package prbnmcn-basic-structures

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prbnmcn-basic-structures
- Basic_structures
  - Basic_impl
    
    Bool_map
    
    Float_map
    
    Free_module
    
    Float_valued
    
    Bool
    
    Basis
    
    R
    
    Float
    
    Basis
    
    R
    
    Int
    
    Basis
    
    R
    
    Make_with_map
    
    Basis
    
    Map
    
    R
    
    X
    
    String
    
    Basis
    
    R
    
    Free_module_with_map
    
    Basis
    
    Map
    
    R
    
    Make
    
    Basis
    
    M
    
    R
    
    Make_with_map
    
    Basis
    
    Map
    
    R
    
    X
    
    Rational_valued
    
    Bool
    
    Basis
    
    R
    
    Float
    
    Basis
    
    R
    
    Int
    
    Basis
    
    R
    
    Make_with_map
    
    Basis
    
    Map
    
    R
    
    X
    
    String
    
    Basis
    
    R
    
    Int_map
    
    Int_set
    
    Integer
    
    Integer_mod2
    
    Lang
    
    Bool
    
    Codegen
    
    Infix
    
    Complex
    
    Empty
    
    Exn
    
    Float
    
    Float_storage
    
    Int
    
    Lambda
    
    Loop
    
    Make_array
    
    X
    
    Make_const
    
    X
    
    Make_enum
    
    X
    
    Make_storage
    
    X
    
    Product
    
    Rational
    
    Sequencing
    
    String
    
    Monad
    
    Codegen_cps
    
    Infix
    
    M
    
    Repr
    
    Codegen_identity
    
    Infix
    
    M
    
    Repr
    
    Cps
    
    Infix
    
    Identity
    
    Infix
    
    Reals
    
    Float
    
    Rational
    
    String_map
  - Basic_intf
    
    Abelian_group
    
    Abelian_group_std
    
    Algebra
    
    R
    
    Codegen_monad
    
    Infix
    
    Field
    
    Field_std
    
    Finitely_generated_free_module
    
    R
    
    Free_module
    
    R
    
    Free_module_std
    
    Basis
    
    R
    
    Infix_order
    
    Lang
    
    Array
    
    Bool
    
    Const
    
    Empty
    
    Enum
    
    Exn
    
    Field
    
    Field_std
    
    Infix_order
    
    Lambda
    
    Loop
    
    Product
    
    Ring
    
    Ring_std
    
    Sequencing
    
    Shape
    
    Morphism
    
    Storage
    
    Std
    
    Storage
    
    Metric
    
    Module
    
    R
    
    Module_std
    
    R
    
    Monad
    
    Infix
    
    Monoid
    
    Monoid_std
    
    Ordered
    
    Partial_order
    
    Pp
    
    Reals
    
    Ring
    
    Ring_std
    
    Std
  - Std
    
    Bool
    
    Complex
    
    Float
    
    Int
    
    Q
    
    String
    
    Z

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include module type of struct include Std.Complex end

include module type of struct include Complex end

type t = Complex.t = {

re : float;
im : float;

}

The type of complex numbers. re is the real part and im the imaginary part.

val zero : t

The complex number 0.

val one : t

The complex number 1.

val i : t

The complex number i.

val neg : t -> t

Unary negation.

val conj : t -> t

Conjugate: given the complex x + i.y, returns x - i.y.

val add : t -> t -> t

Addition

val sub : t -> t -> t

Subtraction

val mul : t -> t -> t

Multiplication

val inv : t -> t

Multiplicative inverse (1/z).

val div : t -> t -> t

Division

val sqrt : t -> t

Square root. The result x + i.y is such that x > 0 or x = 0 and y >= 0. This function has a discontinuity along the negative real axis.

val norm2 : t -> float

Norm squared: given x + i.y, returns x^2 + y^2.

val norm : t -> float

Norm: given x + i.y, returns sqrt(x^2 + y^2).

val arg : t -> float

Argument. The argument of a complex number is the angle in the complex plane between the positive real axis and a line passing through zero and the number. This angle ranges from -pi to pi. This function has a discontinuity along the negative real axis.

val polar : float -> float -> t

polar norm arg returns the complex having norm norm and argument arg.

val exp : t -> t

Exponentiation. exp z returns e to the z power.

val log : t -> t

Natural logarithm (in base e).

val pow : t -> t -> t

Power function. pow z1 z2 returns z1 to the z2 power.

val pp : Format.formatter -> Complex.t -> unit

val hash : Complex.t -> int

val equal : Complex.t -> Complex.t -> bool

val compare : Complex.t -> Complex.t -> int

include module type of struct include Empty end

type 'a m = 'a

'a m is the type of programs computing a value of type 'a

val of_int : int -> Complex.t