source: branches/f4grobner/criterion.lisp

;;; -*-  Mode: Lisp -*- 
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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
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(defpackage "CRITERION"
  (:use :cl :monom :pair-queue :grobner-debug :polynomial)
  (:export "CRITERION-1"
           "CRITERION-2"
           )
  (:documentation "Implements Buchberger pair selection criteria.")
  )

(in-package :criterion)

(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))

(defgeneric criterion-1 (pair)
  (:documentation "Returns T if the leading monomials of the two
polynomials in G pointed to by the integers in PAIR have
disjoint (relatively prime) monomials. This test is known as the first
Buchberger criterion.")
  (:method ((pair critical-pair))
    (let ((f (critical-pair-first pair))
          (g (critical-pair-second pair)))
      (when (rel-prime-p (leading-monomial f) (leading-monomial g))
        (debug-cgb ":1")
        (return-from criterion-1 t)))))

(defgeneric criterion-2 (pair b-done partial-basis)
  (:documentation "Returns T if the leading monomial of some element P
of PARTIAL-BASIS divides the LCM of the leading monomials of the two
polynomials in the polynomial list PARTIAL-BASIS, and P paired with
each of the polynomials pointed to by the the PAIR has already been
treated, as indicated by the absence in the hash table B-done.")
  (:method ((pair critical-pair) (b-done hash-table) partial-basis
            &aux (f (critical-pair-first pair)) (g (critical-pair-second pair))
              (place :before))
    (declare (type poly f g))
    ;; In the code below we assume that pairs are ordered as follows: 
    ;; if PAIR is (I J) then I appears before J in the PARTIAL-BASIS.
    ;; We traverse the list PARTIAL-BASIS and keep track of where we
    ;; are, so that we can produce the pairs in the correct order
    ;; when we check whether they have been processed, i.e they
    ;; appear in the hash table B-done
    (dolist (h partial-basis nil)
      (cond
        ((eq h f)
         #+grobner-check(assert (eq place :before))
         (setf place :in-the-middle))
        ((eq h g)
         #+grobner-check(assert (eq place :in-the-middle))
         (setf place :after))
        ((and (divides-lcm-p (leading-monomial h) 
                             (leading-monomial f)
                             (leading-monomial g))
              (gethash (case place
                         (:before (list h f))
                         ((:in-the-middle :after) (list f h)))
                       b-done)
              (gethash (case place
                         ((:before :in-the-middle) (list h g))
                         (:after (list g h)))
                       b-done)
              )
         (debug-cgb ":2")
         (return-from criterion-2 t))))))