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Solving (HGRAIL) using NCProcess

The first step is to assemble all of the key polynomial equations in executable form:

The polynomials we shall input to NCProcess1 are naturally thought of in several groups. First, to enforce that the 2 × 2 matrix tex2html_wrap_inline5614 is symmetric, we require each of the following polynomials to be zero:


We also assume that tex2html_wrap_inline5608 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