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

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

Minimal complete definition

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

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 #
Methods zero :: C a => [a] Source # (<+>) :: C a => [a] -> [a] -> [a] Source # (*>) :: C a => a -> [a] -> [a] Source #
C T Source #
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 #
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 #
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 #
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 #
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 #
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 #
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 a => C (T a) Source #
Methods zero :: C a => T a a Source # (<+>) :: C a => T a a -> T a a -> T a a Source # (*>) :: C a => a -> T a a -> T a a Source #
Ord i => C (T i) Source #
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 #
Methods zero :: C a => T a a Source # (<+>) :: C a => T a a -> T a a -> T a a Source # (*>) :: C a => a -> T a a -> T a a Source #
C ((->) LiftedRep LiftedRep b) Source #
Methods zero :: C a => (LiftedRep -> LiftedRep) b a Source # (<+>) :: C a => (LiftedRep -> LiftedRep) b a -> (LiftedRep -> LiftedRep) b a -> (LiftedRep -> LiftedRep) b a Source # (*>) :: C a => a -> (LiftedRep -> LiftedRep) b a -> (LiftedRep -> LiftedRep) b a Source #

class Eq v where Source #

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 Source #

Instances

Eq [] Source #
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 #