Data.Algebra.Split

Documentation

type S = Split

data Split a

A dual number.

Constructors

Split a a

Instances

Functor Split

Defined in Data.Algebra.Split

Methods

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

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

Applicative Split

Defined in Data.Algebra.Split

Methods

pure :: a -> Split a

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

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

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

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

Foldable Split

Defined in Data.Algebra.Split

Methods

fold :: Monoid m => Split m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Split a -> a

foldl1 :: (a -> a -> a) -> Split a -> a

toList :: Split a -> [a]

null :: Split a -> Bool

length :: Split a -> Int

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

maximum :: Ord a => Split a -> a

minimum :: Ord a => Split a -> a

sum :: Num a => Split a -> a

product :: Num a => Split a -> a

Traversable Split

Defined in Data.Algebra.Split

Methods

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

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

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

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

Distributive Split

Defined in Data.Algebra.Split

Methods

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

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

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

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

Representable Split

Defined in Data.Algebra.Split

Associated Types

type Rep Split :: Type

Methods

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

index :: Split a -> Rep Split -> a

Show1 Split

Defined in Data.Algebra.Split

Methods

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

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

Foldable1 Split

Defined in Data.Algebra.Split

Methods

fold1 :: Semigroup m => Split m -> m

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

toNonEmpty :: Split a -> NonEmpty a

Semiring a => Bisemimodule a a (Split a)

Defined in Data.Algebra.Split

Methods

discale :: a -> a -> Split a -> Split a

Semiring a => RightSemimodule a (Split a)

Defined in Data.Algebra.Split

Methods

rscale :: a -> Split a -> Split a

Semiring a => LeftSemimodule a (Split a)

Defined in Data.Algebra.Split

Methods

lscale :: a -> Split a -> Split a

Eq a => Eq (Split a)

Defined in Data.Algebra.Split

Methods

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

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

Show a => Show (Split a)

Defined in Data.Algebra.Split

Methods

showsPrec :: Int -> Split a -> ShowS

show :: Split a -> String

showList :: [Split a] -> ShowS

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

Defined in Data.Algebra.Split

Methods

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

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

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

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

Defined in Data.Algebra.Split

Methods

mempty :: Additive (Split a)

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

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

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

Defined in Data.Algebra.Split

Methods

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

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

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

Defined in Data.Algebra.Split

Methods

lempty :: Additive (Split a)

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

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

Defined in Data.Algebra.Split

Methods

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

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

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

Defined in Data.Algebra.Split

Methods

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

type Rep Split

Defined in Data.Algebra.Split

type Rep Split = S2