Assignment 5 : Structure and Signature

Date: 18.3.2010
Due Date: 2.4.2010

Develop a package using SML for complex arithmatics according to the following signature.

signature Complex =
  sig

    datatype complex = RECT of real * real;
    val make_complex: real * real -> complex
    val real_to_complex: real -> complex
    val real_component   : complex -> real
    val imag_component   : complex -> real
    val conjugate   : complex -> complex
    val magnitude   : complex -> real
    val add         : complex * complex -> complex
    val subtract    : complex * complex -> complex
    val mult        : complex * complex -> complex
    val reciprocal  : complex -> complex
    val divide      : complex * complex -> complex
    val square      : complex -> complex
    val size_equalto     : real * complex * complex -> bool
  end;

Note

make_complex takes two real numbers and makes a complex number in rectangular coordinates.
real_to_complex takes a real number and converts it into a complex number with imaginary component 0.0.
real_component and imag_component take a complex number and yield the real and imaginary components respectively.
conjugate takes a complex number and yields its complex conjugate.
magnitude takes a complex number and yields its distance from the origin of the coordinate system.
size_equalto is the approximate equality which takes a real number $\epsilon$ and judges two complex numbers z₁ and z₂ to be equal upto $\epsilon$ if the euclidean distance between z₁ and z₂ is less than $\epsilon$ .