-------------------------------------------------------------------------------
-- | Constructive Algebra Library
--
-- Anders Mortberg <mortberg@student.chalmers.se>
-- Bassel Mannaa <mannaa@student.chalmers.se>
--
-- Abstract:
-- This is a library written as part of our master theses. It focuses mainly
-- on the theory of commutative rings from a constructive point of view.
--
-------------------------------------------------------------------------------
module README where
--------------------------------------------------------------------------------
-- Structures
-- Rings with basic operations.
import Algebra.Structures.Ring
-- Commutative rings.
import Algebra.Structures.CommutativeRing
-- Integral domains.
import Algebra.Structures.IntegralDomain
-- Fields.
import Algebra.Structures.Field
-- Strongly discrete rings - Rings with decidable ideal membership.
import Algebra.Structures.StronglyDiscrete
-- EuclideanDomains - Integral domains with decidable division and and Euclidean
-- function. Contains lots of functions that are possible at the level of
-- Euclidean domain like the Euclidean algorithm and extended Euclidean
-- algorithm.
import Algebra.Structures.EuclideanDomain
-- Bezout domains - Non-Noetherian analogues of principal ideal domains. All
-- finitely generated ideals are principal.
import Algebra.Structures.BezoutDomain
-- GCD domains - Non-Noetherian analogues of unique factorization domains.
-- All pairs of nonzero elements have a greatest common divisor.
import Algebra.Structures.GCDDomain
-- Field of fractions of a GCD domain.
import Algebra.Structures.FieldOfFractions
-- Coherent rings. That is rings in which it is possible to solve homogenous
-- linear equations.
import Algebra.Structures.Coherent
-------------------------------------------------------------------------------
-- Special constructions.
-- Finitely generated ideals over commutative rings.
import Algebra.Ideal
-- Simple matrix library
import Algebra.Matrix
-- Principle localization matrices
import Algebra.PLM
-------------------------------------------------------------------------------
-- Instances.
-- The integers.
import Algebra.Z
-- The rational numbers as the field of fractions of Z.
import Algebra.Q
-------------------------------------------------------------------------------
-- The end.