Stability	experimental
Maintainer	conal@conal.net, andygill@ku.edu
Safe Haskell	Safe-Infered

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 ()
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