Every polynomial ring in Macaulay2 comes equipped with an ordering on the monomials. See below for the definitions of all implemented orderings. The default ordering is GRevLex, the graded reverse lexicographic order.
Polynomials are displayed by ordering the monomials in decreasing order. The choice of monomial order can make a difference in the time and space required for various computations, especially Gröbner basis computations.

- weightGrevlex -- transform a weight matrix into a monomial ordering matrix
- grevlexWeight -- transform a weight matrix into a monomial ordering matrix

- examples of specifying alternate monomial orders
- monomial orders for free modules
- packing monomials for efficiency

- GRevLex -- graded reverse lexicographical monomial order.
- Lex -- lexicographical monomial order.
- GLex -- graded lexicographic ordering
- Weights -- assigning weights to the variables
- Eliminate -- elimination order
- GroupLex -- defines a ring where some variables are inverted
- GroupRevLex
- definition of product (block) orders
- RevLex -- reverse lexicographic ordering
- NCLex -- Non-commutative lexicographical order.

- MonomialOrder -- monomial ordering