numeric-prelude-0.4.4: An experimental alternative hierarchy of numeric type classes
Safe HaskellNone
LanguageHaskell98

Algebra.NormedSpace.Sum

Description

Abstraction of normed vector spaces

Synopsis

Documentation

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

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 Source #

Instances

Instances details
C Double Double Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Double -> Double Source #

C Float Float Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Float -> Float Source #

C Int Int Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Int -> Int Source #

C Integer Integer Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Integer -> Integer Source #

(C a v, RealFloat v) => C a (Complex v) Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: Complex v -> a Source #

(C a, C a v) => C a [v] Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: [v] -> a Source #

(C a, C a v) => C a (T v) Source # 
Instance details

Defined in Number.Complex

Methods

norm :: T v -> a Source #

(C a, C a v0, C a v1) => C a (v0, v1) Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: (v0, v1) -> a Source #

(Ord i, Eq a, Eq v, C a v) => C a (Map i v) Source # 
Instance details

Defined in MathObj.DiscreteMap

Methods

norm :: Map i v -> a Source #

(C a, C a v0, C a v1, C a v2) => C a (v0, v1, v2) Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

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

(C a, C a) => C (T a) (T a) Source # 
Instance details

Defined in Algebra.NormedSpace.Sum

Methods

norm :: T a -> T a Source #

C a v => C (T a) (T v) Source # 
Instance details

Defined in MathObj.Wrapper.NumericPrelude

Methods

norm :: T v -> T a Source #

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

Default definition for norm that is based on Foldable class.

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

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