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])

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

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

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