Maintainer	numericprelude@henning-thielemann.de
Stability	provisional
Portability	requires multi-parameter type classes
Safe Haskell	None
Language	Haskell98

Algebra.ModuleBasis

Contents

Description

Abstraction of bases of finite dimensional modules

Synopsis

Documentation

class C a v => C a v where #

It must hold:

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

Minimal complete definition

Methods

basis :: a -> [v] #

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

flatten :: v -> [a] #

scale a vector by a scalar

dimension :: a -> v -> Int #

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 #
Methods basis :: Double -> [Double] # flatten :: Double -> [Double] # dimension :: Double -> Double -> Int #
C Float Float #
Methods basis :: Float -> [Float] # flatten :: Float -> [Float] # dimension :: Float -> Float -> Int #
C Int Int #
Methods basis :: Int -> [Int] # flatten :: Int -> [Int] # dimension :: Int -> Int -> Int #
C Integer Integer #
Methods basis :: Integer -> [Integer] # flatten :: Integer -> [Integer] # dimension :: Integer -> Integer -> Int #
(C a v0, C a v1) => C a (v0, v1) #
Methods basis :: a -> [(v0, v1)] # flatten :: (v0, v1) -> [a] # dimension :: a -> (v0, v1) -> Int #
(C a v0, C a v1, C a v2) => C a (v0, v1, v2) #
Methods basis :: a -> [(v0, v1, v2)] # flatten :: (v0, v1, v2) -> [a] # dimension :: a -> (v0, v1, v2) -> Int #
C a => C (T a) (T a) #
Methods basis :: T a -> [T a] # flatten :: T a -> [T a] # dimension :: T a -> T a -> Int #

Instances for atomic types