The Mathematica code and the C++ code both attach numbers
to the polynomials which occur in the running of
the GB algorithm. While these numbers are not externally
visible at least in the commands described so far,
they can be accessed by the user and are quite useful.
One feature is that they can save typing time for the user
who chooses
to select or deselect relations in later runs of
NCMakeGB. Also, if one is running the C++ version of
the code, this will save considerable computer time
because the C++ version of the code only has to send
a number rather than the full polynomial to the
Mathematica session. This time can be very significant when
the polynomial has a large number of terms.
See also section 33.2.
Recall the Option ReturnRelationsToMma
False for NCMakeGB stops the partial
GB calculated by the C++ program from transferring
the answer
back to Mathematica.
This is the typical prelude to a ``play by numbers "
session.
Recall the option ReturnRelationsToMma
False
for NCMakeGB stops the results from the
NCMakeGB command from being returned to
Mathematica. This is typically the first step
in ``playing by numbers".