Stability	experimental
Maintainer	conal@conal.net, andygill@ku.edu
Safe Haskell	None

Data.AdditiveGroup

Description

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

Synopsis

Documentation

Additive group v.

Methods

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

(^+^) :: v -> v -> vSource

Add vectors

Additive inverse

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)

Group subtraction

Sum over several vectors

newtype Sum a Source

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 bSource

Application a unary function inside a Sum

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

Application a binary function inside a Sum