Polynom-0.1: A commutative algebra package Contents Index

Data.Ring

Synopsis

class Eq a => Ring a where zero :: a fromInt :: Integer -> a (+°) :: a -> a -> a (-°) :: a -> a -> a (*°) :: a -> a -> a minus :: a -> a data Ring a => Ideal a = MakeIdeal [a] principal_ideal :: Ring a => a -> Ideal a add_ideals :: Ring a => Ideal a -> Ideal a -> Ideal a mult_ideals :: Ring a => Ideal a -> Ideal a -> Ideal a

Documentation

class Eq a => Ring a where

This defines a Ring Class with zero, sum '+' and product |'*'. Rign operations are represented by a small ring . Methods zero :: a fromInt :: Integer -> a (+°) :: a -> a -> a (-°) :: a -> a -> a (*°) :: a -> a -> a minus :: a -> a Instances (Num r, OrdMonoid m) => Ring (MonoidRing r m)

data Ring a => Ideal a

Ideals of a ring are represented by lists of elements. Constructors MakeIdeal [a] Instances (Ring a, Show a) => Show (Ideal a) Ring a => Lattice (Ideal a)

principal_ideal :: Ring a => a -> Ideal a

add_ideals :: Ring a => Ideal a -> Ideal a -> Ideal a

The principal_ideal constructor creates a principal ideal from an element of the ring

mult_ideals :: Ring a => Ideal a -> Ideal a -> Ideal a

Ideals can be added.

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