numeric-prelude-0.1.1: An experimental alternative hierarchy of numeric type classesSource codeContentsIndex
Algebra.Module
Portabilityrequires multi-parameter type classes
Stabilityprovisional
Maintainernumericprelude@henning-thielemann.de
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 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
show/hide Instances
C Double Double
C Float Float
C Int Int
C Integer Integer
C a => C Integer (T a)
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)
C a b => C a (T b)
C a b => C a (T b)
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
Instances for composed types
Related functions
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.

Better move to Algebra.Additive?

Properties
propCascade :: (Eq v, C a v) => v -> a -> a -> BoolSource
propRightDistributive :: (Eq v, C a v) => a -> v -> v -> BoolSource
propLeftDistributive :: (Eq v, C a v) => v -> a -> a -> BoolSource
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