Copyright	(C) 2012-2015 Edward Kmett
License	BSD-style (see the file LICENSE)
Maintainer	Edward Kmett <ekmett@gmail.com>
Stability	experimental
Portability	non-portable
Safe Haskell	Safe
Language	Haskell98

Linear.Conjugate

Description

Involutive rings

Synopsis

class Num a => Conjugate a where
- conjugate :: a -> a
class Conjugate a => TrivialConjugate a

Documentation

class Num a => Conjugate a where #

An involutive ring

Minimal complete definition

Nothing

Methods

conjugate :: a -> a #

Conjugate a value. This defaults to the trivial involution.

>>> conjugate (1 :+ 2)
1.0 :+ (-2.0)

>>> conjugate 1
1

conjugate :: TrivialConjugate a => a -> a #

Conjugate a value. This defaults to the trivial involution.

>>> conjugate (1 :+ 2)
1.0 :+ (-2.0)

>>> conjugate 1
1

Instances

Conjugate Double #
Instance details Defined in Linear.Conjugate Methods conjugate :: Double -> Double #
Conjugate Float #
Instance details Defined in Linear.Conjugate Methods conjugate :: Float -> Float #
Conjugate Int #
Instance details Defined in Linear.Conjugate Methods conjugate :: Int -> Int #
Conjugate Int8 #
Instance details Defined in Linear.Conjugate Methods conjugate :: Int8 -> Int8 #
Conjugate Int16 #
Instance details Defined in Linear.Conjugate Methods conjugate :: Int16 -> Int16 #
Conjugate Int32 #
Instance details Defined in Linear.Conjugate Methods conjugate :: Int32 -> Int32 #
Conjugate Int64 #
Instance details Defined in Linear.Conjugate Methods conjugate :: Int64 -> Int64 #
Conjugate Integer #
Instance details Defined in Linear.Conjugate Methods conjugate :: Integer -> Integer #
Conjugate Word #
Instance details Defined in Linear.Conjugate Methods conjugate :: Word -> Word #
Conjugate Word8 #
Instance details Defined in Linear.Conjugate Methods conjugate :: Word8 -> Word8 #
Conjugate Word16 #
Instance details Defined in Linear.Conjugate Methods conjugate :: Word16 -> Word16 #
Conjugate Word32 #
Instance details Defined in Linear.Conjugate Methods conjugate :: Word32 -> Word32 #
Conjugate Word64 #
Instance details Defined in Linear.Conjugate Methods conjugate :: Word64 -> Word64 #
Conjugate CFloat #
Instance details Defined in Linear.Conjugate Methods conjugate :: CFloat -> CFloat #
Conjugate CDouble #
Instance details Defined in Linear.Conjugate Methods conjugate :: CDouble -> CDouble #
(Conjugate a, RealFloat a) => Conjugate (Complex a) #
Instance details Defined in Linear.Conjugate Methods conjugate :: Complex a -> Complex a #
(Conjugate a, RealFloat a) => Conjugate (Quaternion a) #
Instance details Defined in Linear.Quaternion Methods conjugate :: Quaternion a -> Quaternion a #

class Conjugate a => TrivialConjugate a #

Requires and provides a default definition such that

conjugate = id

Instances

TrivialConjugate Double #
Instance details Defined in Linear.Conjugate
TrivialConjugate Float #
Instance details Defined in Linear.Conjugate
TrivialConjugate Int #
Instance details Defined in Linear.Conjugate
TrivialConjugate Int8 #
Instance details Defined in Linear.Conjugate
TrivialConjugate Int16 #
Instance details Defined in Linear.Conjugate
TrivialConjugate Int32 #
Instance details Defined in Linear.Conjugate
TrivialConjugate Int64 #
Instance details Defined in Linear.Conjugate
TrivialConjugate Integer #
Instance details Defined in Linear.Conjugate
TrivialConjugate Word #
Instance details Defined in Linear.Conjugate
TrivialConjugate Word8 #
Instance details Defined in Linear.Conjugate
TrivialConjugate Word16 #
Instance details Defined in Linear.Conjugate
TrivialConjugate Word32 #
Instance details Defined in Linear.Conjugate
TrivialConjugate Word64 #
Instance details Defined in Linear.Conjugate
TrivialConjugate CFloat #
Instance details Defined in Linear.Conjugate
TrivialConjugate CDouble #
Instance details Defined in Linear.Conjugate