Glover Problem A

The first task in solving these problems is to translate the definition of the problem into equations that Mathematica can understand. This is all done in the file called ``basefile.m''. These are put in a seperate file, because the same equations are used in all three problems.

The next step is to create a file which is specific to problem A. In this file we set the monomial order and gather the equations that we will actually be using. This file is called ``problem1.m''. The Mathematica variable equations is set equal to the matrix equations (1) (2) and (3). The assumptions that we are making in this problem are assigned to the variable allOfTheAssumptions. These assumptions include the equations () and (), as well as the specific forms of the matricies and and the fact that is a self-adjoint operator.

Once these two files are loaded into Mathematica, the only command that needs to be executed is

In[3]:= ans = NCSR6[equations,allOfTheAssumptions,1]

The command NCSR6 computes a partial Gröbner basis for the equations in allOfTheAssumptions and uses this partial Gröbner basis to reduce the equations in equations to ``canonical'' form.

The result of the command is

Out[3]:= { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

This verifies that the equations (1) (2) and (3) follow from equations () and (), if we make the assumptions mentioned above.

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