7) This is a CS 4110 question

The set POLYNOMIAL defined in this chapter contains only the polynomials in the one variable x. Write a recursive definition for the set of all polynomials in the two variables x and y.

(Here is the definition in the chapter.)

The set POLYNOMIAL is defined by these three rules:

Rule 1: Any number is in POLYNOMIAL. Rule 2: The variable x is in POLYNOMIAL. Rule 3: If p and q are in POLYNOMIAL, then so are p + q, p - q, (p), and pq.