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

Developed for CSci 658, Software Language Engineering, Fall 2013

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2013-09-22: Separated out Polar Representation module


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 }

local POLAR = "Polar"

local function magnitude(z) return z.mag end
local function angle(z)     return z.ang end

local function real_part(z)
  return magnitude(z) * math.cos(angle(z))
end

local function imag_part(z)
  return magnitude(z) * math.sin(angle(z))
end

local function make_from_real_imag(x,y)
  return { mag = math.sqrt(square(x) + square(y)),
           ang = math.atan2(y,x)                   
         }
end

local function make_from_mag_ang(r,a) 
  return { mag = r,  ang = a }
end


-- Added function: Convert representation to string
local function to_string(z)
  return POLAR .. "(" .. tostring(magnitude(z)) .. ", " 
                      .. tostring(angle(z))     .. ")"
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,
    to_string           = to_string
  }