Object-oriented design principles in mathematics

It is astonishingly simple to implement complex mathematical structures into an object-oriented environment, but it is harmful to “reinvent the wheel” every time you create a program. Furthermore, you should follow some rules in order to achieve accuracy, modularity, deferred commitment, reusability and naturalness. In this paper, I am going to present some object-oriented design principles to solve the “software crisis” between “pure mathematics” and computer science.