Copyright	(c) Conal Elliott and Andy J Gill 2008
License	BSD3
Maintainer	conal@conal.net, andygill@ku.edu
Stability	experimental
Safe Haskell	Safe
Language	Haskell98

Data.AdditiveGroup

Description

Groups: zero, addition, and negation (additive inverse)

Synopsis

class AdditiveGroup v where
- zeroV :: v
- (^+^) :: v -> v -> v
- negateV :: v -> v
- (^-^) :: v -> v -> v
sumV :: (Foldable f, AdditiveGroup v) => f v -> v
newtype Sum a = Sum {
- getSum :: a
}
inSum :: (a -> b) -> Sum a -> Sum b
inSum2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c

Documentation

class AdditiveGroup v where #

Additive group v.

Minimal complete definition

Nothing

Methods

zeroV :: v #

The zero element: identity for '(^+^)'

zeroV :: (Generic v, AdditiveGroup (VRep v)) => v #

The zero element: identity for '(^+^)'

(^+^) :: v -> v -> v infixl 6 #

Add vectors

(^+^) :: (Generic v, AdditiveGroup (VRep v)) => v -> v -> v infixl 6 #

Add vectors

negateV :: v -> v #

Additive inverse

negateV :: (Generic v, AdditiveGroup (VRep v)) => v -> v #

Additive inverse

(^-^) :: v -> v -> v infixl 6 #

Group subtraction

Instances

AdditiveGroup Double #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Double # (^+^) :: Double -> Double -> Double # negateV :: Double -> Double # (^-^) :: Double -> Double -> Double #
AdditiveGroup Float #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Float # (^+^) :: Float -> Float -> Float # negateV :: Float -> Float # (^-^) :: Float -> Float -> Float #
AdditiveGroup Int #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Int # (^+^) :: Int -> Int -> Int # negateV :: Int -> Int # (^-^) :: Int -> Int -> Int #
AdditiveGroup Integer #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Integer # (^+^) :: Integer -> Integer -> Integer # negateV :: Integer -> Integer # (^-^) :: Integer -> Integer -> Integer #
AdditiveGroup () #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: () # (^+^) :: () -> () -> () # negateV :: () -> () # (^-^) :: () -> () -> () #
AdditiveGroup CSChar #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CSChar # (^+^) :: CSChar -> CSChar -> CSChar # negateV :: CSChar -> CSChar # (^-^) :: CSChar -> CSChar -> CSChar #
AdditiveGroup CShort #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CShort # (^+^) :: CShort -> CShort -> CShort # negateV :: CShort -> CShort # (^-^) :: CShort -> CShort -> CShort #
AdditiveGroup CInt #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CInt # (^+^) :: CInt -> CInt -> CInt # negateV :: CInt -> CInt # (^-^) :: CInt -> CInt -> CInt #
AdditiveGroup CLong #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CLong # (^+^) :: CLong -> CLong -> CLong # negateV :: CLong -> CLong # (^-^) :: CLong -> CLong -> CLong #
AdditiveGroup CLLong #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CLLong # (^+^) :: CLLong -> CLLong -> CLLong # negateV :: CLLong -> CLLong # (^-^) :: CLLong -> CLLong -> CLLong #
AdditiveGroup CFloat #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CFloat # (^+^) :: CFloat -> CFloat -> CFloat # negateV :: CFloat -> CFloat # (^-^) :: CFloat -> CFloat -> CFloat #
AdditiveGroup CDouble #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CDouble # (^+^) :: CDouble -> CDouble -> CDouble # negateV :: CDouble -> CDouble # (^-^) :: CDouble -> CDouble -> CDouble #
AdditiveGroup CIntMax #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: CIntMax # (^+^) :: CIntMax -> CIntMax -> CIntMax # negateV :: CIntMax -> CIntMax # (^-^) :: CIntMax -> CIntMax -> CIntMax #
AdditiveGroup a => AdditiveGroup (Maybe a) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Maybe a # (^+^) :: Maybe a -> Maybe a -> Maybe a # negateV :: Maybe a -> Maybe a # (^-^) :: Maybe a -> Maybe a -> Maybe a #
Integral a => AdditiveGroup (Ratio a) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Ratio a # (^+^) :: Ratio a -> Ratio a -> Ratio a # negateV :: Ratio a -> Ratio a # (^-^) :: Ratio a -> Ratio a -> Ratio a #
(RealFloat v, AdditiveGroup v) => AdditiveGroup (Complex v) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Complex v # (^+^) :: Complex v -> Complex v -> Complex v # negateV :: Complex v -> Complex v # (^-^) :: Complex v -> Complex v -> Complex v #
AdditiveGroup a => AdditiveGroup (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Sum a # (^+^) :: Sum a -> Sum a -> Sum a # negateV :: Sum a -> Sum a # (^-^) :: Sum a -> Sum a -> Sum a #
AdditiveGroup v => AdditiveGroup (a -> v) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: a -> v # (^+^) :: (a -> v) -> (a -> v) -> a -> v # negateV :: (a -> v) -> a -> v # (^-^) :: (a -> v) -> (a -> v) -> a -> v #
(AdditiveGroup u, AdditiveGroup v) => AdditiveGroup (u, v) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: (u, v) # (^+^) :: (u, v) -> (u, v) -> (u, v) # negateV :: (u, v) -> (u, v) # (^-^) :: (u, v) -> (u, v) -> (u, v) #
(HasTrie u, AdditiveGroup v) => AdditiveGroup (u :->: v) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: u :->: v # (^+^) :: (u :->: v) -> (u :->: v) -> u :->: v # negateV :: (u :->: v) -> u :->: v # (^-^) :: (u :->: v) -> (u :->: v) -> u :->: v #
(HasTrie (Basis u), AdditiveGroup v) => AdditiveGroup (u :-* v) #
Instance details Defined in Data.LinearMap Methods zeroV :: u :-* v # (^+^) :: (u :-* v) -> (u :-* v) -> u :-* v # negateV :: (u :-* v) -> u :-* v # (^-^) :: (u :-* v) -> (u :-* v) -> u :-* v #
(HasBasis a, HasTrie (Basis a), AdditiveGroup u) => AdditiveGroup (a :> u) #
Instance details Defined in Data.Maclaurin Methods zeroV :: a :> u # (^+^) :: (a :> u) -> (a :> u) -> a :> u # negateV :: (a :> u) -> a :> u # (^-^) :: (a :> u) -> (a :> u) -> a :> u #
AdditiveGroup a => AdditiveGroup (Rec0 a s) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Rec0 a s # (^+^) :: Rec0 a s -> Rec0 a s -> Rec0 a s # negateV :: Rec0 a s -> Rec0 a s # (^-^) :: Rec0 a s -> Rec0 a s -> Rec0 a s #
(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w) => AdditiveGroup (u, v, w) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: (u, v, w) # (^+^) :: (u, v, w) -> (u, v, w) -> (u, v, w) # negateV :: (u, v, w) -> (u, v, w) # (^-^) :: (u, v, w) -> (u, v, w) -> (u, v, w) #
(AdditiveGroup (f p), AdditiveGroup (g p)) => AdditiveGroup ((f :*: g) p) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: (f :: g) p # (^+^) :: (f :: g) p -> (f :: g) p -> (f :: g) p # negateV :: (f :: g) p -> (f :: g) p # (^-^) :: (f :: g) p -> (f :: g) p -> (f :*: g) p #
(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w, AdditiveGroup x) => AdditiveGroup (u, v, w, x) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: (u, v, w, x) # (^+^) :: (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x) # negateV :: (u, v, w, x) -> (u, v, w, x) # (^-^) :: (u, v, w, x) -> (u, v, w, x) -> (u, v, w, x) #
AdditiveGroup (f p) => AdditiveGroup (M1 i c f p) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: M1 i c f p # (^+^) :: M1 i c f p -> M1 i c f p -> M1 i c f p # negateV :: M1 i c f p -> M1 i c f p # (^-^) :: M1 i c f p -> M1 i c f p -> M1 i c f p #

sumV :: (Foldable f, AdditiveGroup v) => f v -> v #

Sum over several vectors

newtype Sum a #

Monoid under group addition. Alternative to the Sum in Data.Monoid, which uses Num instead of AdditiveGroup.

Constructors

Sum
Fields getSum :: a

Instances

Functor Sum #
Instance details Defined in Data.AdditiveGroup Methods fmap :: (a -> b) -> Sum a -> Sum b # (<$) :: a -> Sum b -> Sum a #
Applicative Sum #
Instance details Defined in Data.AdditiveGroup Methods pure :: a -> Sum a # (<>) :: Sum (a -> b) -> Sum a -> Sum b # liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c # (>) :: Sum a -> Sum b -> Sum b # (<*) :: Sum a -> Sum b -> Sum a #
Bounded a => Bounded (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods minBound :: Sum a # maxBound :: Sum a #
Eq a => Eq (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods (==) :: Sum a -> Sum a -> Bool # (/=) :: Sum a -> Sum a -> Bool #
Ord a => Ord (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods compare :: Sum a -> Sum a -> Ordering # (<) :: Sum a -> Sum a -> Bool # (<=) :: Sum a -> Sum a -> Bool # (>) :: Sum a -> Sum a -> Bool # (>=) :: Sum a -> Sum a -> Bool # max :: Sum a -> Sum a -> Sum a # min :: Sum a -> Sum a -> Sum a #
Read a => Read (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods readsPrec :: Int -> ReadS (Sum a) # readList :: ReadS [Sum a] # readPrec :: ReadPrec (Sum a) # readListPrec :: ReadPrec [Sum a] #
Show a => Show (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods showsPrec :: Int -> Sum a -> ShowS # show :: Sum a -> String # showList :: [Sum a] -> ShowS #
AdditiveGroup a => Semigroup (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods (<>) :: Sum a -> Sum a -> Sum a # sconcat :: NonEmpty (Sum a) -> Sum a # stimes :: Integral b => b -> Sum a -> Sum a #
AdditiveGroup a => Monoid (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods mempty :: Sum a # mappend :: Sum a -> Sum a -> Sum a # mconcat :: [Sum a] -> Sum a #
AdditiveGroup a => AdditiveGroup (Sum a) #
Instance details Defined in Data.AdditiveGroup Methods zeroV :: Sum a # (^+^) :: Sum a -> Sum a -> Sum a # negateV :: Sum a -> Sum a # (^-^) :: Sum a -> Sum a -> Sum a #

inSum :: (a -> b) -> Sum a -> Sum b #

Application a unary function inside a Sum

inSum2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c #

Application a binary function inside a Sum