Copyright	(c) Henning Thielemann 2004-2005
Maintainer	numericprelude@henning-thielemann.de
Stability	provisional
Portability	portable
Safe Haskell	Safe
Language	Haskell98

Algebra.Vector

Contents

Instances for standard type constructors
Related functions
Properties

Description

Abstraction of vectors

Synopsis

class C v where
class Eq v where
functorScale :: (Functor v, C a) => a -> v a -> v a
linearComb :: (C a, C v) => [a] -> [v a] -> v a
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

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 [] #
Instance details Defined in Algebra.Vector Methods zero :: C a => [a] # (<+>) :: C a => [a] -> [a] -> [a] # (*>) :: C a => a -> [a] -> [a] #
C T #
Instance details Defined in MathObj.PowerSeries Methods zero :: C a => T a # (<+>) :: C a => T a -> T a -> T a # (*>) :: C a => a -> T a -> T a #
C T #
Instance details Defined in MathObj.PowerSeries2 Methods zero :: C a => T a # (<+>) :: C a => T a -> T a -> T a # (*>) :: C a => a -> T a -> T a #
C T #
Instance details Defined in MathObj.Polynomial Methods zero :: C a => T a # (<+>) :: C a => T a -> T a -> T a # (*>) :: C a => a -> T a -> T a #
C T #
Instance details Defined in MathObj.Matrix Methods zero :: C a => T a # (<+>) :: C a => T a -> T a -> T a # (*>) :: C a => a -> T a -> T a #
C T #
Instance details Defined in Number.Complex Methods zero :: C a => T a # (<+>) :: C a => T a -> T a -> T a # (*>) :: C a => a -> T a -> T a #
C T #
Instance details Defined in Number.Quaternion Methods zero :: C a => T a # (<+>) :: C a => T a -> T a -> T a # (*>) :: C a => a -> T a -> T a #
C T #
Instance details Defined in MathObj.LaurentPolynomial Methods zero :: C a => T a # (<+>) :: C a => T a -> T a -> T a # (*>) :: C a => a -> T a -> T a #
Ord i => C (Map i) #
Instance details Defined in MathObj.DiscreteMap Methods zero :: C a => Map i a # (<+>) :: C a => Map i a -> Map i a -> Map i a # (*>) :: C a => a -> Map i a -> Map i a #
Ord a => C (T a) #
Instance details Defined in MathObj.Algebra Methods zero :: C a0 => T a a0 # (<+>) :: C a0 => T a a0 -> T a a0 -> T a a0 # (*>) :: C a0 => a0 -> T a a0 -> T a a0 #
Ord i => C (T i) #
Instance details Defined in Number.Physical 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) #
Instance details Defined in Number.SI Methods zero :: C a0 => T a a0 # (<+>) :: C a0 => T a a0 -> T a a0 -> T a a0 # (*>) :: C a0 => a0 -> T a a0 -> T a a0 #
C ((->) b :: * -> *) #
Instance details Defined in Algebra.Vector Methods zero :: C a => b -> a # (<+>) :: C a => (b -> a) -> (b -> a) -> b -> a # (*>) :: C a => a -> (b -> a) -> 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 [] #
Instance details Defined in Algebra.Vector 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 #