) and
(
),
as well as the specific forms of the
matricies
and 
and the fact
that 
is a self-adjoint operator.
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.
