--[[ Complex Number Rectangular Coordinates Module
     H. Conrad Cunningham, Professor
     Computer and Information Science
     University of Mississippi

The Complex Number set of modules illustrates how we can use data
abstraction to design a module that allows multiple representations of
the data to be used simultaneously.

Developed for CSci 658, Software Language Engineering, Fall 2013

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2013-09-20: Translated SICP Scheme code to Lua draft
2013-09-21: Prototyped complex number modules
2013-09-22: Added require of utilities and representation modules

This is a Lua implementation of the Scheme example in Section 2.4
"Multiple Representations for Abstract Data" of SICP:

  Harold Abelson and Gerald J. Sussman with Julie Sussmann. 
  Structure and Interpretation of Computer Programs, Second Edition, 
  The MIT Press, 1996. 
  Full text online at http://mitpress.mit.edu/sicp/

This package implements implement complex numbers in terms of the four
selector functions (real_part, imag_part, magnitude, angle) and two
constructor functions (make_from_real_imag, make_from_mag_ang).

Whatever concrete representation is used, the constructors and
selectors must satisfy the following properties for all complex
numbers z:

    z == make_from_real_imag ( real_part(z), imag_part(z) )
    z == make_from_mag_ang   ( magnitude(z), angle(z)     )

The Lua implementations seek to keep the same function names as in the
Scheme examples except:

(1) an underscore replaces a dash in a function name, e.g.,
    Scheme "real-part" becomes Lua "real_part".

(2) the prefix "is_" replaces the suffice "?" in a query function
    name, e.g., Scheme "polar?" becomes Lua "is_polar".

(3) strings stored in MANIFEST CONSTANTS (just variables that we do
    not reassign and we give names in all upper case) replace Scheme's
    quoted symbols
    
(4) the representations of the complex number ordered pairs use Lua
    record-style tables with two elements.  The Scheme "cons", "car",
    "cdr", and "pair?" calls are replaced by appropriate manipulation
    of the two-element record-style tables.

This module represents complex numbers with rectangular coordinates
stored in record-style tables.

--]]

-- Load complex number utilities module
local util = require "complexUtilities"

-- local definitions for convenience
local square    = util.square
local show_data = util.show_data


-- SCIP Section 2.4.1: Representations for Complex Numbers

-- Rectangular representation (character Ben in SICP)
-- Uses table { real = real_part, imag = imag_part }

-- Load representation module
local rr = require "complexRectangularRep"

-- local definitions for convenience
local make_from_real_imag = rr.make_from_real_imag
local make_from_mag_ang   = rr.make_from_mag_ang 
local real_part           = rr.real_part
local imag_part           = rr.imag_part
local magnitude           = rr.magnitude
local angle               = rr.angle
local to_string           = rr.to_string


-- Arithmetic operations

local function add_complex(z1,z2)
  return make_from_real_imag( real_part(z1) + real_part(z2), 
                              imag_part(z1) + imag_part(z2) )
end

local function sub_complex(z1,z2)
  return make_from_real_imag( real_part(z1) - real_part(z2),
                              imag_part(z1) - imag_part(z2) )
end

local function mul_complex(z1,z2)
  return make_from_mag_ang( magnitude(z1) * magnitude(z2),
                            angle(z1) + angle(z2)         )
end

local function div_complex(z1,z2)
  return make_from_mag_ang( magnitude(z1) / magnitude(z2),
                            angle(z1) - angle(z2)         )
end


-- Module Export

return {
    make_from_real_imag = make_from_real_imag,
    make_from_mag_ang   = make_from_mag_ang,
    real_part           = real_part,
    imag_part           = imag_part,
    magnitude           = magnitude,
    angle               = angle,
    add_complex         = add_complex,
    sub_complex         = sub_complex,
    mul_complex         = mul_complex,
    div_complex         = div_complex,
    to_string           = to_string
  }