Algebra.Vector
 Portability portable Stability provisional Maintainer numericprelude@henning-thielemann.de
 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 Source
add and subtract elements
 (*>) :: C a => a -> v a -> v a Source
scale a vector by a scalar Instances
 C [] C T C T C T C T C T C T C T C ((->) b) Ord i => C (Map i) Ord a => C (T a) Ord i => C (T i) C (T a)
 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 Source Instances
 Eq []
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
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