algebra-4.3: Constructive abstract algebra

Numeric.Ring.Opposite

Synopsis

# Documentation

newtype Opposite r Source #

Constructors

 Opposite FieldsrunOpposite :: r

Instances

 Source # Methodsfmap :: (a -> b) -> Opposite a -> Opposite b #(<\$) :: a -> Opposite b -> Opposite a # Source # Methodsfold :: 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 # Source # Methodstraverse :: 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) # Source # Methodstraverse1 :: Apply f => (a -> f b) -> Opposite a -> f (Opposite b) #sequence1 :: Apply f => Opposite (f b) -> f (Opposite b) # Source # Methodsfold1 :: 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 # Methodscompare :: 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 # MethodsreadsPrec :: Int -> ReadS (Opposite r) # Show r => Show (Opposite r) Source # MethodsshowsPrec :: 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 #sumWith1 :: Foldable1 f => (a -> Opposite r) -> f a -> Opposite r Source # Monoidal r => Monoidal (Opposite r) Source # Methodssinnum :: Natural -> Opposite r -> Opposite r Source #sumWith :: Foldable f => (a -> Opposite r) -> f a -> Opposite r Source # Semiring r => Semiring (Opposite r) Source # 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 # Methods(-) :: Opposite r -> Opposite r -> Opposite r Source #subtract :: Opposite r -> Opposite r -> Opposite r Source #times :: Integral n => n -> Opposite r -> Opposite r Source # Unital r => Unital (Opposite r) Source # Methodspow :: Opposite r -> Natural -> Opposite r Source #productWith :: Foldable f => (a -> Opposite r) -> f a -> Opposite r Source # Division r => Division (Opposite r) Source # Methodsrecip :: Opposite r -> Opposite r Source #(/) :: Opposite r -> Opposite r -> Opposite r Source #(\\) :: Opposite r -> Opposite r -> Opposite r Source #(^) :: Integral n => Opposite r -> n -> Opposite r Source # Band r => Band (Opposite r) Source # Source # MethodsisAssociate :: Opposite r -> Opposite r -> Bool Source # Source # Methods(^?) :: Integral n => Opposite r -> n -> Maybe (Opposite r) Source # Source # Methods Rig r => Rig (Opposite r) Source # Methods Ring r => Ring (Opposite r) Source # Methods 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 #