
[README] [Japanese]

Algebra

Version: 0.57 (2002.03.18)

Author: Shin-ichiro HARA (sinara@blade.nagaokaut.ac.jp)

This is a library of one-variate and multi-variate polynomials.

0. Frist Step

Begin with 'require "algebra"'.
require "algebra"
x = Polynomial(Integer, "x").var
puts( (x+1)**7 )
  #=> x^7 + 7x^6 + 21x^5 + 35x^4 + 35x^3 + 21x^2 + 7x + 1
puts( (x**7 + 7*x**6 + 21*x**5 + 35*x**4 + 35*x**3 + 21*x**2 + 7*x + 1).factorize )
  #=> (x + 1)^7

1. Samples

  Samples

2. Class and Module

  Algebra (Module of Algebra)
      Algebra::Polynomial (Class of Polynomial Ring)
      Algebra::EuclidianRing (Eulcidian Ring Module)
      Algebra::MPolynomial (Multi-variate Polynomial Ring Class)
      Algebra::ResidueClassRing (Residue Class Ring Class)
      Algebra::AlgebraicExtentsionField (Algebraic Extension Class)
      Algebra::LocalizedRing (Localized Ring Class)
      Algebra::MatrixAlgebra (Matrix Algebra Class)
      Algebra::AlgebraicParser (evaluation of algebraic strings)
      Algebra::Set (Sets)
      Algebra::Map (Maps)
      Algebra::Group (Groups)
      Algebra::PermutationGroup (PermutationGroups)
   

3. Other

  Algebra::ElementaryDivisor (Elementary Divisor Module)
  Algebra::JordanForm (Jordan Matrix Class)
  Algebra::MatrixAlgebraTriplet (Triplete of Matrices Class)
  Algebraic Equations
  Conversions of Polynomial Classes

4. Contents of package

General

algebra.rb               File for using Algebra libraries

One variate polynomial

polynomial.rb            Class of one variate polynomial
euclidian-ring.rb        Module of Euclidian domain
polynomial-factor.rb     Factorization:
  polynomial-factor-int.rb   Integer version
  polynomial-factor-zp.rb    Zp version
  polynomial-factor-alg.rb   Algebraic number version

Multi variate polynomial

m-polynomial.rb         Class of multi-variate polynomial
  m-index.rb            Class of indices of degrees
m-polynomial-factor.rb     Factorization:
  m-polynomial-factor-int.rb   Integer version
  m-polynomial-factor-zp.rb    Zp version
groebner-basis.rb       Module of Groebner basis
groebner-basis-coeff.rb Module of division by Groebner basis

Foundation

finite-set.rb           Sets
  finite-map.rb         Maps
  finite-group.rb       Groups
    permutation-group.rb  Permutation Groups

Common part

numeric-supplement.rb   Supplement of Numeric
prime-gen.rb            Class of prime numbers
polynomial-converter.rb Conversions between polynomial classes
algebraic-parser.rb     Evaluation of strings
algebra-system.rb       Common specification of algebras

General algebra

localized-ring.rb       Quotient fields
matrix-algebra.rb       Matrix
  elementary-divisor.rb Elementary Divisor Class
  matrix-algebra-triplet.rb  Triplet of Matrices Class
  jordan-form.rb        Jordan Block Class
residue-class-ring.rb   Residue class ring
algebraic-extention-field.rb Algebraic Extention Field of Polynomial
splitting-field.rb      Minimal Splitting Field of Polynomial
galois-group.rb         Galois Group of Polynomial
linear-algebra.rb       library for linear algebra
algebraic-equation.rb   library for algebraic equation

Others

array-supplement.rb    Supplement of Array
doc/                   English Manuals(RD, HTML, TXT)
doc-ja/                Japanese Manuals(RD, HTML, TXT)
sample/                Sample Codes
work/                  (working directory for the developer)

5. ToDo

  todo.html

6. Changes

  changes.html

