Possible settings for order are "Lexicographic", "DegreeLexicographic", "DegreeReverseLexicographic", "NegativeLexicographic", "NegativeDegreeLexicographic", "NegativeDegreeReverseLexicographic" or an explicit weight matrix.
Monomials are sorted on the basis of their exponent vectors with respect to the variables xi.
"NegativeLexicographic" corresponds to applying Sort to the list of exponent vectors.
"Lexicographic" gives the reverse of "NegativeLexicographic", and is the default for MonomialList.
"DegreeLexicographic" sorts first with respect to total degree, then by using the ordering defined by "Lexicographic".
"DegreeReverseLexicographic" sorts first with respect to total degree, then in the negative lexicographic order by starting from the last variable.
"NegativeDegreeLexicographic" and "NegativeDegreeReverseLexicographic" sort from lower to higher total degree.
An explicit weight matrix w defines an ordering given by "Lexicographic" ordering of the w.vi, where the vi are the exponent vectors.