# ocaml / stdlib / complex.mli

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86``` ```(***********************************************************************) (* *) (* OCaml *) (* *) (* Xavier Leroy, projet Cristal, INRIA Rocquencourt *) (* *) (* Copyright 2002 Institut National de Recherche en Informatique et *) (* en Automatique. All rights reserved. This file is distributed *) (* under the terms of the GNU Library General Public License, with *) (* the special exception on linking described in file ../LICENSE. *) (* *) (***********************************************************************) (* \$Id\$ *) (** 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]). *) type 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. *) ```