Glover Problem B

Just as in problem A, we will use the file ``basefile.m''. This is a Mathematica executable file which contains the definitions which are common to all three parts of the problem.

The next step is to create a file which is specific to problem B. In this file we set the monomial order and gather the equations that we will actually be using. This file is called ``problem2.m''.

The NCProcess command in this file creates a spreadsheet in the file ``Banswer1.dvi''. This spreadsheet is rather large, but if we can make some progress then we can run the algorithm again and produce a much more simple spreadsheet. Anything which allows us to solve for an unknown would be significant progress. The following portion of the spreadsheet motivates us to do just that.

This is one of the categories from the spreadsheet ``Banswer1.dvi''.

The expressions with unknown variables
and knowns

After looking at the first equation in this category, we can see that the remaining three equations are equations in one unkown, . Recall that in this part of the problem, the matricies A, B and C are known. Furthermore, we could factor on the right, since it appears in every term. So, each of these equations tell us that when we multiply on the the left by some stuff, we get zero. While this may not prove that is zero, it does motivate us to assume that this is the case.

We have at least made some progress, and we have new information for a second run of NCProcess.

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