
Algebra

2002.03.18
   
  Version: 0.57
  Author: Shin-ichiro HARA
  e-mail: sinara@blade.nagaokaut.ac.jp
  Home Page: <URL:http://blade.nagaokaut.ac.jp/~sinara/ruby/math/>

Preface

This is a library for mathematical computations. Our purpose is to express the
mathematical object naturally in Ruby. Though it is not operated fast, we can
see the algorithm of the mathematical processing not in black box but in
scripts.

This library is in development stage. At present, things we can handle are as
follows:
   
  One-variate polynomial
      Fundamental operations (addition, multiplication, quotient/remainder,
        ...)
      factorization
      Galois group
   
  Multi-variate polynomial
      Fundamental operations (addition, multiplication, ...)
      factorization
      Creating Groebner-basis, quotient/remainder by Groebner-basis.
   
  Algebraic systems
      Creating quotient fields
      Creating residue class fields
      Operating matrices
      Operating permutation groups
   
  Sets and Maps

Installation

Install Ruby (See: <URL:http://www.ruby-lang.org/> ) and set all lib/*.rb files
of this package to the directory where they can be loaded by Ruby.

Usage and Samples

See index.html in doc directory, where manuals and sample codes are.

Reference

  D.Cox, J.Little and D.O'Shea, "IDEALS, VARIETIES AND ALGORITHMS", 1997,
    Springer.
  K. Kodama, "Polynomial", <URL:http://www.math.kobe-u.ac.jp/HOME/kodama/
    tips-RubyPoly.html>
  H.Anai, M.Noro and K.Yokoyama, "Computation of the splitting fields and
    the Galois groups of polynomials", Progres in Mathematics, 28-50, Vo.143,
    1996

