--[[ Complex Number Polar 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

See the "complexRectangular" module for more extensive comments on the
overall package.

This module represents complex numbers in polar coordinates using Lua
record-style table.

--]]

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

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


-- SICP Section 2.4.1: Representations for Complex Numbers

-- Polar representation (character Alyssa in SICP)
-- Uses table { mag = magnitude, ang = angle }


-- Load representation module
local pr = require "complexPolarRep"

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