Fractal.RUFF.Types.Complex

Complex numbers without the RealFloat constraint.

Documentation

data Complex r

Complex number type without the RealFloat constraint.

Constructors

!r :+ !r

Instances

Eq r => Eq (Complex r)

Methods

(==) :: Complex r -> Complex r -> Bool

(/=) :: Complex r -> Complex r -> Bool

(Ord r, Floating r) => Floating (Complex r)

Methods

pi :: Complex r

exp :: Complex r -> Complex r

log :: Complex r -> Complex r

sqrt :: Complex r -> Complex r

(**) :: Complex r -> Complex r -> Complex r

logBase :: Complex r -> Complex r -> Complex r

sin :: Complex r -> Complex r

cos :: Complex r -> Complex r

tan :: Complex r -> Complex r

asin :: Complex r -> Complex r

acos :: Complex r -> Complex r

atan :: Complex r -> Complex r

sinh :: Complex r -> Complex r

cosh :: Complex r -> Complex r

tanh :: Complex r -> Complex r

asinh :: Complex r -> Complex r

acosh :: Complex r -> Complex r

atanh :: Complex r -> Complex r

log1p :: Complex r -> Complex r

expm1 :: Complex r -> Complex r

log1pexp :: Complex r -> Complex r

log1mexp :: Complex r -> Complex r

Fractional r => Fractional (Complex r)

Methods

(/) :: Complex r -> Complex r -> Complex r

recip :: Complex r -> Complex r

fromRational :: Rational -> Complex r

Data r => Data (Complex r)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Complex r -> c (Complex r)

gunfold :: (forall b a. Data b => c (b -> a) -> c a) -> (forall a. a -> c a) -> Constr -> c (Complex r)

toConstr :: Complex r -> Constr

dataTypeOf :: Complex r -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Complex r))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Complex r))

gmapT :: (forall b. Data b => b -> b) -> Complex r -> Complex r

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Complex r -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Complex r -> r

gmapQ :: (forall d. Data d => d -> u) -> Complex r -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Complex r -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Complex r -> m (Complex r)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex r -> m (Complex r)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Complex r -> m (Complex r)

Num r => Num (Complex r)

Methods

(+) :: Complex r -> Complex r -> Complex r

(-) :: Complex r -> Complex r -> Complex r

(*) :: Complex r -> Complex r -> Complex r

negate :: Complex r -> Complex r

abs :: Complex r -> Complex r

signum :: Complex r -> Complex r

fromInteger :: Integer -> Complex r

Read r => Read (Complex r)

Methods

readsPrec :: Int -> ReadS (Complex r)

readList :: ReadS [Complex r]

readPrec :: ReadPrec (Complex r)

readListPrec :: ReadPrec [Complex r]

Show r => Show (Complex r)

Methods

showsPrec :: Int -> Complex r -> ShowS

show :: Complex r -> String

showList :: [Complex r] -> ShowS

NearZero r => NearZero (Complex r)

Methods

nearZero :: Complex r -> Bool

cis :: Floating r => r -> Complex r

Complex number with magnitude 1 and the given phase.

mkPolar :: Floating r => r -> r -> Complex r

Complex number with the given magnitude and phase.

realPart :: Complex r -> r

Extract the real part.

imagPart :: Complex r -> r

Extract the imaginary part.

conjugate :: Num r => Complex r -> Complex r

Complex conjugate.

magnitude2 :: Num r => Complex r -> r

Complex magnitude squared.

magnitude :: Floating r => Complex r -> r

Complex magnitude.

phase :: (Ord r, Floating r) => Complex r -> r

Complex phase.

polar :: (Ord r, Floating r) => Complex r -> (r, r)

Convert to polar form.