algebra-4.3.1: Constructive abstract algebra

Safe HaskellSafe
LanguageHaskell98

Numeric.Decidable.Associates

Documentation

class Unital r => DecidableAssociates r where Source #

Minimal complete definition

isAssociate

Methods

isAssociate :: r -> r -> Bool Source #

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 Source # 

Methods

isAssociate :: Bool -> Bool -> Bool Source #

DecidableAssociates Int Source # 

Methods

isAssociate :: Int -> Int -> Bool Source #

DecidableAssociates Int8 Source # 

Methods

isAssociate :: Int8 -> Int8 -> Bool Source #

DecidableAssociates Int16 Source # 
DecidableAssociates Int32 Source # 
DecidableAssociates Int64 Source # 
DecidableAssociates Integer Source # 
DecidableAssociates Natural Source # 
DecidableAssociates Word Source # 

Methods

isAssociate :: Word -> Word -> Bool Source #

DecidableAssociates Word8 Source # 
DecidableAssociates Word16 Source # 
DecidableAssociates Word32 Source # 
DecidableAssociates Word64 Source # 
DecidableAssociates () Source # 

Methods

isAssociate :: () -> () -> Bool Source #

DecidableAssociates r => DecidableAssociates (Opposite r) Source # 
DecidableAssociates (BasisCoblade m) Source # 
GCDDomain d => DecidableAssociates (Fraction d) Source # 
(DecidableAssociates a, DecidableAssociates b) => DecidableAssociates (a, b) Source # 

Methods

isAssociate :: (a, b) -> (a, b) -> Bool Source #

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

Methods

isAssociate :: (a, b, c) -> (a, b, c) -> Bool Source #

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

Methods

isAssociate :: (a, b, c, d) -> (a, b, c, d) -> Bool Source #

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

Methods

isAssociate :: (a, b, c, d, e) -> (a, b, c, d, e) -> Bool Source #

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

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