$define C = 7

class pt
    static function zero() return new pt(math.inf, math.inf) end

    static function from_num(n) return new pt(math.cbrt(n * n - C), n) end

    function __construct(public x, public y) end

    function iszero() return math.abs(self.x) > 1e20 end

    function double()
        if self:iszero() then return self end
        local l = 3 * self.x * self.x / (2 * self.y)
        local t = l * l - 2 * self.x
        return new pt(t, l * (self.x - t) - self.y)
    end

    function __unm() return new pt(self.x, - self.y) end

    function __add(other)
        assert(other instanceof pt, "argument must be a pt object")
        if self.x == other.x and self.y == other.y then return self:double() end
        if self:iszero() then return other end
        if other:iszero() then return self end
        local l = (other.y - self.y) / (other.x - self.x)
        local t = l * l - self.x - other.x
        return new pt(t, l * (self.x - t) - self.y)
    end

    function __mul(n)
        assert(math.type(n) == "integer", "argument must be an integer")
        local r = pt.zero()
        local p = self
        local i = 1
        while i <= n do
            if (i & n) != 0 then r += p end
            p = p:double()
            i <<= 1
        end
        return r
    end

    function __tostring()
        return self:iszero() ? "Zero" : string.format("(%0.3f, %0.3f)", self.x, self.y)
    end
end

local a = pt.from_num(1)
local b = pt.from_num(2)
local c = a + b
local d = -c
print($"a         = {a}")
print($"b         = {b}")
print($"c = a + b = {c}")
print($"d = -c    = {d}")
print($"c + d     = {c + d}")
print($"a + b + d = {a + b + d}")
print($"a * 12345 = {a * 12345}")