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	Haskell2010

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 Source #

An involutive ring

Minimal complete definition

Nothing

Methods

conjugate :: a -> a Source #

Conjugate a value. This defaults to the trivial involution.

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

>>> conjugate 1
1

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

Conjugate a value. This defaults to the trivial involution.

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

>>> conjugate 1
1

Instances

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

class Conjugate a => TrivialConjugate a Source #

Requires and provides a default definition such that

conjugate = id

Instances

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