The polynomials we shall input to NCProcess1 are naturally thought of in several groups. First, to enforce that the 2 × 2 matrix is symmetric, we require each of the following polynomials to be zero:

We also assume that is invertible for *i*=1,2
and *j*=1,2. We assume the following polynomials are zero:

Naturally we also assume the following polynomials are zero:

The multigraded lexicographic order
(see
§)
which we use is:
*A* <
*A*
<
*B*
<
*B*
<
*B*
<
*B*
<
*C*
<
*C*
<
*C*
<
*C*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*E*
«
*b*
«
*b*
«
*c*
«
*c*
«
*a*
«
*a*.

We ran NCProcess1 for 2 iterations
with the option *NCCollectOnVariables* turned on.
*NCCollectOnVariables* was applied to each equation.

The algorithm did not run the full two iterations but finished after one. Our program produced a message saying that, in fact, the output is a Gröbner Basis (rather than a partial GB).

Wed Jul 3 10:27:42 PDT 1996