Package com.singularsys.extensions.polynomials.comparators

Class GrlexComparator

java.lang.Object
com.singularsys.extensions.polynomials.comparators.LexComparator
com.singularsys.extensions.polynomials.comparators.GrlexComparator
All Implemented Interfaces:
Comparator<PNodeI>
public class GrlexComparator extends LexComparator
Graded Lexical Order comparator. First orders by the total degree, then by degree of leftmost entry. hence quadratic monomials in 3 variables are ordered as 
 "x^2",   // (2,0,0)
 "x y",   // (1,1,0)
 "x z",   // (1,0,1)
 "y^2",   // (0,2,0)
 "y z",   // (0,1,1)
 "z^2",   // (0,0,2)
 "x",     // (1,0,0)
 "y",     // (0,1,0)
 "z",     // (0,0,1)
With higher degree terms first, then those with the higher power of x first, then with highest power of y. Bracket are (deg x, deg y, deg z).

Note that variables are ordered in reverse alphabetical order so x > y > z.

See Cox, Little and O'Shea, Ideals, Varieties and Algorithms, pp57-58