Copyright	(c) Conal Elliott and Andy J Gill 2008
License	BSD3
Maintainer	conal@conal.net, andygill@ku.edu
Stability	experimental
Safe Haskell	None
Language	Haskell98

Data.AdditiveGroup

Description

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

Synopsis

Documentation

Additive group v.

Minimal complete definition

Methods

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

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

Add vectors

Additive inverse

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

Group subtraction

Instances

AdditiveGroup Double Source
AdditiveGroup Float Source
AdditiveGroup Int Source
AdditiveGroup Integer Source
AdditiveGroup () Source
AdditiveGroup CSChar Source
AdditiveGroup CShort Source
AdditiveGroup CInt Source
AdditiveGroup CLong Source
AdditiveGroup CLLong Source
AdditiveGroup CFloat Source
AdditiveGroup CDouble Source
AdditiveGroup CIntMax Source
Integral a => AdditiveGroup (Ratio a) Source
(RealFloat v, AdditiveGroup v) => AdditiveGroup (Complex v) Source
AdditiveGroup a => AdditiveGroup (Maybe a) Source
AdditiveGroup a => AdditiveGroup (Sum a) Source
AdditiveGroup v => AdditiveGroup (a -> v) Source
(AdditiveGroup u, AdditiveGroup v) => AdditiveGroup (u, v) Source
(HasTrie u, AdditiveGroup v) => AdditiveGroup ((:->:) u v) Source
(HasTrie (Basis u), AdditiveGroup v) => AdditiveGroup ((:-*) u v) Source
(HasBasis a, HasTrie (Basis a), AdditiveGroup u) => AdditiveGroup ((:>) a u) Source
(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w) => AdditiveGroup (u, v, w) Source
(AdditiveGroup u, AdditiveGroup v, AdditiveGroup w, AdditiveGroup x) => AdditiveGroup (u, v, w, x) Source

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 Source
Applicative Sum Source
Bounded a => Bounded (Sum a) Source
Eq a => Eq (Sum a) Source
Ord a => Ord (Sum a) Source
Read a => Read (Sum a) Source
Show a => Show (Sum a) Source
AdditiveGroup a => Monoid (Sum a) Source
AdditiveGroup a => AdditiveGroup (Sum a) Source

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

Application a unary function inside a Sum

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

Application a binary function inside a Sum