Ex. 1 → Implement a method __add__, which constructs a new polynomial p+q by adding two given polynomials p and q. In monomial form, polynomials are added by just adding the coefficients, whereas in Newton form, the coefficients depend on the abscissa x_i of the interpolation points. Before adding the coefficients of both polynomials, the polynomial q has to get new interpolation points with the property that their abscissa x_i coincides with those of p and the method __changepoints__ has to be provided for that. It should change the interpolation points and return a new set of coefficients.

Ex. 2 → Write conversion methods to convert a polynomial from Newton form into monomial form and vice versa.

Ex. 3 → Write a method called add_point that takes a polynomial q and a tuple (x,y) as parameters and returns a new polynomial that interpolates self.points and (x,y).

Ex. 4 → Write a class called LagrangePolynomial that implements polynomials in Lagrange form and inherits as much as possible from the polynomial base class.

Ex. 5 → Write tests for the polynomial class.