GRÖBNER offers the possibility to choose among several term orderings. This ordering determines the ordering of monomials in a polynomial. The result of a Gröbner basis calculation as well as the computing time heavily depends on the chosen ordering of monomials.
In the following, and denote exponent vectors, which represent power products (terms) in n variables. We provide the following term orderings:
Details about the properties of the matrix U, which guarantee that this yields an admissible ordering, are given in  or .
Ordering of monomials is done by the predicate is_greater_mon , which is mapped to one of those predicates in the file GB.to.setup.