local fmt = require "fmt"

class vector2
    static function polar(r, theta)
        return new vector2(r * math.cos(theta), r * math.sin(theta))
    end

    static function scale(s, v) return v * s end

    function __construct(public x, public y) end

    function __add(v) return new vector2(self.x + v.x, self.y + v.y) end
    function __sub(v) return new vector2(self.x - v.x, self.y - v.y) end
    function __mul(s) return new vector2(self.x * s,   self.y * s)   end
    function __div(s) return new vector2(self.x / s,   self.y / s)   end

    function __tostring() return $"({self.x}, {self.y})" end
end

local v1 = new vector2(5, 7)
local v2 = new vector2(2, 3)
local v3 = vector2.polar(math.sqrt(2.0), math.pi / 4)
fmt.print("v1 = %s", v1)
fmt.print("v2 = %s", v2)
fmt.print("v3 = %s", v3)
print()
fmt.print("v1 + v2 = %s", v1 + v2)
fmt.print("v1 - v2 = %s", v1 - v2)
fmt.print("v1 * 11 = %s", v1 * 11)
fmt.print("11 * v2 = %s", vector2.scale(11, v2))
fmt.print("v1 / 2  = %s", v1 / 2)