mathnet-numerics/src/FSharp/Complex.fsi

// First version copied from the F# Power Pack
// https://raw.github.com/fsharp/powerpack/master/src/FSharp.PowerPack/math/complex.fsi

// (c) Microsoft Corporation 2005-2009.

namespace MathNet.Numerics

    open System
    open System.Numerics

    [<AutoOpen>]
    module ComplexExtensions =
        /// The type of complex numbers stored as pairs of 64-bit floating point numbers in rectangular coordinates
        type Complex with
            /// 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