vector-space-0.7.6: Vector & affine spaces, linear maps, and derivatives (requires ghc 6.9 or better) Source code Contents Index

Data.AdditiveGroup Stability experimental Maintainer conal@conal.net, andygill@ku.edu

Description

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

Synopsis

class AdditiveGroup v where zeroV :: v (^+^) :: v -> v -> v negateV :: v -> v (^-^) :: AdditiveGroup 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 Source

Additive group v. Methods zeroV :: v Source The zero element: identity for '(^+^)' (^+^) :: v -> v -> v Source Add vectors negateV :: v -> v Source Additive inverse Instances AdditiveGroup Double AdditiveGroup Float AdditiveGroup Int AdditiveGroup Integer AdditiveGroup () (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)

(^-^) :: AdditiveGroup v => v -> v -> v Source

Group subtraction

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

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