Numeric.Decidable.Associates

Documentation

class Unital r => DecidableAssociates r where

Methods

isAssociate :: r -> r -> Bool

b is an associate of a if there exists a unit u such that b = a*u

This relationship is symmetric because if u is a unit, u^-1 exists and is a unit, so

 b*u^-1 = a*u*u^-1 = a

Instances

DecidableAssociates Bool

DecidableAssociates Int

DecidableAssociates Int8

DecidableAssociates Int16

DecidableAssociates Int32

DecidableAssociates Int64

DecidableAssociates Integer

DecidableAssociates Word

DecidableAssociates Word8

DecidableAssociates Word16

DecidableAssociates Word32

DecidableAssociates Word64

DecidableAssociates ()

DecidableAssociates Natural

DecidableAssociates r => DecidableAssociates (Opposite r)

(DecidableAssociates a, DecidableAssociates b) => DecidableAssociates (a, b)

(DecidableAssociates a, DecidableAssociates b, DecidableAssociates c) => DecidableAssociates (a, b, c)

(DecidableAssociates a, DecidableAssociates b, DecidableAssociates c, DecidableAssociates d) => DecidableAssociates (a, b, c, d)

(DecidableAssociates a, DecidableAssociates b, DecidableAssociates c, DecidableAssociates d, DecidableAssociates e) => DecidableAssociates (a, b, c, d, e)

isAssociateIntegral :: Num n => n -> n -> Bool

isAssociateWhole :: Eq n => n -> n -> Bool