Safe Haskell	None
Language	Haskell2010

NumHask.Data.Complex

Description

Complex numbers.

Synopsis

data Complex a = !a :+ !a
realPart :: Complex a -> a
imagPart :: Complex a -> a

Documentation

data Complex a Source #

Complex numbers have real and imaginary parts.

The Foldable and Traversable instances traverse the real part first.

Constructors

!a :+ !a infix 6

forms a complex number from its real and imaginary rectangular components.

Instances

Instances details

Functor Complex Source #
Instance details Defined in NumHask.Data.Complex Methods fmap :: (a -> b) -> Complex a -> Complex b # (<$) :: a -> Complex b -> Complex a #
Foldable Complex Source #
Instance details Defined in NumHask.Data.Complex Methods fold :: Monoid m => Complex m -> m # foldMap :: Monoid m => (a -> m) -> Complex a -> m # foldMap' :: Monoid m => (a -> m) -> Complex a -> m # foldr :: (a -> b -> b) -> b -> Complex a -> b # foldr' :: (a -> b -> b) -> b -> Complex a -> b # foldl :: (b -> a -> b) -> b -> Complex a -> b # foldl' :: (b -> a -> b) -> b -> Complex a -> b # foldr1 :: (a -> a -> a) -> Complex a -> a # foldl1 :: (a -> a -> a) -> Complex a -> a # toList :: Complex a -> [a] # null :: Complex a -> Bool # length :: Complex a -> Int # elem :: Eq a => a -> Complex a -> Bool # maximum :: Ord a => Complex a -> a # minimum :: Ord a => Complex a -> a # sum :: Num a => Complex a -> a # product :: Num a => Complex a -> a #
Traversable Complex Source #
Instance details Defined in NumHask.Data.Complex Methods traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) # sequenceA :: Applicative f => Complex (f a) -> f (Complex a) # mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) # sequence :: Monad m => Complex (m a) -> m (Complex a) #
Eq a => Eq (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods (==) :: Complex a -> Complex a -> Bool # (/=) :: Complex a -> Complex a -> Bool #
Data a => Data (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Complex a -> c (Complex a) # gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Complex a) # toConstr :: Complex a -> Constr # dataTypeOf :: Complex a -> DataType # dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Complex a)) # dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Complex a)) # gmapT :: (forall b. Data b => b -> b) -> Complex a -> Complex a # gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r # gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Complex a -> r # gmapQ :: (forall d. Data d => d -> u) -> Complex a -> [u] # gmapQi :: Int -> (forall d. Data d => d -> u) -> Complex a -> u # gmapM :: Monad m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) # gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) # gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex a -> m (Complex a) #
Read a => Read (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods readsPrec :: Int -> ReadS (Complex a) # readList :: ReadS [Complex a] # readPrec :: ReadPrec (Complex a) # readListPrec :: ReadPrec [Complex a] #
Show a => Show (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods showsPrec :: Int -> Complex a -> ShowS # show :: Complex a -> String # showList :: [Complex a] -> ShowS #
Generic (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Associated Types type Rep (Complex a) :: Type -> Type # Methods from :: Complex a -> Rep (Complex a) x # to :: Rep (Complex a) x -> Complex a #
Subtractive a => Subtractive (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods negate :: Complex a -> Complex a Source # (-) :: Complex a -> Complex a -> Complex a Source #
Additive a => Additive (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods (+) :: Complex a -> Complex a -> Complex a Source # zero :: Complex a Source #
(Subtractive a, Divisive a) => Divisive (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods recip :: Complex a -> Complex a Source # (/) :: Complex a -> Complex a -> Complex a Source #
(Subtractive a, Multiplicative a) => Multiplicative (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods (*) :: Complex a -> Complex a -> Complex a Source # one :: Complex a Source #
(Distributive a, Subtractive a) => InvolutiveRing (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods adj :: Complex a -> Complex a Source #
(Distributive a, Subtractive a) => Distributive (Complex a) Source #
Instance details Defined in NumHask.Data.Complex
LowerBoundedField a => LowerBoundedField (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods negInfinity :: Complex a Source #
(UpperBoundedField a, Subtractive a) => UpperBoundedField (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods infinity :: Complex a Source # nan :: Complex a Source #
(Ord a, TrigField a, ExpField a) => ExpField (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods exp :: Complex a -> Complex a Source # log :: Complex a -> Complex a Source # logBase :: Complex a -> Complex a -> Complex a Source # (**) :: Complex a -> Complex a -> Complex a Source # sqrt :: Complex a -> Complex a Source #
Field a => Field (Complex a) Source #
Instance details Defined in NumHask.Data.Complex
BoundedMeetSemiLattice a => BoundedMeetSemiLattice (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods top :: Complex a Source #
BoundedJoinSemiLattice a => BoundedJoinSemiLattice (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods bottom :: Complex a Source #
MeetSemiLattice a => MeetSemiLattice (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods (/\) :: Complex a -> Complex a -> Complex a Source #
JoinSemiLattice a => JoinSemiLattice (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods (\/) :: Complex a -> Complex a -> Complex a Source #
(Ord a, Signed a, Subtractive a, Epsilon a) => Epsilon (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods epsilon :: Complex a Source # nearZero :: Complex a -> Bool Source # aboutEqual :: Complex a -> Complex a -> Bool Source #
Generic1 Complex Source #
Instance details Defined in NumHask.Data.Complex Associated Types type Rep1 Complex :: k -> Type # Methods from1 :: forall (a :: k). Complex a -> Rep1 Complex a # to1 :: forall (a :: k). Rep1 Complex a -> Complex a #
(Additive a, FromIntegral a b) => FromIntegral (Complex a) b Source #
Instance details Defined in NumHask.Data.Complex Methods fromIntegral :: b -> Complex a Source #
TrigField a => Direction (Complex a) a Source #
Instance details Defined in NumHask.Data.Complex Methods angle :: Complex a -> a Source # ray :: a -> Complex a Source #
ExpField a => Norm (Complex a) a Source #	A euclidean-style norm is strong convention for Complex.
Instance details Defined in NumHask.Data.Complex Methods norm :: Complex a -> a Source # basis :: Complex a -> Complex a Source #
type Rep (Complex a) Source #
Instance details Defined in NumHask.Data.Complex type Rep (Complex a) = D1 ('MetaData "Complex" "NumHask.Data.Complex" "numhask-0.8.1.0-6vtGETGPv6z5KBqA0pprnK" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 a)))
type Rep1 Complex Source #
Instance details Defined in NumHask.Data.Complex type Rep1 Complex = D1 ('MetaData "Complex" "NumHask.Data.Complex" "numhask-0.8.1.0-6vtGETGPv6z5KBqA0pprnK" 'False) (C1 ('MetaCons ":+" ('InfixI 'NotAssociative 6) 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1 :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) Par1))

realPart :: Complex a -> a Source #

Extracts the real part of a complex number.

imagPart :: Complex a -> a Source #

Extracts the imaginary part of a complex number.