DEFINITION MODULE ComplexMath;

IMPORT COMPLEX;

(* Mathematical Constants and Functions for Type COMPLEX *)

CONST
  i =    { 0.0, 1.0 };
  one =  { 1.0, 0.0 };
  zero = { 0.0, 0.0 };

PROCEDURE arg ( z : COMPLEX ) : REAL;
(* Returns the argument of z. *)

PROCEDURE conj ( z : COMPLEX ) : COMPLEX;
(* Returns the complex conjugate of z. *)

PROCEDURE power ( base : COMPLEX; exponent : REAL ) : COMPLEX;
(* Returns the value of base raised to the power exponent. *)

PROCEDURE sqrt ( z : COMPLEX ) : COMPLEX;
(* Returns the square root of z. *)

PROCEDURE ln ( z : COMPLEX ) : COMPLEX;
(* Returns the natural logarithm of z. *)

PROCEDURE log ( z : COMPLEX ) : COMPLEX;
(* Returns the decimal logarithm of z. *)

PROCEDURE sin ( z : COMPLEX ) : COMPLEX;
(* Returns the sine of z. *)

PROCEDURE cos ( z : COMPLEX ) : COMPLEX;
(* Returns the cosine of z. *)

PROCEDURE tan ( z : COMPLEX ) : COMPLEX;
(* Returns the tangent of z. *)

PROCEDURE arcsin ( z : COMPLEX ) : COMPLEX;
(* Returns the arcsine of z. *)

PROCEDURE arccos ( z : COMPLEX ) : COMPLEX;
(* Returns the arccosine of z. *)

PROCEDURE arctan ( z : COMPLEX ) : COMPLEX;
(* Returns the arctangent of z. *)

PROCEDURE polarToComplex ( abs, arg : REAL ) : COMPLEX;
(* Returns the complex value with the specified polar coordinates. *)

PROCEDURE scalarMult ( scalar : REAL; z : COMPLEX ) : COMPLEX;
(* Returns the scalar product of scalar and z. *)

END ComplexMath.