes some applications of representation theory of non-abelian groups to various fields and gives some references. However, I am entirely to blame for the subtitle.

Construction progressive d'une loi interne associative, éventuellement commutative, sur un ensemble fini.

R. Guillermo Moreno

Felix Kwok July 18, 2001

The problems of cube duplication, angle trisection and circle quadrature are three famous problems that mathematicians have sought to solve since antiquity. In this paper, I will use eld theory to prove that these problems are impossible to solve

These notes are a companion volume to the book Abstract Algebra, Second Edition Commutative rings , Introductory lectures on rings and modules , Online study guide John A. Beachy and William D. Blair.

Bas Edixhoven

Excerpted from Beachy/Blair, Abstract Algebra, 2nd Ed., © 1996 Chapter 5, Excerpted from Abstract Algebra II, © 1996 by John Beachy Sections 5.5 through 5.8

John A. Beachy and William D. Blair