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

Unital (BasisCoblade m) => DecidableAssociates (BasisCoblade m)

(Unital (Opposite r), DecidableAssociates r) => DecidableAssociates (Opposite r)

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

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

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

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

isAssociateIntegral :: (Eq n, Num n) => n -> n -> Bool

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