Package com.singularsys.extensions.polynomials.comparators

Class LexComparator

java.lang.Object
com.singularsys.extensions.polynomials.comparators.LexComparator
All Implemented Interfaces:
Comparator<PNodeI>
Direct Known Subclasses:
GrevlexComparator, GrlexComparator
public class LexComparator extends Object implements Comparator<PNodeI>
Lexical Order comparator. First orders by degree of leftmost entry. hence quadratic monomial in 3 variables are ordered as 
 "x^2",   // (2,0,0)
 "x y",   // (1,1,0)
 "x z",   // (1,0,1)
 "x",     // (1,0,0)
 "y^2",   // (0,2,0)
 "y z",   // (0,1,1)
 "y",     // (0,1,0)
 "z^2",   // (0,0,2)
 "z",     // (0,0,1)
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

  • Constructor Details

    • LexComparator

      public LexComparator(PolynomialCreator pc)
      Constructor using alphabetical orders for variables. To set up use 
      
 
 PolynomialCreator pc = new PolynomialCreator();
 Comparator<PNodeI> lex = new LexComparator(pc);
 pc.setComparator(lex);
      Parameters:
      pc -

    • LexComparator

      public LexComparator(PolynomialCreator pc, String[] orderedNames)
      Constructor with a given order for the variables
      Parameters:
      pc -
      orderedNames -

  • Method Details