How to order lexicographically the monomers of a parametrized polynomial?

Question

I want to order lexicographically the monomials in a "parametrized polynomial", i.e. polynomials whose "symbolic bits" may be either "variables" or "parameters". For example:

In[1]:= Expand[(x + a y + a^2 z)^3] /. a^n_ -> a^Mod[n, 3]

Out[1]= x^3 + y^3 + 6 x y z + z^3 + 3 x^2 y a + 3 y^2 z a + 3 x z^2 a +  3 x y^2 a^2 +
 3 x^2 z a^2 + 3 y z^2 a^2

In the polynomial above x, y, and z are intended as "variables", whereas a is intended as a "parameter".

The documentation for Mathematica states that monomials in a polynomial are ordered lexicographically by default, but if so, I don't understand why the two terms with x^2 come after the y^3 term in the polynomial above, for example.

So my question is: how can I force a lexicographic ordering of the monomials with respect to the "variables" (i.e. x, y, and z). (In particular, for the polynomial above, the symbol a should be disregarded for the ordering.)

For example, the desired ordering for the polynomial above would be

x^3 + 3 x^2 y a + 3 x^2 z a^2 + 3 x y^2 a^2 + 3 x z^2 a + 6 x y z + y^3 + 3 y^2 z a + 3 y z^2 a^2 + z^3

Answer 1

In this case you can use something like:

TraditionalForm[Expand[(x+a y+a^2 z)^3]/.a^n_->a^Mod[n,3], ParameterVariables:>{a}] 

This information can be found in the following: http://reference.wolfram.com/mathematica/tutorial/PolynomialOrderings.html (toward the bottom)