Algebra.Vector

Abstraction of vectors

Documentation

class C 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

zero :: C a => v a

zero element of the vector space

(<+>) :: C a => v a -> v a -> v a infixl 6

add and subtract elements

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

scale a vector by a scalar

Instances

C []

C T

C T

C T

C T

C T

C T

C T

C ((->) b)

Ord i => C (Map i)

Ord a => C (T a)

Ord i => C (T i)

C (T a)

class Eq v where

We need a Haskell 98 type class which provides equality test for Vector type constructors.

Methods

eq :: Eq a => v a -> v a -> Bool infix 4

Instances

Eq []

Instances for standard type constructors

functorScale :: (Functor v, C a) => a -> v a -> v a

Related functions

linearComb :: (C a, C v) => [a] -> [v a] -> v a

Compute the linear combination of a list of vectors.

Properties

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

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

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