In this section, the impact of the chosen domain of coefficients will be discussed. It should be obvious that the resulting Gröbner basis depends on the chosen domain of coefficients. We shall illustrate this fact by some examples.

Consider the set of polynomials

We fix *total degree inverse lexical* ordering w.r.t. *x*>*y*>*z* (*x*>*y* in
Example 3) for monomials.

Wed Sep 2 09:42:51 MDT 1998