package batteries

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package batteries
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Additional and modified functions for complex numbers.

Complex numbers.

This module provides arithmetic operations on complex numbers. Complex numbers are represented by their real and imaginary parts (cartesian representation). Each part is represented by a double-precision floating-point number (type float).

  • author Xavier Leroy (base module)
  • author Gabriel Scherer
  • author David Teller
type t = Complex.t = {
  1. re : float;
  2. im : float;
}
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 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 operations : t BatNumber.numeric
val inv : t -> t

inv x returns the value of 1/x

val succ : t -> t

Add one to this number.

val pred : t -> t

Remove one from this number.

val abs : t -> t

abs c returns the module of this complex number, i.e. abs c = Float.sqrt((re c) *. (re c) +. (im c) *. (im c) )

val modulo : t -> t -> t
val pow : t -> t -> t
val compare : t -> t -> int
val ord : t -> t -> BatOrd.order
val equal : t -> t -> bool
val of_int : int -> t
val to_int : t -> int

to_int c is the integer part of the real part of c

val of_string : string -> t

of_string s accepts strings with the following formats:

(<int>|<float>) (+|-) i ( * | . | ) (<int>|<float>)

where (a|b|c) is either a or b or c.

In addition the following degenerate formats are also accepted:

(+|-) i ( * | . | ) (<int>|<float>)

(<int>|<float>) (+|-) i

(<int>|<float>)

val to_string : t -> string
val (+) : t -> t -> t
val (-) : t -> t -> t
val (*) : t -> t -> t
val (/) : t -> t -> t
val (**) : t -> t -> t
val (--) : t -> t -> t BatEnum.t
val (---) : t -> t -> t BatEnum.t
val of_float : float -> t

Complex.of_float x returns the complex number x+0i

val to_float : t -> float

Complex.to_float (a+bi) returns the float a

Submodules grouping all infix operators
module Infix : BatNumber.Infix with type bat__infix_t = t
Boilerplate code
val print : 'a BatInnerIO.output -> t -> unit

Printing