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

class C a v => C a v where
- basis :: a -> [v]
- flatten :: v -> [a]
- dimension :: a -> v -> Int
propFlatten :: (Eq v, C a v) => a -> v -> Bool
propDimension :: C a v => a -> v -> Bool

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.

scale a vector by a scalar

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

Instances details

C Double Double Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: Double -> [Double] Source # flatten :: Double -> [Double] Source # dimension :: Double -> Double -> Int Source #
C Float Float Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: Float -> [Float] Source # flatten :: Float -> [Float] Source # dimension :: Float -> Float -> Int Source #
C Int Int Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: Int -> [Int] Source # flatten :: Int -> [Int] Source # dimension :: Int -> Int -> Int Source #
C Integer Integer Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: Integer -> [Integer] Source # flatten :: Integer -> [Integer] Source # dimension :: Integer -> Integer -> Int Source #
(C a v0, C a v1) => C a (v0, v1) Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: a -> [(v0, v1)] Source # flatten :: (v0, v1) -> [a] Source # dimension :: a -> (v0, v1) -> Int Source #
(C a v0, C a v1, C a v2) => C a (v0, v1, v2) Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: a -> [(v0, v1, v2)] Source # flatten :: (v0, v1, v2) -> [a] Source # dimension :: a -> (v0, v1, v2) -> Int Source #
C a => C (T a) (T a) Source #
Instance details Defined in Algebra.ModuleBasis Methods basis :: T a -> [T a] Source # flatten :: T a -> [T a] Source # dimension :: T a -> T a -> Int Source #

Instances for atomic types