A monomial order, also called a monomial ordering, is a total order on monomials with coefficient
1 in a fixed finite set of variables
that makes them a well ordered set and satisfies
the condition "
implies 
"
for all monomials 
, 
,
and 
.
Examples are the lexicographic order and the
order that compares total degree first and uses lexicographic order to break ties.
Monomial Order
See also
Gröbner Basis, Leading Monomial, Leading Term, Lexicographic Order, Polynomial Reduction, Reduced Gröbner Basis, Total Degree, Total Order, Well Ordered SetExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Monomial Order." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MonomialOrder.html