Copyright	(c) Ross Paterson 2011
License	BSD-style (see the file LICENSE)
Maintainer	[email protected]
Stability	provisional
Portability	portable
Safe Haskell	None
Language	Haskell2010

Data.YAP.Quaternion

Description

An example instance of the algebraic classes: quaternions.

Synopsis

data Quaternion a = Q a a a a
conjugate :: AbelianGroup a => Quaternion a -> Quaternion a

Documentation

data Quaternion a Source #

Quaternions

Constructors

Q a a a a

Q a b c d represents $a + b i + c j + d k$.

Instances

Instances details

Functor Quaternion Source #
Instance details Defined in Data.YAP.Quaternion Methods fmap :: (a -> b) -> Quaternion a -> Quaternion b # (<$) :: a -> Quaternion b -> Quaternion a #
Show a => Show (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods showsPrec :: Int -> Quaternion a -> ShowS # show :: Quaternion a -> String # showList :: [Quaternion a] -> ShowS #
Eq a => Eq (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods (==) :: Quaternion a -> Quaternion a -> Bool # (/=) :: Quaternion a -> Quaternion a -> Bool #
Ord a => Ord (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods compare :: Quaternion a -> Quaternion a -> Ordering # (<) :: Quaternion a -> Quaternion a -> Bool # (<=) :: Quaternion a -> Quaternion a -> Bool # (>) :: Quaternion a -> Quaternion a -> Bool # (>=) :: Quaternion a -> Quaternion a -> Bool # max :: Quaternion a -> Quaternion a -> Quaternion a # min :: Quaternion a -> Quaternion a -> Quaternion a #
AbelianGroup a => AbelianGroup (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods (-) :: Quaternion a -> Quaternion a -> Quaternion a # negate :: Quaternion a -> Quaternion a # gtimes :: (AbelianGroup b, ToInteger b) => b -> Quaternion a -> Quaternion a #
AdditiveMonoid a => AdditiveMonoid (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods (+) :: Quaternion a -> Quaternion a -> Quaternion a # zero :: Quaternion a # atimes :: ToInteger b => b -> Quaternion a -> Quaternion a #
Field a => DivisionRing (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion
Field a => DivisionSemiring (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods recip :: Quaternion a -> Quaternion a #
FromRational a => FromRational (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods fromRational :: Rational -> Quaternion a #
Ring a => Ring (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods fromInteger :: Integer -> Quaternion a #
Ring a => Semiring (Quaternion a) Source #
Instance details Defined in Data.YAP.Quaternion Methods (*) :: Quaternion a -> Quaternion a -> Quaternion a # one :: Quaternion a # fromNatural :: Natural -> Quaternion a # rescale :: Quaternion a -> Quaternion a -> (Quaternion a, Quaternion a, Quaternion a -> Quaternion a) #

conjugate :: AbelianGroup a => Quaternion a -> Quaternion a Source #

The conjugate of a quaternion.