Copyright	(c) Dylan Thurston Henning Thielemann 2004-2005
Maintainer	numericprelude@henning-thielemann.de
Stability	provisional
Portability	requires multi-parameter type classes
Safe Haskell	None
Language	Haskell98

Algebra.Module

Contents

Instances for atomic types
Instances for composed types
Related functions
Properties

Description

Abstraction of modules

Synopsis

class (C a, C v) => C a v where
- (*>) :: a -> v -> v
(<*>.*>) :: C a x => T (a, v) (x -> c) -> (v -> x) -> T (a, v) c
linearComb :: C a v => [a] -> [v] -> v
integerMultiply :: (C a, C v) => a -> v -> v
propCascade :: (Eq v, C a v) => v -> a -> a -> Bool
propRightDistributive :: (Eq v, C a v) => a -> v -> v -> Bool
propLeftDistributive :: (Eq v, C a v) => v -> a -> a -> Bool

Documentation

class (C a, C v) => C a 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

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

scale a vector by a scalar

Instances

C Double Double Source #
Instance details Defined in Algebra.Module Methods (*>) :: Double -> Double -> Double Source #
C Float Float Source #
Instance details Defined in Algebra.Module Methods (*>) :: Float -> Float -> Float Source #
C Int Int Source #
Instance details Defined in Algebra.Module Methods (*>) :: Int -> Int -> Int Source #
C Int8 Int8 Source #
Instance details Defined in Algebra.Module Methods (*>) :: Int8 -> Int8 -> Int8 Source #
C Int16 Int16 Source #
Instance details Defined in Algebra.Module Methods (*>) :: Int16 -> Int16 -> Int16 Source #
C Int32 Int32 Source #
Instance details Defined in Algebra.Module Methods (*>) :: Int32 -> Int32 -> Int32 Source #
C Int64 Int64 Source #
Instance details Defined in Algebra.Module Methods (*>) :: Int64 -> Int64 -> Int64 Source #
C Integer Integer Source #
Instance details Defined in Algebra.Module Methods (*>) :: Integer -> Integer -> Integer Source #
C T T Source #
Instance details Defined in Number.GaloisField2p32m5 Methods (*>) :: T -> T -> T Source #
C a => C Integer (T a) Source #
Instance details Defined in Algebra.Module Methods (*>) :: Integer -> T a -> T a Source #
(C a b, RealFloat b) => C a (Complex b) Source #
Instance details Defined in Algebra.Module Methods (*>) :: a -> Complex b -> Complex b Source #
C a v => C a [v] Source #
Instance details Defined in Algebra.Module Methods (*>) :: a -> [v] -> [v] Source #
C a b => C a (T b) Source #
Instance details Defined in MathObj.PowerSeries Methods (*>) :: a -> T b -> T b Source #
C a b => C a (T b) Source #
Instance details Defined in MathObj.Polynomial Methods (*>) :: a -> T b -> T b Source #
(C a v, C v) => C a (T v) Source #
Instance details Defined in MathObj.PowerSum Methods (*>) :: a -> T v -> T v Source #
C a b => C a (T b) Source #
Instance details Defined in MathObj.Matrix Methods (*>) :: a -> T b -> T b Source #
C a b => C a (T b) Source #	The '(*>)' method can't replace `scale` because it requires the Algebra.Module constraint
Instance details Defined in Number.Complex Methods (*>) :: a -> T b -> T b Source #
C a b => C a (T b) Source #	The '(*>)' method can't replace `scale` because it requires the Algebra.Module constraint
Instance details Defined in Number.Quaternion Methods (*>) :: a -> T b -> T b Source #
C a b => C a (T b) Source #
Instance details Defined in MathObj.LaurentPolynomial Methods (*>) :: a -> T b -> T b Source #
C a v => C a (c -> v) Source #
Instance details Defined in Algebra.Module Methods (*>) :: a -> (c -> v) -> c -> v Source #
(C a b0, C a b1) => C a (b0, b1) Source #
Instance details Defined in Algebra.Module Methods (*>) :: a -> (b0, b1) -> (b0, b1) Source #
(C u, C a b) => C a (T u b) Source #
Instance details Defined in Number.DimensionTerm Methods (*>) :: a -> T u b -> T u b Source #
(Ord i, Eq a, Eq v, C a v) => C a (Map i v) Source #
Instance details Defined in MathObj.DiscreteMap Methods (*>) :: a -> Map i v -> Map i v Source #
(Ord i, C a v) => C a (T i v) Source #
Instance details Defined in Number.Physical Methods (*>) :: a -> T i v -> T i v Source #
C a v => C a (T b v) Source #
Instance details Defined in Number.SI Methods (*>) :: a -> T b v -> T b v Source #
(C a b0, C a b1, C a b2) => C a (b0, b1, b2) Source #
Instance details Defined in Algebra.Module Methods (*>) :: a -> (b0, b1, b2) -> (b0, b1, b2) Source #
C a => C (T a) (T a) Source #
Instance details Defined in Algebra.Module Methods (*>) :: T a -> T a -> T a Source #
C a v => C (T a) (T v) Source #
Instance details Defined in MathObj.Wrapper.NumericPrelude Methods (*>) :: T a -> T v -> T v Source #

(<*>.*>) :: C a x => T (a, v) (x -> c) -> (v -> x) -> T (a, v) c Source #

Instances for atomic types

Instances for composed types

Related functions

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

Compute the linear combination of a list of vectors.

ToDo: Should it use zipWith ?

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

This function can be used to define any C as a module over Integer.

Better move to Algebra.Additive?

Properties

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

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

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