Numeric.Ring.Opposite

Documentation

newtype Opposite r

http://en.wikipedia.org/wiki/Opposite_ring

Constructors

Opposite

Fields

• runOpposite :: r

Instances

Functor Opposite

Methods

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

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

Foldable Opposite

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

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

Methods

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

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

Foldable1 Opposite

Methods

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

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

toNonEmpty :: Opposite a -> NonEmpty a

LeftModule r s => RightModule r (Opposite s)

Methods

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

RightModule r s => LeftModule r (Opposite s)

Methods

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

Eq r => Eq (Opposite r)

Methods

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

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

Ord r => Ord (Opposite r)

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)

Methods

readsPrec :: Int -> ReadS (Opposite r)

readList :: ReadS [Opposite r]

readPrec :: ReadPrec (Opposite r)

readListPrec :: ReadPrec [Opposite r]

Show r => Show (Opposite r)

Methods

showsPrec :: Int -> Opposite r -> ShowS

show :: Opposite r -> String

showList :: [Opposite r] -> ShowS

Idempotent r => Idempotent (Opposite r)

Abelian r => Abelian (Opposite r)

Additive r => Additive (Opposite r)

Methods

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

sinnum1p :: Natural -> Opposite r -> Opposite r

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

Monoidal r => Monoidal (Opposite r)

Methods

zero :: Opposite r

sinnum :: Natural -> Opposite r -> Opposite r

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

Semiring r => Semiring (Opposite r)

Multiplicative r => Multiplicative (Opposite r)

Methods

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

pow1p :: Opposite r -> Natural -> Opposite r

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

Group r => Group (Opposite r)

Methods

(-) :: Opposite r -> Opposite r -> Opposite r

negate :: Opposite r -> Opposite r

subtract :: Opposite r -> Opposite r -> Opposite r

times :: Integral n => n -> Opposite r -> Opposite r

Unital r => Unital (Opposite r)

Methods

one :: Opposite r

pow :: Opposite r -> Natural -> Opposite r

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

Band r => Band (Opposite r)

Division r => Division (Opposite r)

Methods

recip :: Opposite r -> Opposite r

(/) :: Opposite r -> Opposite r -> Opposite r

(\\) :: Opposite r -> Opposite r -> Opposite r

(^) :: Integral n => Opposite r -> n -> Opposite r

Commutative r => Commutative (Opposite r)

DecidableAssociates r => DecidableAssociates (Opposite r)

Methods

isAssociate :: Opposite r -> Opposite r -> Bool

DecidableUnits r => DecidableUnits (Opposite r)

Methods

recipUnit :: Opposite r -> Maybe (Opposite r)

isUnit :: Opposite r -> Bool

(^?) :: Integral n => Opposite r -> n -> Maybe (Opposite r)

DecidableZero r => DecidableZero (Opposite r)

Methods

isZero :: Opposite r -> Bool

Rig r => Rig (Opposite r)

Methods

fromNatural :: Natural -> Opposite r

Ring r => Ring (Opposite r)

Methods

fromInteger :: Integer -> Opposite r

Semiring r => RightModule (Opposite r) (Opposite r)

Methods

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

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

Methods

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