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Contents
module ComplexNumbers
(Complex,
conjugate,
abs,
mul,
add,
sub,
div,
real,
imaginary,
complex) where
import Prelude hiding (div, abs)
-- Data definition -------------------------------------------------------------
data Complex a = Complex a a deriving (Eq, Show)
--------------------------------------------------------------------------------
complex :: (a, a) -> Complex a
complex = uncurry Complex
exp2 :: Num a => a -> a
exp2 x = x^(2 :: Integer)
-- unary operators -------------------------------------------------------------
real :: Num a => Complex a -> a
real (Complex a _) = a
imaginary :: Num a => Complex a -> a
imaginary (Complex _ b) = b
conjugate :: Num a => Complex a -> Complex a
conjugate (Complex a b) = Complex a (-b)
abs :: Floating a => Complex a -> a
abs (Complex a b) = sqrt (exp2 a + exp2 b)
-- binary operators ------------------------------------------------------------
mul :: Num a => Complex a -> Complex a -> Complex a
mul (Complex a b) (Complex c d) = Complex (a*c - b*d) (a*d + b*c)
add :: Num a => Complex a -> Complex a -> Complex a
add (Complex a b) (Complex c d) = Complex (a+c) (b+d)
sub :: Num a => Complex a -> Complex a -> Complex a
sub (Complex a b) (Complex c d) = Complex (a-c) (b-d)
div :: Fractional a => Complex a -> Complex a -> Complex a
div (Complex a b) (Complex c d) = Complex ((a*c + b*d)/(exp2 c + exp2 d))
((b*c - a*d)/(exp2 c + exp2 d))
Version data entries
133 entries across 133 versions & 1 rubygems