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// (c) Microsoft Corporation 2005-2009.
namespace Microsoft.FSharp.Math
open System
/// The type of complex numbers stored as pairs of 64-bit floating point numbers in rectangular coordinates
[<Struct>]
[<CustomEquality; CustomComparison>]
type Complex =
/// The real part of a complex number
member r: float
/// The imaginary part of a complex number
member i: float
/// The polar-coordinate magnitude of a complex number
member Magnitude: float
/// The polar-coordinate phase of a complex number
member Phase: float
/// The real part of a complex number
member RealPart: float
/// The imaginary part of a complex number
member ImaginaryPart: float
/// The conjugate of a complex number, i.e. x-yi
member Conjugate: Complex
/// Create a complex number x+ij using rectangular coordinates
static member Create : float * float -> Complex
/// Create a complex number using magnitude/phase polar coordinates
static member CreatePolar : float * float -> Complex
/// The complex number 0+0i
static member Zero : Complex
/// The complex number 1+0i
static member One : Complex
/// The complex number 0+1i
static member OneI : Complex
/// Add two complex numbers
static member ( + ) : Complex * Complex -> Complex
/// Subtract one complex number from another
static member ( - ) : Complex * Complex -> Complex
/// Multiply two complex numbers
static member ( * ) : Complex * Complex -> Complex
/// Complex division of two complex numbers
static member ( / ) : Complex * Complex -> Complex
/// Unary negation of a complex number
static member ( ~- ) : Complex -> Complex
/// Multiply a scalar by a complex number
static member ( * ) : float * Complex -> Complex
/// Multiply a complex number by a scalar
static member ( * ) : Complex * float -> Complex
static member Sin : Complex -> Complex
static member Cos : Complex -> Complex
/// Computes the absolute value of a complex number: e.g. Abs x+iy = sqrt(x**2.0 + y**2.0.)
/// Note: Complex.Abs(z) is the same as z.Magnitude
static member Abs : Complex -> float
static member Tan : Complex -> Complex
static member Log : Complex -> Complex
static member Exp : Complex -> Complex
static member Sqrt : Complex -> Complex
override ToString : unit -> string
override Equals : obj -> bool
interface System.IComparable
member ToString : format:string -> string
member ToString : format:string * provider:System.IFormatProvider -> string
/// The type of complex numbers
type complex = Complex
[<CompilationRepresentation(CompilationRepresentationFlags.ModuleSuffix)>]
[<RequireQualifiedAccess>]
module Complex =
val mkRect: float * float -> complex
/// The polar-coordinate magnitude of a complex number
val magnitude: complex -> float
/// The polar-coordinate phase of a complex number
val phase : complex -> float
/// The real part of a complex number
val realPart : complex -> float
/// The imaginary part of a complex number
val imagPart : complex -> float
/// Create a complex number using magnitude/phase polar coordinates
val mkPolar : float * float -> complex
/// A complex of magnitude 1 and the given phase and , i.e. cis x = mkPolar 1.0 x
val cis : float -> complex
/// The conjugate of a complex number, i.e. x-yi
val conjugate : complex -> complex
/// The complex number 0+0i
val zero : complex
/// The complex number 1+0i
val one : complex
/// The complex number 0+1i
val onei : complex
/// Add two complex numbers
val add : complex -> complex -> complex
/// Subtract one complex number from another
val sub : complex -> complex -> complex
/// Multiply two complex numbers
val mul : complex -> complex -> complex
/// Complex division of two complex numbers
val div : complex -> complex -> complex
/// Unary negation of a complex number
val neg : complex -> complex
/// Multiply a scalar by a complex number
val smul : float -> complex -> complex
/// Multiply a complex number by a scalar
val muls : complex -> float -> complex
/// pi
val pi : Complex
/// exp(x) = e^x
val exp : Complex -> Complex
/// log(x) is natural log (base e)
val log : Complex -> Complex
/// sqrt(x) and 0 <= phase(x) < pi
val sqrt : Complex -> Complex
/// Sine
val sin : Complex -> Complex
/// Cosine
val cos : Complex -> Complex
/// Tagent
val tan : Complex -> Complex
[<AutoOpen>]
module ComplexTopLevelOperators =
/// Constructs a complex number from both the real and imaginary part.
val complex : float -> float -> complex
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