Copyright	(c) 2015 Conal Elliott and David Banas
License	BSD3
Maintainer	conal@conal.net
Stability	experimental
Safe Haskell	Safe-Inferred
Language	Haskell2010

ConCat.Complex

Description

Simplified Complex type

Synopsis

data Complex a = a :+ a
cis :: RealFloat a => a -> Complex a

Documentation

data Complex a Source #

Constructors

a :+ a infixl 1

Instances

Instances details

Functor Complex Source #
Instance details Defined in ConCat.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b Source # (<$) :: a -> Complex b -> Complex a Source #
Arbitrary a => Arbitrary (Complex a) Source #
Instance details Defined in ConCat.Complex Methods arbitrary :: Gen (Complex a) Source # shrink :: Complex a -> [Complex a] Source #
CoArbitrary a => CoArbitrary (Complex a) Source #
Instance details Defined in ConCat.Complex Methods coarbitrary :: Complex a -> Gen b -> Gen b Source #
Data a => Data (Complex a) Source #
Instance details Defined in ConCat.Complex Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Complex a -> c (Complex a) Source # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Complex a) Source # toConstr :: Complex a -> Constr Source # dataTypeOf :: Complex a -> DataType Source # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Complex a)) Source # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Complex a)) Source # gmapT :: (forall b. Data b => b -> b) -> Complex a -> Complex a Source # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r Source # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r Source # gmapQ :: (forall d. Data d => d -> u) -> Complex a -> [u] Source # gmapQi :: Int -> (forall d. Data d => d -> u) -> Complex a -> u Source # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) Source # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) Source # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) Source #
RealFloat a => Floating (Complex a) Source #
Instance details Defined in ConCat.Complex Methods pi :: Complex a Source # exp :: Complex a -> Complex a Source # log :: Complex a -> Complex a Source # sqrt :: Complex a -> Complex a Source # (**) :: Complex a -> Complex a -> Complex a Source # logBase :: Complex a -> Complex a -> Complex a Source # sin :: Complex a -> Complex a Source # cos :: Complex a -> Complex a Source # tan :: Complex a -> Complex a Source # asin :: Complex a -> Complex a Source # acos :: Complex a -> Complex a Source # atan :: Complex a -> Complex a Source # sinh :: Complex a -> Complex a Source # cosh :: Complex a -> Complex a Source # tanh :: Complex a -> Complex a Source # asinh :: Complex a -> Complex a Source # acosh :: Complex a -> Complex a Source # atanh :: Complex a -> Complex a Source # log1p :: Complex a -> Complex a Source # expm1 :: Complex a -> Complex a Source # log1pexp :: Complex a -> Complex a Source # log1mexp :: Complex a -> Complex a Source #
RealFloat a => Num (Complex a) Source #
Instance details Defined in ConCat.Complex Methods (+) :: Complex a -> Complex a -> Complex a Source # (-) :: Complex a -> Complex a -> Complex a Source # (*) :: Complex a -> Complex a -> Complex a Source # negate :: Complex a -> Complex a Source # abs :: Complex a -> Complex a Source # signum :: Complex a -> Complex a Source # fromInteger :: Integer -> Complex a Source #
RealFloat a => Fractional (Complex a) Source #
Instance details Defined in ConCat.Complex Methods (/) :: Complex a -> Complex a -> Complex a Source # recip :: Complex a -> Complex a Source # fromRational :: Rational -> Complex a Source #
Show a => Show (Complex a) Source #
Instance details Defined in ConCat.Complex Methods showsPrec :: Int -> Complex a -> ShowS Source # show :: Complex a -> String Source # showList :: [Complex a] -> ShowS Source #
Eq a => Eq (Complex a) Source #
Instance details Defined in ConCat.Complex Methods (==) :: Complex a -> Complex a -> Bool Source # (/=) :: Complex a -> Complex a -> Bool Source #
Ord a => Ord (Complex a) Source #
Instance details Defined in ConCat.Complex Methods compare :: Complex a -> Complex a -> Ordering Source # (<) :: Complex a -> Complex a -> Bool Source # (<=) :: Complex a -> Complex a -> Bool Source # (>) :: Complex a -> Complex a -> Bool Source # (>=) :: Complex a -> Complex a -> Bool Source # max :: Complex a -> Complex a -> Complex a Source # min :: Complex a -> Complex a -> Complex a Source #

cis :: RealFloat a => a -> Complex a Source #

Complex Identity Scaler Returns a point on the unit circle, such that the angle between the vector to that point and the positive x-axis is equal to the function argument, given in radians.