human
Give me a the Python code you requested given the following:
I am working on the file "ExercisesSolutions.ipynb".
The first task is:
A basis for the polynomials
In the section on classes we defined a Monomial class to represent a polynomial with leading coefficient $1$. As the $N+1$ monomials $1, x, x^2, \dots, x^N$ form a basis for the vector space of polynomials of order $N$, $\mathbb{P}^N$, we can use the Monomial class to return this basis.
Exercise 1
Define a generator that will iterate through this basis of $\mathbb{P}^N$ and test it on $\mathbb{P}^3$.
Solution
Again we first take the definition of the crucial class from the notes.
Can you write Python code for it?
assistant
#Here is the Python code you requested.

class Polynomial(object):
    """Representing a polynomial."""
    explanation = "I am a polynomial"
    
    def __init__(self, roots, leading_term):
        self.roots = roots
        self.leading_term = leading_term
        self.order = len(roots)
        
    def __repr__(self):
        string = str(self.leading_term)
        for root in self.roots:
            if root == 0:
                string = string + "x"
            elif root > 0:
                string = string + "(x - {})".format(root)
            else:
                string = string + "(x + {})".format(-root)
        return string
    
    def __mul__(self, other):
        roots = self.roots + other.roots
        leading_term = self.leading_term * other.leading_term
        return Polynomial(roots, leading_term)
    
    def explain_to(self, caller):
        print("Hello, {}. {}.".format(caller,self.explanation))
        print("My roots are {}.".format(self.roots))
        return None

class Monomial(Polynomial):
    """Representing a monomial, which is a polynomial with leading term 1."""
    explanation = "I am a monomial"
    
    def __init__(self, roots):
        Polynomial.__init__(self, roots, 1)
        
    def __repr__(self):
        string = ""
        for root in self.roots:
            if root == 0:
                string = string + "x"
            elif root > 0:
                string = string + "(x - {})".format(root)
            else:
                string = string + "(x + {})".format(-root)
        return string