Shady.Complex

Complex numbers. This version is modified from Data.Complex in base. It eliminates the RealFloat requirement by using a more naive definition of magnitude. Also, defines instances for vector-space classes.

Rectangular form

data Complex a

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.

Constructors

!a :+ !a

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

Instances

Typeable1 Complex

Eq a => Eq (Complex a)

Floating a => Floating (Complex a)

Floating a => Fractional (Complex a)

Data a => Data (Complex a)

Floating a => Num (Complex a)

Read a => Read (Complex a)

Show a => Show (Complex a)

Floating a => VectorSpace (Complex a)

Floating a => InnerSpace (Complex a)

Floating a => AdditiveGroup (Complex a)

FMod s => FMod (Complex s)

Frac s => Frac (Complex s)

HasExpr a => HasExpr (Complex a)

(Show a, IsScalar a) => FromE (ComplexE a)

(Show a, IsScalar a) => ToE (ComplexE a)

realPart :: Complex a -> a

Extracts the real part of a complex number.

imagPart :: Complex a -> a

Extracts the imaginary part of a complex number.

Polar form

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

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

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

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

polar :: Floating a => Complex a -> (a, a)

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.

phase :: Floating a => Complex a -> a

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 => Unop (Complex a)

The conjugate of a complex number.

Misc interface additions

onRI :: Unop a -> Unop (Complex a)

Operate on the real & imaginary components

onRI2 :: Binop a -> Binop (Complex a)

Operate on the real & imaginary components