ComplexNumbers

A module for complex numbers

Types

type Real r

= Real r

Real portion

type Imaginary i

= Imaginary i

Imaginary portion

type Modulus m

= Modulus m

Modulus or magnitude portion

type Theta t

= Theta t

Angle in real-complex plane of modulus

type ComplexNumberCartesian a

= ComplexNumberCartesian (Real a) (Imaginary a)

Cartesian representation of a complex number

type ComplexNumberPolar a

= ComplexNumberPolar (Modulus a) (Theta a)

Polar representation of a complex number

Arithmetic operations on complex numbers

i : ComplexNumberCartesian number

The number i

zero : ComplexNumberCartesian number

zero

realPart : ComplexNumberCartesian a -> a

Extracts the real part of a complex number

imaginaryPart : ComplexNumberCartesian a -> a

Extracts the imaginary part of a complex number

modulusPart : ComplexNumberPolar a -> a

Extracts the modulus part of a complex number

thetaPart : ComplexNumberPolar a -> a

Extracts the imaginary part of a complex number

add :

ComplexNumberCartesian number

-> ComplexNumberCartesian number

Add two complex numbers together

sum : Monoid (ComplexNumberCartesian number)

Monoidally add two complex numbers together

multiply :

ComplexNumberCartesian number

-> ComplexNumberCartesian number

Multiply two complex numbers together

product : Monoid (ComplexNumberCartesian number)

Monoidally multiply two complex numbers together

subtract :

ComplexNumberCartesian number

-> ComplexNumberCartesian number

Subtract two complex numbers together

divide :

ComplexNumberCartesian Float

-> ComplexNumberCartesian Float

-> Result String (ComplexNumberCartesian Float)

Divide two complex numbers together

modulus : ComplexNumberCartesian Float -> Float

Calculate the modulus of a complex number

conjugate : ComplexNumberCartesian number -> ComplexNumberCartesian number

Calculate the conjugate of a complex number

convertFromCartesianToPolar : ComplexNumberCartesian Float -> ComplexNumberPolar Float

Convert from the Cartesian representation of a complex number to the polar representation

convertFromPolarToCartesian : ComplexNumberPolar Float -> ComplexNumberCartesian Float

Convert from the polar representation of a complex number to the Cartesian representation

multiplyPolar :

ComplexNumberPolar number

-> ComplexNumberPolar number

Multiply two complex numbers in polar representations together

dividePolar :

ComplexNumberPolar Float

-> ComplexNumberPolar Float

-> Result String (ComplexNumberPolar Float)

Divide two complex numbers in polar representations together

power : number -> ComplexNumberPolar number -> ComplexNumberPolar number

Calculate a complex number raised to a power

mapCartesian : (a -> b) -> ComplexNumberCartesian a -> ComplexNumberCartesian b

Map over a complex number

mapPolar : (a -> b) -> ComplexNumberPolar a -> ComplexNumberPolar b

Map over a complex number in polar representation

pureCartesian : a -> ComplexNumberCartesian a

Place a value in the minimal Complex Number Cartesian context

purePolar : a -> ComplexNumberPolar a

Place a value in the minimal Complex Number polar context

applyCartesian :

ComplexNumberCartesian (a -> b)

-> ComplexNumberCartesian a

-> ComplexNumberCartesian b

Apply for Complex Number Cartesian representaiton applicative

applyPolar :

ComplexNumberPolar (a -> b)

-> ComplexNumberPolar a

-> ComplexNumberPolar b

Apply for Complex Number polar representaiton applicative

bindCartesian :

ComplexNumberCartesian a

-> (a -> ComplexNumberCartesian b)

-> ComplexNumberCartesian b

Monadic bind for Complex Number Cartesian representaiton

bindPolar :

ComplexNumberPolar a

-> (a -> ComplexNumberPolar b)

-> ComplexNumberPolar b

Monadic bind for Complex Number polar representaiton

Modules

ComplexNumbers

jonathanfishbein1/complex-numbers/2.1.0

ComplexNumbers

Types

Arithmetic operations on complex numbers

Modules