# RevLex -- reverse lexicographic ordering

## Description

The reverse lexicographic order is defined by: $x^A > x^B$ if the FIRST non-zero entry of the vector of integers A-B is NEGATIVE. This is a local order, not a global order. Therefore Gröbner bases over this ring only give generators over the local ring whose fractions are all elements not in the ideal generated by the variables.
 i1 : R = QQ[a..d,MonomialOrder => RevLex, Global => false]; i2 : a^3 + b^2 + b*c + a*c^2 + b^2*c + a + b + c 2 2 2 3 o2 = c + b + b*c + b + b c + a + a*c + a o2 : R
Computations of Gröbner bases for local orders are done using Mora's algorithm.

## See also

• GRevLex -- graded reverse lexicographical monomial order.
• Global -- monomial ordering

## For the programmer

The object RevLex is .