Safe Haskell	None
Language	Haskell2010

NumHask.Algebra.Module

Contents

Module
Tensoring

Description

Algebra

Synopsis

Module

class (Representable m, Additive a) => AdditiveModule m a where Source #

AdditiveModule

Methods

(.+) :: m a -> a -> m a infixl 6 Source #

(+.) :: a -> m a -> m a infixl 6 Source #

Instances

(Representable r, Additive a) => AdditiveModule r a Source #
Methods (.+) :: r a -> a -> r a Source # (+.) :: a -> r a -> r a Source #

class (Representable m, AdditiveGroup a) => AdditiveGroupModule m a where Source #

AdditiveGroupModule

Methods

(.-) :: m a -> a -> m a infixl 6 Source #

(-.) :: a -> m a -> m a infixl 6 Source #

Instances

(Representable r, AdditiveGroup a) => AdditiveGroupModule r a Source #
Methods (.-) :: r a -> a -> r a Source # (-.) :: a -> r a -> r a Source #

class (Representable m, Multiplicative a) => MultiplicativeModule m a where Source #

MultiplicativeModule

Methods

(.*) :: m a -> a -> m a infixl 7 Source #

(*.) :: a -> m a -> m a infixl 7 Source #

Instances

(Representable r, Multiplicative a) => MultiplicativeModule r a Source #
Methods (.) :: r a -> a -> r a Source # (.) :: a -> r a -> r a Source #

class (Representable m, MultiplicativeGroup a) => MultiplicativeGroupModule m a where Source #

MultiplicativeGroupModule

Methods

(./) :: m a -> a -> m a infixl 7 Source #

(/.) :: a -> m a -> m a infixl 7 Source #

Instances

(Representable r, MultiplicativeGroup a) => MultiplicativeGroupModule r a Source #
Methods (./) :: r a -> a -> r a Source # (/.) :: a -> r a -> r a Source #

Tensoring

class (Representable m, ExpField a, Normed (m a) a) => Banach m a where Source #

Banach

Methods

normalize :: m a -> m a Source #

Instances

(Normed (r a) a, ExpField a, Representable r) => Banach r a Source #
Methods normalize :: r a -> r a Source #

class Additive (m a) => Hilbert m a where Source #

Hilbert

Minimal complete definition

(<.>)

Methods

(<.>) :: m a -> m a -> a infix 8 Source #

Instances

(Additive (r a), Foldable r, Representable r, CRing a) => Hilbert r a Source #
Methods (<.>) :: r a -> r a -> a Source #

type family (a :: k1) >< (b :: k2) :: * infix 8 Source #

tensorial tomfoolery

Instances

type (><) * * (r a) b Source #
type (><) * * (r a) b
type (><) * * Double Double Source #
type (><) * * Double Double = Double
type (><) * * Float Float Source #
type (><) * * Float Float = Float
type (><) * * Int Int Source #
type (><) * * Int Int = Int
type (><) * * Integer Integer Source #
type (><) * * Integer Integer = Integer

class TensorProduct a where Source #

TensorAlgebra

Minimal complete definition

(><), timesleft, timesright

Methods

(><) :: a -> a -> a >< a infix 8 Source #

timesleft :: a -> (a >< a) -> a Source #

timesright :: (a >< a) -> a -> a Source #

Instances

(AdditiveGroup (r a), Foldable r, Representable r, CRing a) => TensorProduct (r a) Source #
Methods (><) :: r a -> r a -> (* >< ) (r a) (r a) Source # timesleft :: r a -> ( >< ) (r a) (r a) -> r a Source # timesright :: ( >< *) (r a) (r a) -> r a -> r a Source #