Point = {}
Point.__index = Point

function Point:new(x, y)
   local o = { x = x, y = y }
   setmetatable(o, self)
   return o
end

function Point:__add(other)
   return Point:new(self.x+other.x, self.y+other.y)
end

function Point:__sub(other)
   return Point:new(self.x-other.x, self.y-other.y)
end

function Point:__mul(n)
   return Point:new(self.x*n, self.y*n)
end

function Point:__div(n)
   return Point:new(self.x/n, self.y/n)
end

-- absolute value, or the distance from the origin
function Point:abs()
   return math.sqrt(self.x ^ 2 + self.y ^ 2)
end

function Point:__tostring()
    return "("..self.x..","..self.y..")"
end