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/Haskell 8

Data.Complex

Copyright (c) The University of Glasgow 2001
License BSD-style (see the file libraries/base/LICENSE)
Maintainer [email protected]
Stability provisional
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

Description

Complex numbers.

Rectangular form

data Complex a Source

Complex numbers are an algebraic type.

For a complex number z, abs z is a number with the magnitude of z, but oriented in the positive real direction, whereas signum z has the phase of z, but unit magnitude.

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

Monad Complex

Since: 4.9.0.0

Methods

(>>=) :: Complex a -> (a -> Complex b) -> Complex b Source

(>>) :: Complex a -> Complex b -> Complex b Source

return :: a -> Complex a Source

fail :: String -> Complex a Source

Functor Complex

Methods

fmap :: (a -> b) -> Complex a -> Complex b Source

(<$) :: a -> Complex b -> Complex a Source

Applicative Complex

Since: 4.9.0.0

Methods

pure :: a -> Complex a Source

(<*>) :: Complex (a -> b) -> Complex a -> Complex b Source

liftA2 :: (a -> b -> c) -> Complex a -> Complex b -> Complex c Source

(*>) :: Complex a -> Complex b -> Complex b Source

(<*) :: Complex a -> Complex b -> Complex a Source

Foldable Complex

Methods

fold :: Monoid m => Complex m -> m Source

foldMap :: Monoid m => (a -> m) -> Complex a -> m Source

foldr :: (a -> b -> b) -> b -> Complex a -> b Source

foldr' :: (a -> b -> b) -> b -> Complex a -> b Source

foldl :: (b -> a -> b) -> b -> Complex a -> b Source

foldl' :: (b -> a -> b) -> b -> Complex a -> b Source

foldr1 :: (a -> a -> a) -> Complex a -> a Source

foldl1 :: (a -> a -> a) -> Complex a -> a Source

toList :: Complex a -> [a] Source

null :: Complex a -> Bool Source

length :: Complex a -> Int Source

elem :: Eq a => a -> Complex a -> Bool Source

maximum :: Ord a => Complex a -> a Source

minimum :: Ord a => Complex a -> a Source

sum :: Num a => Complex a -> a Source

product :: Num a => Complex a -> a Source

Traversable Complex

Methods

traverse :: Applicative f => (a -> f b) -> Complex a -> f (Complex b) Source

sequenceA :: Applicative f => Complex (f a) -> f (Complex a) Source

mapM :: Monad m => (a -> m b) -> Complex a -> m (Complex b) Source

sequence :: Monad m => Complex (m a) -> m (Complex a) Source

Eq a => Eq (Complex a)

Methods

(==) :: Complex a -> Complex a -> Bool Source

(/=) :: Complex a -> Complex a -> Bool Source

RealFloat a => Floating (Complex a)

Since: 2.1
RealFloat a => Fractional (Complex a)

Since: 2.1
Data a => Data (Complex a)

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 :: (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 => Num (Complex a)

Since: 2.1
Read a => Read (Complex a)
Show a => Show (Complex a)
Generic (Complex a)

Associated Types

type Rep (Complex a) :: * -> * Source

Methods

from :: Complex a -> Rep (Complex a) x Source

to :: Rep (Complex a) x -> Complex a Source

Storable a => Storable (Complex a)

Since: 4.8.0.0

Methods

sizeOf :: Complex a -> Int Source

alignment :: Complex a -> Int Source

peekElemOff :: Ptr (Complex a) -> Int -> IO (Complex a) Source

pokeElemOff :: Ptr (Complex a) -> Int -> Complex a -> IO () Source

peekByteOff :: Ptr b -> Int -> IO (Complex a) Source

pokeByteOff :: Ptr b -> Int -> Complex a -> IO () Source

peek :: Ptr (Complex a) -> IO (Complex a) Source

poke :: Ptr (Complex a) -> Complex a -> IO () Source

Generic1 * Complex

Associated Types

type Rep1 Complex (f :: Complex -> *) :: k -> * Source

Methods

from1 :: f a -> Rep1 Complex f a Source

to1 :: Rep1 Complex f a -> f a Source

type Rep (Complex a)
type Rep1 * Complex

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.

Polar form

mkPolar :: Floating a => a -> a -> Complex a Source

Form a complex number from polar components of magnitude and phase.

cis :: Floating a => a -> Complex a Source

cis t is a complex value with magnitude 1 and phase t (modulo 2*pi).

polar :: RealFloat a => Complex a -> (a, a) Source

The function polar takes a complex number and returns a (magnitude, phase) pair in canonical form: the magnitude is nonnegative, and the phase in the range (-pi, pi]; if the magnitude is zero, then so is the phase.

magnitude :: RealFloat a => Complex a -> a Source

The nonnegative magnitude of a complex number.

phase :: RealFloat a => Complex a -> a Source

The phase of a complex number, in the range (-pi, pi]. If the magnitude is zero, then so is the phase.

Conjugate

conjugate :: Num a => Complex a -> Complex a Source

The conjugate of a complex number.

© The University of Glasgow and others
Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/8.2.1/docs/html/libraries/base-4.10.0.0/Data-Complex.html