ComplexNumbers

A module for complex numbers

Types

type Real r

= Real r

Real portion

type Imaginary i

= Imaginary i

Imaginary portion

type ComplexNumber a

= ComplexNumber (Real a) (Imaginary a)

Cartesian representation of a complex number

Values

i : ComplexNumber number

The number i

zero : ComplexNumber number

zero

one : ComplexNumber number

one

Arithmetic operations on complex numbers

real : ComplexNumber a -> a

Extracts the real part of a complex number

imaginary : ComplexNumber a -> a

Extracts the imaginary part of a complex number

add :

ComplexNumber number

-> ComplexNumber number

Add two complex numbers together

multiply : ComplexNumber Float -> ComplexNumber Float -> ComplexNumber Float

Multiply two complex numbers together

subtract :

ComplexNumber number

-> ComplexNumber number

Subtract two complex numbers together

divide : ComplexNumber Float -> ComplexNumber Float -> ComplexNumber Float

Divide two complex numbers together

modulus : ComplexNumber Float -> Float

Calculate the modulus of a complex number

conjugate : ComplexNumber number -> ComplexNumber number

Calculate the conjugate of a complex number

power : Float -> ComplexNumber Float -> ComplexNumber Float

Calculate a complex number raised to a power

convertFromCartesianToPolar : ComplexNumber Float -> ComplexNumber Float

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

convertFromPolarToCartesian : ComplexNumber Float -> ComplexNumber Float

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

euler : Float -> ComplexNumber Float

Euler's equation

Semigroup, Monoid, Group, Ring, Field, Functor, Applicative Functor, and Monad

complexSumSemigroup : CommutativeSemigroup (ComplexNumber number)

Semigroup for Complex Numbers with addition as the operation

complexProductSemigroup : CommutativeSemigroup (ComplexNumber Float)

Semigroup for Complex Numbers with multiplicatoin as the operation

complexSumMonoid : Monoid (ComplexNumber number)

Monoid for Complex Numbers with addition as the operation

complexProductMonoid : Monoid (ComplexNumber Float)

Monoid for Complex Numbers with multiplication as the operation

complexSumCommutativeMonoid : CommutativeMonoid (ComplexNumber number)

Monoid for Complex Numbers with addition as the operation

complexProductCommutativeMonoid : CommutativeMonoid (ComplexNumber Float)

Monoid for Complex Numbers with multiplication as the operation

complexSumGroup : Group (ComplexNumber number)

Group for Complex Numbers with addition as the operation

complexProductGroup : Group (ComplexNumber Float)

Group for Complex Numbers with multiplication as the operation

complexAbelianGroup : AbelianGroup (ComplexNumber number)

Group for Complex Numbers with addition as the operation

complexRing : Ring (ComplexNumber Float)

Ring for Complex Numbers

complexDivisionRing : DivisionRing (ComplexNumber Float)

Division Ring for Complex Numbers

complexCommutativeRing : CommutativeRing (ComplexNumber Float)

Commutative Ring for Complex Numbers

complexCommutativeDivisionRing : CommutativeDivisionRing (ComplexNumber Float)

Commutative Division Ring for Complex Numbers

complexField : Field (ComplexNumber Float)

Field for Complex Numbers

map : (a -> b) -> ComplexNumber a -> ComplexNumber b

Map over a complex number

pure : a -> ComplexNumber a

Place a value in the minimal Complex Number Cartesian context

andMap : ComplexNumber a -> ComplexNumber (a -> b) -> ComplexNumber b

Apply for Complex Number Cartesian representaiton applicative

andThen : (a -> ComplexNumber b) -> ComplexNumber a -> ComplexNumber b

Monadic bind for Complex Number Cartesian representaiton

#Equality

equal : ComplexNumber Float -> ComplexNumber Float -> Bool

Compare two ComplexNumbers for equality

Read and Print

parseComplexNumber : Parser (ComplexNumber Float)

Parse ComplexNumber

read : String -> Result (List DeadEnd) (ComplexNumber Float)

Read ComplexNumber

print : ComplexNumber Float -> String

Print ComplexNumber

Modules

ComplexNumbers

jonathanfishbein1/complex-numbers/9.1.1