[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