coefficients is used to extract the coefficients of a polynomial.
Define a polynomial in variables x and y, with coefficients parameterized by s and t.
p = x^2+x*y*(s+t)+s^2+t^2;
The coefficients are easily recovered
By adding a second output, the monomial basis is returned also.
Of course, we might just as well consider this to be a polynomial in s and t with coefficients parameterized by x and y.