Data.AdditiveGroup

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

Documentation

class AdditiveGroup v where

Additive group v.

Minimal complete definition

zeroV, (^+^), negateV

Methods

zeroV :: v

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

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

Add vectors

negateV :: v -> v

Additive inverse

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

Group subtraction

Instances

AdditiveGroup Double

AdditiveGroup Float

AdditiveGroup Int

AdditiveGroup Integer

AdditiveGroup ()

AdditiveGroup CSChar

AdditiveGroup CShort

AdditiveGroup CInt

AdditiveGroup CLong

AdditiveGroup CLLong

AdditiveGroup CFloat

AdditiveGroup CDouble

AdditiveGroup CIntMax

Integral a => AdditiveGroup (Ratio a)

(RealFloat v, AdditiveGroup v) => AdditiveGroup (Complex v)

AdditiveGroup a => AdditiveGroup (Maybe a)

AdditiveGroup a => AdditiveGroup (Sum a)

AdditiveGroup v => AdditiveGroup (a -> v)

(AdditiveGroup u, AdditiveGroup v) => AdditiveGroup (u, v)

(HasTrie u, AdditiveGroup v) => AdditiveGroup ((:->:) u v)

(HasTrie (Basis u), AdditiveGroup v) => AdditiveGroup ((:-*) u v)

(HasBasis a, HasTrie (Basis a), AdditiveGroup u) => AdditiveGroup ((:>) a u)

(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w) => AdditiveGroup (u, v, w)

(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w, AdditiveGroup x) => AdditiveGroup (u, v, w, x)

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

Applicative Sum

Bounded a => Bounded (Sum a)

Eq a => Eq (Sum a)

Ord a => Ord (Sum a)

Read a => Read (Sum a)

Show a => Show (Sum a)

AdditiveGroup a => Monoid (Sum a)

AdditiveGroup a => AdditiveGroup (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