source: branches/f4grobner/criterion.lisp@ 62

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;; Pair selection criteria
;;
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(defun criterion-1 (pair)
  "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."
  (declare (type pair pair))
  (let ((f (pair-first pair))
        (g (pair-second pair)))
    (when (monom-rel-prime-p (poly-lm f) (poly-lm g))
      (debug-cgb ":1")
      (return-from criterion-1 t))))

(defun criterion-2 (pair b-done partial-basis
                    &aux (f (pair-first pair)) (g (pair-second pair))
                         (place :before))
  "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."
  (declare (type pair pair) (type hash-table b-done)
           (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 (monom-divides-monom-lcm-p (poly-lm h) (poly-lm f) (poly-lm 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)))))