Algebra.ModuleBasis

Abstraction of bases of finite dimensional modules

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

basis, flatten, dimension

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

Defined in Algebra.ModuleBasis

Methods

basis :: Double -> [Double]

flatten :: Double -> [Double]

dimension :: Double -> Double -> Int

C Float Float

Defined in Algebra.ModuleBasis

Methods

basis :: Float -> [Float]

flatten :: Float -> [Float]

dimension :: Float -> Float -> Int

C Int Int

Defined in Algebra.ModuleBasis

Methods

basis :: Int -> [Int]

flatten :: Int -> [Int]

dimension :: Int -> Int -> Int

C Integer Integer

Defined in Algebra.ModuleBasis

Methods

basis :: Integer -> [Integer]

flatten :: Integer -> [Integer]

dimension :: Integer -> Integer -> Int

(C a v0, C a v1) => C a (v0, v1)

Defined in Algebra.ModuleBasis

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)

Defined in Algebra.ModuleBasis

Methods

basis :: a -> [(v0, v1, v2)]

flatten :: (v0, v1, v2) -> [a]

dimension :: a -> (v0, v1, v2) -> Int

C a => C (T a) (T a)

Defined in Algebra.ModuleBasis

Methods

basis :: T a -> [T a]

flatten :: T a -> [T a]

dimension :: T a -> T a -> Int

Instances for atomic types

Instances for composed types

Properties

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

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