module MapRingExamples where

import MapRing

--Examples: Lists and Integers
instance (Eq a) => Semigroup [a] where
    semigroupOperation = (++)
    semigroupIdentity = []

instance Semigroup Integer where 
    semigroupOperation = (+)
    semigroupIdentity = 0

--Z^2 lattice, for a two variable poly ring.
newtype Z2 = Z2 (Integer,Integer)
    deriving (Eq,Show,Ord)

instance Semigroup Z2 where
    semigroupOperation (Z2 (x,y)) (Z2 (z,w)) = Z2 (x+z,y+w)
    semigroupIdentity = Z2 (0,0)


--noncommutative ring of lists of Integers
w = singleMapRing 2 [1,2] 
--x and y in poly ring
x = singleMapRing 1 (Z2 (1,0))
y = singleMapRing 1 (Z2 (0,1))