algebra-4.3: Constructive abstract algebra

Safe HaskellNone
LanguageHaskell98

Numeric.Ring.Opposite

Synopsis

Documentation

newtype Opposite r Source #

Constructors

Opposite 

Fields

Instances

Functor Opposite Source # 

Methods

fmap :: (a -> b) -> Opposite a -> Opposite b #

(<$) :: a -> Opposite b -> Opposite a #

Foldable Opposite Source # 

Methods

fold :: Monoid m => Opposite m -> m #

foldMap :: Monoid m => (a -> m) -> Opposite a -> m #

foldr :: (a -> b -> b) -> b -> Opposite a -> b #

foldr' :: (a -> b -> b) -> b -> Opposite a -> b #

foldl :: (b -> a -> b) -> b -> Opposite a -> b #

foldl' :: (b -> a -> b) -> b -> Opposite a -> b #

foldr1 :: (a -> a -> a) -> Opposite a -> a #

foldl1 :: (a -> a -> a) -> Opposite a -> a #

toList :: Opposite a -> [a] #

null :: Opposite a -> Bool #

length :: Opposite a -> Int #

elem :: Eq a => a -> Opposite a -> Bool #

maximum :: Ord a => Opposite a -> a #

minimum :: Ord a => Opposite a -> a #

sum :: Num a => Opposite a -> a #

product :: Num a => Opposite a -> a #

Traversable Opposite Source # 

Methods

traverse :: Applicative f => (a -> f b) -> Opposite a -> f (Opposite b) #

sequenceA :: Applicative f => Opposite (f a) -> f (Opposite a) #

mapM :: Monad m => (a -> m b) -> Opposite a -> m (Opposite b) #

sequence :: Monad m => Opposite (m a) -> m (Opposite a) #

Traversable1 Opposite Source # 

Methods

traverse1 :: Apply f => (a -> f b) -> Opposite a -> f (Opposite b) #

sequence1 :: Apply f => Opposite (f b) -> f (Opposite b) #

Foldable1 Opposite Source # 

Methods

fold1 :: Semigroup m => Opposite m -> m #

foldMap1 :: Semigroup m => (a -> m) -> Opposite a -> m #

LeftModule r s => RightModule r (Opposite s) Source # 

Methods

(*.) :: Opposite s -> r -> Opposite s Source #

RightModule r s => LeftModule r (Opposite s) Source # 

Methods

(.*) :: r -> Opposite s -> Opposite s Source #

Eq r => Eq (Opposite r) Source # 

Methods

(==) :: Opposite r -> Opposite r -> Bool #

(/=) :: Opposite r -> Opposite r -> Bool #

Ord r => Ord (Opposite r) Source # 

Methods

compare :: Opposite r -> Opposite r -> Ordering #

(<) :: Opposite r -> Opposite r -> Bool #

(<=) :: Opposite r -> Opposite r -> Bool #

(>) :: Opposite r -> Opposite r -> Bool #

(>=) :: Opposite r -> Opposite r -> Bool #

max :: Opposite r -> Opposite r -> Opposite r #

min :: Opposite r -> Opposite r -> Opposite r #

Read r => Read (Opposite r) Source # 
Show r => Show (Opposite r) Source # 

Methods

showsPrec :: Int -> Opposite r -> ShowS #

show :: Opposite r -> String #

showList :: [Opposite r] -> ShowS #

Idempotent r => Idempotent (Opposite r) Source # 
Abelian r => Abelian (Opposite r) Source # 
Additive r => Additive (Opposite r) Source # 

Methods

(+) :: Opposite r -> Opposite r -> Opposite r Source #

sinnum1p :: Natural -> Opposite r -> Opposite r Source #

sumWith1 :: Foldable1 f => (a -> Opposite r) -> f a -> Opposite r Source #

Monoidal r => Monoidal (Opposite r) Source # 

Methods

zero :: Opposite r Source #

sinnum :: Natural -> Opposite r -> Opposite r Source #

sumWith :: Foldable f => (a -> Opposite r) -> f a -> Opposite r Source #

Semiring r => Semiring (Opposite r) Source # 
Multiplicative r => Multiplicative (Opposite r) Source # 

Methods

(*) :: Opposite r -> Opposite r -> Opposite r Source #

pow1p :: Opposite r -> Natural -> Opposite r Source #

productWith1 :: Foldable1 f => (a -> Opposite r) -> f a -> Opposite r Source #

Group r => Group (Opposite r) Source # 
Unital r => Unital (Opposite r) Source # 

Methods

one :: Opposite r Source #

pow :: Opposite r -> Natural -> Opposite r Source #

productWith :: Foldable f => (a -> Opposite r) -> f a -> Opposite r Source #

Division r => Division (Opposite r) Source # 
Band r => Band (Opposite r) Source # 
DecidableAssociates r => DecidableAssociates (Opposite r) Source # 
DecidableUnits r => DecidableUnits (Opposite r) Source # 
DecidableZero r => DecidableZero (Opposite r) Source # 

Methods

isZero :: Opposite r -> Bool Source #

Rig r => Rig (Opposite r) Source # 
Ring r => Ring (Opposite r) Source # 
Commutative r => Commutative (Opposite r) Source # 
Semiring r => RightModule (Opposite r) (Opposite r) Source # 

Methods

(*.) :: Opposite r -> Opposite r -> Opposite r Source #

Semiring r => LeftModule (Opposite r) (Opposite r) Source # 

Methods

(.*) :: Opposite r -> Opposite r -> Opposite r Source #