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Macaulay2Doc > rings > monomial orderings > RevLex

RevLex -- reverse lexicographic ordering

Description

The reverse lexicographic order is defined by: xA > xB 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

For the programmer

The object RevLex is a symbol.