Algebra.ModuleBasis

NumericPrelude-0.0: An experimental alternative hierarchy of numeric type classes

Algebra.ModuleBasis

Portability	requires multi-parameter type classes
Stability	provisional
Maintainer	numericprelude@henning-thielemann.de

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

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.

show/hide Instances

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

(C a v0, C a v1, C a v2) => C a (v0, v1, v2)

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

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

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