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

Methods

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

scale a vector by a scalar

Instances

C Double Double

C Float Float

C Int Int

C Integer Integer

C T T

C a => C Integer (T a)

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

C a v => C a [v]

C a b => C a (T b)

C a b => C a (T b)

C a b => C a (T b)

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

C a b => C a (T b)

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

C a b => C a (T b)

C a b => C a (T b)

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

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

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

(Ord i, Eq a, Eq v, C a v) => C a (Map i v)

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

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

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

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

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

C a v => C (T a) (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