source: branches/f4grobner/pair-queue.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-DATA"
           "CRITICAL-PAIR-QUEUE"
           "SELECTION-STRATEGY"
           "*NORMAL-STRATEGY*"
           "*MIN-TOTAL-DEGREE-STRATEGY*"
           "*MIN-COMBINED-LENGTH-STRATEGY*"
           "MAKE-CRITICAL-PAIR-QUEUE"
           "MAKE-CRITICAL-PAIRS"
           )
  (: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)
   (data :initform nil :accessor critical-pair-data))
  (: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 (error "Initarg :pair-key-fn must be specified.")
                :initarg :pair-key-fn 
                :accessor pair-key-fn)
   (pair-order-fn :initform (error "Initarg :pair-order-fn must be specified.")
                  :initarg :pair-order-fn 
                  :accessor pair-order-fn))
  (:documentation "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))))

(defparameter *max-lcm-strategy*
  (make-instance 
   'selection-strategy
   :pair-key-fn #'(lambda (p q) (universal-lcm (leading-monomial p) (leading-monomial q)))
   :pair-order-fn #'lex>)
  "The selection strategy where a pair with the largest LCM of
leading monomials is selected.")

(defparameter *normal-strategy*
  (make-instance 
   'selection-strategy
   :pair-key-fn #'(lambda (p q) (total-degree (universal-lcm (leading-monomial p) (leading-monomial q))))
   :pair-order-fn #'<)
  "A selection strategy where a pair with a minimum total degree of
  LCM of leading monomials is selected. This is known as the normal strategy.")

(defparameter *min-combined-length-strategy*
  (make-instance
   'selection-strategy
   :pair-key-fn #'(lambda (p q) (+ (poly-length p) (poly-length q)))
   :pair-order-fn #'<)
  "A selection strategy where a pair with the minimum combined length of both
polynomials is selected.")

(defclass critical-pair-queue (priority-queue) 
  ()
  (:documentation "Specializes class PRIORITY-QUEUE to ELEMENT-TYPE set to CRITICAL-PAIR."))

(defmethod initialize-instance :before ((self critical-pair-queue) &key) 
  "Initializes the slot ELEMENT-TYPE to symbol CRITICAL-PAIR-QUEUE.
This overrides the default ELEMENT-TYPE in the superclass."
  (with-slots ((element-type-x priority-queue::element-type))
      self
      (setf element-type-x 'critical-pair))
  self)

(defun make-critical-pairs (poly-list 
                            &optional (start 0)
                            &aux 
                              (s (1- (length poly-list))))
  "Create a list of critical pairs. The argument POLY-LIST is 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."
  (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))))

(defgeneric enqueue-critical-pairs (self pair-lst) 
  (:documentation "Place pairs in PAIR-LST on the queue SELF.")
  (:method ((self critical-pair-queue) pair-lst)
    "Enqueue into queue QUEUE the elements of the list PAIR-LST."
    (dolist (pair pair-lst self)
      (enqueue self pair))))

(defgeneric make-critical-pair-queue (object &optional poly-lst start)
  (:documentation "Creates a CRITICAL-PAIR-QUEUE from an object OBJECT.")
  (:method ((object selection-strategy) &optional (poly-lst nil) (start 0))
    "Creates a CRITICAL-PAIR-QUEUE from a selection strategy OBJECT."
    (with-slots (pair-key-fn pair-order-fn)
        object
      (let ((queue (make-instance 'critical-pair-queue
                                  :element-key #'(lambda (pair)
                                                   (funcall pair-key-fn 
                                                            (critical-pair-first pair)
                                                            (critical-pair-second pair)))
                                  :test pair-order-fn)))
           (enqueue-critical-pairs queue (make-critical-pairs poly-lst start))))))