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

Minimal complete definition

zero, (<+>), (*>)

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 []

Methods

zero :: C a => [a]

(<+>) :: C a => [a] -> [a] -> [a]

(*>) :: C a => a -> [a] -> [a]

C T

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

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

C T

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

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

C T

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

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

C T

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

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

C T

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

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

C T

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

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

C T

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

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

Ord a => C (T a)

Methods

zero :: C a => T a a

(<+>) :: C a => T a a -> T a a -> T a a

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

Ord i => C (T i)

Methods

zero :: C a => T i a

(<+>) :: C a => T i a -> T i a -> T i a

(*>) :: C a => a -> T i a -> T i a

C (T a)

Methods

zero :: C a => T a a

(<+>) :: C a => T a a -> T a a -> T a a

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

C ((->) LiftedRep LiftedRep b)

Methods

zero :: C a => (LiftedRep -> LiftedRep) b a

(<+>) :: C a => (LiftedRep -> LiftedRep) b a -> (LiftedRep -> LiftedRep) b a -> (LiftedRep -> LiftedRep) b a

(*>) :: C a => a -> (LiftedRep -> LiftedRep) b a -> (LiftedRep -> LiftedRep) b a

class Eq v where

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

Minimal complete definition

eq

Methods

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

Instances

Eq []

Methods

eq :: Eq a => [a] -> [a] -> Bool

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