Copyright	(c) Henning Thielemann 2004-2005
Maintainer	numericprelude@henning-thielemann.de
Stability	provisional
Portability	portable
Safe Haskell	None
Language	Haskell98

Algebra.Vector

Contents

Instances for standard type constructors
Related functions
Properties

Description

Abstraction of vectors

Synopsis

class C v where
- zero :: C a => v a
- (<+>) :: C a => v a -> v a -> v a
- (*>) :: C a => a -> v a -> v a
class Eq v where
- eq :: Eq a => v a -> v a -> Bool
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 Source #

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 Source #

zero element of the vector space

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

add and subtract elements

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

scale a vector by a scalar

Instances

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

class Eq v where Source #

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 Source #

Instances

Eq [] Source #
Instance details Defined in Algebra.Vector Methods eq :: Eq a => [a] -> [a] -> Bool Source #

Instances for standard type constructors

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

Related functions

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

Compute the linear combination of a list of vectors.

Properties

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

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

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