Algebra.NormedSpace.Sum

Abstraction of normed vector spaces

Documentation

class (C a, C a v) => C a v where

The super class is only needed to state the laws v == zero == norm v == zero norm (scale x v) == abs x * norm v norm (u+v) <= norm u + norm v

Methods

norm :: v -> a

Instances

C Double Double

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Double -> Double

C Float Float

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Float -> Float

C Int Int

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Int -> Int

C Integer Integer

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Integer -> Integer

(C a v, RealFloat v) => C a (Complex v)

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Complex v -> a

(C a, C a v) => C a [v]

Defined in Algebra.NormedSpace.Sum

Methods

norm :: [v] -> a

(C a, C a v) => C a (T v)

Defined in Number.Complex

Methods

norm :: T v -> a

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

Defined in Algebra.NormedSpace.Sum

Methods

norm :: (v0, v1) -> a

(Ord i, Eq a, Eq v, C a v) => C a (Map i v)

Defined in MathObj.DiscreteMap

Methods

norm :: Map i v -> a

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

Defined in Algebra.NormedSpace.Sum

Methods

norm :: (v0, v1, v2) -> a

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

Defined in Algebra.NormedSpace.Sum

Methods

norm :: T a -> T a

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

Defined in MathObj.Wrapper.NumericPrelude

Methods

norm :: T v -> T a

normFoldable :: (C a v, Foldable f) => f v -> a

Default definition for norm that is based on Foldable class.

normFoldable1 :: (C a v, Foldable f, Functor f) => f v -> a

Default definition for norm that is based on Foldable class and the argument vector has at least one component.