Orbits of U(n,n) acting on Mn: Step 1
The first step is always to create an input file. In this case it is called
OrbitStep1.m.
In this file the variables are set noncommutative, the ordering is
declared, and the ``starting relations'' are assembled.
These starting relations include the fact that a linear fractional
transformation
F(x)
exists, and we set y = F(x).
We also assume that the two
J equations hold.
We have also set all of the variables to be invertible.
The monomial ordering that we have used is the following.
Once this is done,
NCProcess can be run. The result is a spreadsheet.
The first spreadsheet reveals a couple of substitutions which might
be helpful. The entire
spreadsheet is available,
but here are some the equations which motivate the next substitution.
The expressions with unknown variables
and knowns
There is nothing special about this category except for the
appearance of the factor
.
If we substitute a new variable for this term, then the equation
above will be simplified somewhat, and perhaps several others will
also. With a little
foresight we will choose the variable Tp[f]. The next two equations
have another collected term.
The expressions with unknown variables
and knowns
The factor
appears in
both of these categories.
In the above category, the transpose of this term also appears,
while in the category below, the term appears with an extra
d multiplied on the right. In the
second step, this factor
will be called Tp[F].
The expressions with unknown variables
and knowns
