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).