;;; -*-  Mode: Lisp -*- 
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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>		 
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(defpackage "PAIR-QUEUE"
  (:use :cl :priority-queue :monom :polynomial :symbolic-polynomial :utils)
  (:export "CRITICAL-PAIR"
	   "CRITICAL-PAIR-FIRST"
	   "CRITICAL-PAIR-SECOND"
	   "CRITICAL-PAIR-QUEUE"
	   "SELECTION-STRATEGY"
	   "MIN-TOTAL-DEGREE-STRATEGY"
	   "MIN-COMBINED-LENGTH-STRATEGY"
	   "ENQUEUE"
	   "DEQUEUE"
	   "QUEUE-SIZE"
	   "QUEUE-EMPTY-P"
	   )
  (:documentation "Critical pair queue implementation. The pair queue is a list of critical
pairs, ordered by some partial order. Pair queue is a kind of priority queue.")
  )
	   
(in-package :pair-queue)

(defclass critical-pair ()
  ((first :initform nil  :initarg :first :accessor critical-pair-first :type poly)
   (second :initform nil :initarg :second :accessor critical-pair-second :type poly))
  (:documentation "Represents a critical pair, i.e. a pair of two polynomials. The derived
classes may add extra data used in computing the order of critical pairs."))

(defmethod print-object ((self critical-pair) stream)
  (print-unreadable-object (self stream :type t :identity t)
    (with-accessors ((first critical-pair-first)
		     (second critical-pair-second))
	self
      (format stream "FIRST=~A SECOND=~A" 
	      first second))))

(defclass selection-strategy ()
  ((pair-key-fn :initform #'(lambda (p q) (universal-lcm (leading-monomial p) (leading-monomial q))) 
		:initarg :pair-key-fn 
		:accessor pair-key-fn)
   (pair-order-fn :initform #'lex> 
		  :initarg :pair-order-fn 
		  :accessor pair-order-fn))
  (:documentation "Represents the normal critical pair selection
strategy.  The two ingredients of a strategy is a function
PAIR-KEY-FUNCTION which computes a key from the critical pair, which
can be any type of data, and a function PAIR-ORDER-FN used to compaire
the calculated keys to determine which pair is more promising and
should be considered first.  The normal selection strategy for a given
monomial order PAIR-ORDER-FN consists in selecting the pair with the
minimal LCM of leading monomials first."))

(defmethod print-object ((self selection-strategy) stream)
  (print-unreadable-object (self stream :type t :identity t)
    (with-accessors ((pair-key-fn pair-key-fn)
		     (pair-order-fn pair-order-fn))
	self
      (format stream "PAIR-KEY-FN=~A PAIR-ORDER-FN=~A" 
	      pair-key-fn pair-order-fn))))

(defclass min-total-degree-strategy (selection-strategy)
  ((pair-key-fn :initform #'(lambda (p q) (total-degree (universal-lcm (leading-monomial p) (leading-monomial q)))))
   (pair-order-fn :initform #'<))
  (:documentation "Make a selection strategy where a pair with a
minimum total degree of LCM of leading monomials is selected."))

(defclass min-combined-length-strategy (selection-strategy)
  ((pair-key-fn :initform #'(lambda (p q) (+ (poly-length p) (poly-length q))))
   (pair-order-fn :initform #'<))
  (:documentation "Make a selection strategy where a pair with the minimum combined length of both
polynomials is selected."))

(defun make-critical-pair-queue (&key pair-key-fn pair-order-fn (poly-list nil) (start 1)
				 &aux (pq (make-priority-queue
					   :element-type 'critical-pair
					   :element-key #'(lambda (pair) (funcall pair-key-fn 
										  (critical-pair-first pair)
										  (critical-pair-second pair)))
					   :test pair-order-fn)))
  "Makes a priority queue for critical pairs. The argument POLY-LIST should the initial list of polynomials.
and START is the first position beyond the elements which form a
partial Grobner basis, i.e. satisfy the Buchberger criterion."
    ;; Add critical pairs for polynomials in POLY-LIST
  (let* ((s (1- (length poly-list)))
	 (b (nconc (makelist (make-instance 'critical-pair :first (elt poly-list i) :second (elt poly-list j))
			     (i 0 (1- start)) (j start s))
		   (makelist (make-instance 'critical-pair :first (elt poly-list i) :second (elt poly-list j))
			     (i start (1- s)) (j (1+ i) s)))))
    (dolist (pair b pq)
      (priority-queue-insert pq pair)))))