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;; Pair queue implementation
;;
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(defun sugar-pair-key (p q &aux (lcm (monom-lcm (poly-lm p) (poly-lm q)))
				(d (monom-sugar lcm)))
  "Returns list (S LCM-TOTAL-DEGREE) where S is the sugar of the S-polynomial of
polynomials P and Q, and LCM-TOTAL-DEGREE is the degree of is LCM(LM(P),LM(Q))."
  (declare (type poly p q) (type monom lcm) (type fixnum d))
  (cons (max 
	 (+  (- d (monom-sugar (poly-lm p))) (poly-sugar p))
	 (+  (- d (monom-sugar (poly-lm q))) (poly-sugar q)))
	lcm))

(defstruct (pair
	    (:constructor make-pair (first second
					   &aux
					   (sugar (car (sugar-pair-key first second)))
					   (division-data nil))))
  (first nil :type poly)
  (second nil :type poly)
  (sugar 0 :type fixnum)
  (division-data nil :type list))
  
;;(defun pair-sugar (pair &aux (p (pair-first pair)) (q (pair-second pair)))
;;  (car (sugar-pair-key p q)))

(defun sugar-order (x y)
  "Pair order based on sugar, ties broken by normal strategy."
  (declare (type cons x y))
  (or (< (car x) (car y))
      (and (= (car x) (car y))
	   (< (monom-total-degree (cdr x))
	      (monom-total-degree (cdr y))))))

(defvar *pair-key-function* #'sugar-pair-key
  "Function that, given two polynomials as argument, computed the key
in the pair queue.")

(defvar *pair-order* #'sugar-order
  "Function that orders the keys of pairs.")

(defun make-pair-queue ()
  "Constructs a priority queue for critical pairs."
  (make-priority-queue
   :element-type 'pair
   :element-key #'(lambda (pair) (funcall *pair-key-function* (pair-first pair) (pair-second pair)))
   :test *pair-order*))

(defun pair-queue-initialize (pq f start
			      &aux
			      (s (1- (length f)))
			      (b (nconc (makelist (make-pair (elt f i) (elt f j))
						 (i 0 (1- start)) (j start s))
					(makelist (make-pair (elt f i) (elt f j))
						 (i start (1- s)) (j (1+ i) s)))))
  "Initializes the priority for critical pairs. F is the initial list of polynomials.
START is the first position beyond the elements which form a partial
grobner basis, i.e. satisfy the Buchberger criterion."
  (declare (type priority-queue pq) (type fixnum start))
  (dolist (pair b pq)
    (priority-queue-insert pq pair)))

(defun pair-queue-insert (b pair)
  (priority-queue-insert b pair))

(defun pair-queue-remove (b)
  (priority-queue-remove b))

(defun pair-queue-size (b)
  (priority-queue-size b))

(defun pair-queue-empty-p (b)
  (priority-queue-empty-p b))