Algebra.Module

Abstraction of modules

Documentation

class (C a, C v) => C a v where

A Module over a ring satisfies:

  a *> (b + c) === a *> b + a *> c
  (a * b) *> c === a *> (b *> c)
  (a + b) *> c === a *> c + b *> c

Minimal complete definition

(*>)

Methods

(*>) :: a -> v -> v infixr 7

scale a vector by a scalar

Instances

C Double Double

Methods

(*>) :: Double -> Double -> Double

C Float Float

Methods

(*>) :: Float -> Float -> Float

C Int Int

Methods

(*>) :: Int -> Int -> Int

C Int8 Int8

Methods

(*>) :: Int8 -> Int8 -> Int8

C Int16 Int16

Methods

(*>) :: Int16 -> Int16 -> Int16

C Int32 Int32

Methods

(*>) :: Int32 -> Int32 -> Int32

C Int64 Int64

Methods

(*>) :: Int64 -> Int64 -> Int64

C Integer Integer

Methods

(*>) :: Integer -> Integer -> Integer

C T T

Methods

(*>) :: T -> T -> T

C a => C Integer (T a)

Methods

(*>) :: Integer -> T a -> T a

(C a b, RealFloat b) => C a (Complex b)

Methods

(*>) :: a -> Complex b -> Complex b

C a v => C a [v]

Methods

(*>) :: a -> [v] -> [v]

C a b => C a (T b)

Methods

(*>) :: a -> T b -> T b

C a b => C a (T b)

Methods

(*>) :: a -> T b -> T b

(C a v, C v) => C a (T v)

Methods

(*>) :: a -> T v -> T v

C a b => C a (T b)

Methods

(*>) :: a -> T b -> T b

C a b => C a (T b)

The '(*>)' method can't replace scale because it requires the Algebra.Module constraint

Methods

(*>) :: a -> T b -> T b

C a b => C a (T b)

The '(*>)' method can't replace scale because it requires the Algebra.Module constraint

Methods

(*>) :: a -> T b -> T b

C a b => C a (T b)

Methods

(*>) :: a -> T b -> T b

C a v => C a (c -> v)

Methods

(*>) :: a -> (c -> v) -> c -> v

(C a b0, C a b1) => C a (b0, b1)

Methods

(*>) :: a -> (b0, b1) -> (b0, b1)

(C u, C a b) => C a (T u b)

Methods

(*>) :: a -> T u b -> T u b

(Ord i, C a v) => C a (T i v)

Methods

(*>) :: a -> T i v -> T i v

C a v => C a (T b v)

Methods

(*>) :: a -> T b v -> T b v

(C a b0, C a b1, C a b2) => C a (b0, b1, b2)

Methods

(*>) :: a -> (b0, b1, b2) -> (b0, b1, b2)

C a => C (T a) (T a)

Methods

(*>) :: T a -> T a -> T a

C a v => C (T a) (T v)

Methods

(*>) :: T a -> T v -> T v

(<*>.*>) :: C a x => T (a, v) (x -> c) -> (v -> x) -> T (a, v) c

Instances for atomic types

Instances for composed types

Related functions

linearComb :: C a v => [a] -> [v] -> v

Compute the linear combination of a list of vectors.

ToDo: Should it use zipWith ?

integerMultiply :: (C a, C v) => a -> v -> v

This function can be used to define any C as a module over Integer.

Better move to Algebra.Additive?

Properties

propCascade :: (Eq v, C a v) => v -> a -> a -> Bool

propRightDistributive :: (Eq v, C a v) => a -> v -> v -> Bool

propLeftDistributive :: (Eq v, C a v) => v -> a -> a -> Bool