def METHOD_NAME(self, w1, w2):
    r"""
    Return the product of the two basis elements indexed by ``w1`` and ``w2``.
    .. SEEALSO:: :meth:`AlgebrasWithBasis.ParentMethods.product_on_basis`.
    EXAMPLES::
        sage: A = FiniteDimensionalAlgebrasWithBasis(QQ).example()
    Here is the multiplication table for the algebra::
        sage: matrix([[p*q for q in A.basis()] for p in A.basis()])
        [x 0 a b]
        [0 y 0 0]
        [0 a 0 0]
        [0 b 0 0]
    Here we take some products of linear combinations of basis elements::
        sage: x, y, a, b = A.basis()
        sage: a * (1-b)^2 * x
        0
        sage: x*a + b*y
        a + b
        sage: x*x
        x
        sage: x*y
        0
        sage: x*a*y
        a
    """
    if w1+w2 in self._nonzero_products:
        return self.monomial(self._nonzero_products[w1+w2])
    else:
        return self.zero()