-- file: complex.lua
-- a simple module for complex numbers

local M = {}

function M.tostring(c)
    return "(" ..c.r.. ", " ..c.i.. ")"
end

local mt = {__tostring=M.tostring}

function M.new(r, i)
    local c = {r=r, i=i}
    setmetatable(c, mt)
    return c
end

-- defines constant 'i'
M.i = M.new(0, 1)

function M.add(c1, c2)
    return M.new(c1.r + c2.r, c1.i + c2.i)
end

function M.sub(c1, c2)
    return M.new(c1.r - c2.r, c1.i - c2.i)
end

function M.mul(c1, c2)
    return M.new(c1.r*c2.r - c1.i*c2.i, c1.r*c2.i + c1.i*c2.r)
end

local function inv(c)
    local n = c.r^2 + c.i^2
    return M.new(c.r/n, -c.i/n)
end

function M.div(c1, c2)
    return M.mul(c1, ind(c2))
end

function M.tostring(c)
    return "(" ..c.r.. ", " ..c.i.. ")"
end

return M