numeric-prelude-0.4.2: An experimental alternative hierarchy of numeric type classes

Maintainernumericprelude@henning-thielemann.de
Stabilityprovisional
Portabilityrequires multi-parameter type classes
Safe HaskellNone
LanguageHaskell98

Algebra.ModuleBasis

Contents

Description

Abstraction of bases of finite dimensional modules

Synopsis

Documentation

class C a v => C a v where Source

It must hold:

  Module.linearComb (flatten v `asTypeOf` [a]) (basis a) == v
  dimension a v == length (flatten v `asTypeOf` [a])

Methods

basis :: a -> [v] Source

basis of the module with respect to the scalar type, the result must be independent of argument, undefined should suffice.

flatten :: v -> [a] Source

scale a vector by a scalar

dimension :: a -> v -> Int Source

the size of the basis, should also work for undefined argument, the result must be independent of argument, undefined should suffice.

Instances

C Double Double 
C Float Float 
C Int Int 
C Integer Integer 
(C a v0, C a v1) => C a (v0, v1) 
(C a v0, C a v1, C a v2) => C a (v0, v1, v2) 
C a => C (T a) (T a) 

Instances for atomic types

Instances for composed types

Properties

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

propDimension :: C a v => a -> v -> Bool Source