Portability	requires multi-parameter type classes
Stability	provisional
Maintainer	numericprelude@henning-thielemann.de

Algebra.Module

Contents

Description

Abstraction of modules

Synopsis

Documentation

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

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 -> vSource

scale a vector by a scalar

Instances

C Double Double
C Float Float
C Int Int
C Integer Integer
C T T
C a => C Integer (T a)
C a v => C a [v]
C a b => C a (T b)
C a b => C a (T b)
C a b => C a (T b)
(C a v, C v) => C a (T v)
C a b => C a (T b)	The '(*>)' method can't replace `scale` because it requires the Algebra.Module constraint
C a b => C a (T b)
C a b => C a (T b)	The '(*>)' method can't replace `scale` because it requires the Algebra.Module constraint
C a v => C a (c -> v)
(C a b0, C a b1) => C a (b0, b1)
(Ord i, Eq a, Eq v, C a v) => C a (Map i v)
(C u, C a b) => C a (T u b)
(Ord i, C a v) => C a (T i v)
C a v => C a (T b v)
(C a b0, C a b1, C a b2) => C a (b0, b1, b2)
C a => C (T a) (T a)

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

Instances for atomic types

linearComb :: C a v => [a] -> [v] -> vSource

Compute the linear combination of a list of vectors.

ToDo: Should it use NumericPrelude.List.zipWithMatch ?

integerMultiply :: (C a, C v) => a -> v -> vSource

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

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

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