Data.Algebra.Dual

Documentation

type D = Dual

data Dual a

A dual number.

Constructors

Dual a a

Instances

Functor Dual

Defined in Data.Algebra.Dual

Methods

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

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

Applicative Dual

Defined in Data.Algebra.Dual

Methods

pure :: a -> Dual a

(<*>) :: Dual (a -> b) -> Dual a -> Dual b

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c

(*>) :: Dual a -> Dual b -> Dual b

(<*) :: Dual a -> Dual b -> Dual a

Foldable Dual

Defined in Data.Algebra.Dual

Methods

fold :: Monoid m => Dual m -> m

foldMap :: Monoid m => (a -> m) -> Dual a -> m

foldr :: (a -> b -> b) -> b -> Dual a -> b

foldr' :: (a -> b -> b) -> b -> Dual a -> b

foldl :: (b -> a -> b) -> b -> Dual a -> b

foldl' :: (b -> a -> b) -> b -> Dual a -> b

foldr1 :: (a -> a -> a) -> Dual a -> a

foldl1 :: (a -> a -> a) -> Dual a -> a

toList :: Dual a -> [a]

null :: Dual a -> Bool

length :: Dual a -> Int

elem :: Eq a => a -> Dual a -> Bool

maximum :: Ord a => Dual a -> a

minimum :: Ord a => Dual a -> a

sum :: Num a => Dual a -> a

product :: Num a => Dual a -> a

Traversable Dual

Defined in Data.Algebra.Dual

Methods

traverse :: Applicative f => (a -> f b) -> Dual a -> f (Dual b)

sequenceA :: Applicative f => Dual (f a) -> f (Dual a)

mapM :: Monad m => (a -> m b) -> Dual a -> m (Dual b)

sequence :: Monad m => Dual (m a) -> m (Dual a)

Distributive Dual

Defined in Data.Algebra.Dual

Methods

distribute :: Functor f => f (Dual a) -> Dual (f a)

collect :: Functor f => (a -> Dual b) -> f a -> Dual (f b)

distributeM :: Monad m => m (Dual a) -> Dual (m a)

collectM :: Monad m => (a -> Dual b) -> m a -> Dual (m b)

Representable Dual

Defined in Data.Algebra.Dual

Associated Types

type Rep Dual :: Type

Methods

tabulate :: (Rep Dual -> a) -> Dual a

index :: Dual a -> Rep Dual -> a

Show1 Dual

Defined in Data.Algebra.Dual

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Dual a -> ShowS

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Dual a] -> ShowS

Foldable1 Dual

Defined in Data.Algebra.Dual

Methods

fold1 :: Semigroup m => Dual m -> m

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

toNonEmpty :: Dual a -> NonEmpty a

Semiring a => Bisemimodule a a (Dual a)

Defined in Data.Algebra.Dual

Methods

discale :: a -> a -> Dual a -> Dual a

Semiring a => RightSemimodule a (Dual a)

Defined in Data.Algebra.Dual

Methods

rscale :: a -> Dual a -> Dual a

Semiring a => LeftSemimodule a (Dual a)

Defined in Data.Algebra.Dual

Methods

lscale :: a -> Dual a -> Dual a

Eq a => Eq (Dual a)

Defined in Data.Algebra.Dual

Methods

(==) :: Dual a -> Dual a -> Bool

(/=) :: Dual a -> Dual a -> Bool

Show a => Show (Dual a)

Defined in Data.Algebra.Dual

Methods

showsPrec :: Int -> Dual a -> ShowS

show :: Dual a -> String

showList :: [Dual a] -> ShowS

(Additive - Semigroup) a => Semigroup (Additive (Dual a))

Defined in Data.Algebra.Dual

Methods

(<>) :: Additive (Dual a) -> Additive (Dual a) -> Additive (Dual a)

sconcat :: NonEmpty (Additive (Dual a)) -> Additive (Dual a)

stimes :: Integral b => b -> Additive (Dual a) -> Additive (Dual a)

(Additive - Monoid) a => Monoid (Additive (Dual a))

Defined in Data.Algebra.Dual

Methods

mempty :: Additive (Dual a)

mappend :: Additive (Dual a) -> Additive (Dual a) -> Additive (Dual a)

mconcat :: [Additive (Dual a)] -> Additive (Dual a)

(Additive - Group) a => Group (Additive (Dual a))

Defined in Data.Algebra.Dual

Methods

inv :: Additive (Dual a) -> Additive (Dual a)

greplicate :: Integer -> Additive (Dual a) -> Additive (Dual a)

(Additive - Group) a => Loop (Additive (Dual a))

Defined in Data.Algebra.Dual

Methods

lempty :: Additive (Dual a)

lreplicate :: Natural -> Additive (Dual a) -> Additive (Dual a)

(Additive - Group) a => Quasigroup (Additive (Dual a))

Defined in Data.Algebra.Dual

Methods

(//) :: Additive (Dual a) -> Additive (Dual a) -> Additive (Dual a)

(\\) :: Additive (Dual a) -> Additive (Dual a) -> Additive (Dual a)

(Additive - Group) a => Magma (Additive (Dual a))

Defined in Data.Algebra.Dual

Methods

(<<) :: Additive (Dual a) -> Additive (Dual a) -> Additive (Dual a)

type Rep Dual

Defined in Data.Algebra.Dual

type Rep Dual = D2