text: /*
   * C++ Notes Accompanying Code
   * Compile: Y
   * Run: Y
   * Compile Should Succeed: Y
   * Run Should Succeed: Y
   * Ignore Unused Private Variables: Y
   */
  
  #include <cmath>
  
  class FourVector {
   public:
    void boost_z(const double velocity);
  
   private:
    double t;
    double x;
    double y;
    double z;
  };
  
  // NOTES: BEGIN INCLUSION
  // Change the four-vector in place
  void FourVector::boost_z(const double velocity) {
    // natural units: c = 1
    double original_t = t;
    double gamma = 1.0 / sqrt(1.0 - velocity * velocity);
    t = gamma * (t - velocity * z);
    z = gamma * (z - velocity * original_t);
  }
  // NOTES: END INCLUSION
  
  int main() { return 0; }
  