1 | ;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
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2 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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3 | ;;;
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4 | ;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
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5 | ;;;
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6 | ;;; This program is free software; you can redistribute it and/or modify
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7 | ;;; it under the terms of the GNU General Public License as published by
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8 | ;;; the Free Software Foundation; either version 2 of the License, or
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9 | ;;; (at your option) any later version.
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10 | ;;;
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11 | ;;; This program is distributed in the hope that it will be useful,
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12 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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13 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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14 | ;;; GNU General Public License for more details.
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15 | ;;;
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16 | ;;; You should have received a copy of the GNU General Public License
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17 | ;;; along with this program; if not, write to the Free Software
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18 | ;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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19 | ;;;
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20 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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21 |
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22 | (in-package :grobner)
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23 |
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24 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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25 | ;;
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26 | ;; Pair queue implementation
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27 | ;;
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28 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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29 |
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30 | (defun sugar-pair-key (p q &aux (lcm (monom-lcm (poly-lm p) (poly-lm q)))
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31 | (d (monom-sugar lcm)))
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32 | "Returns list (S LCM-TOTAL-DEGREE) where S is the sugar of the S-polynomial of
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33 | polynomials P and Q, and LCM-TOTAL-DEGREE is the degree of is LCM(LM(P),LM(Q))."
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34 | (declare (type poly p q) (type monom lcm) (type fixnum d))
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35 | (cons (max
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36 | (+ (- d (monom-sugar (poly-lm p))) (poly-sugar p))
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37 | (+ (- d (monom-sugar (poly-lm q))) (poly-sugar q)))
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38 | lcm))
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39 |
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40 | (defstruct (pair
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41 | (:constructor make-pair (first second
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42 | &aux
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43 | (sugar (car (sugar-pair-key first second)))
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44 | (division-data nil))))
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45 | (first nil :type poly)
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46 | (second nil :type poly)
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47 | (sugar 0 :type fixnum)
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48 | (division-data nil :type list))
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49 |
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50 | ;;(defun pair-sugar (pair &aux (p (pair-first pair)) (q (pair-second pair)))
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51 | ;; (car (sugar-pair-key p q)))
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52 |
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53 | (defun sugar-order (x y)
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54 | "Pair order based on sugar, ties broken by normal strategy."
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55 | (declare (type cons x y))
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56 | (or (< (car x) (car y))
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57 | (and (= (car x) (car y))
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58 | (< (monom-total-degree (cdr x))
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59 | (monom-total-degree (cdr y))))))
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60 |
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61 | (defvar *pair-key-function* #'sugar-pair-key
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62 | "Function that, given two polynomials as argument, computed the key
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63 | in the pair queue.")
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64 |
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65 | (defvar *pair-order* #'sugar-order
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66 | "Function that orders the keys of pairs.")
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67 |
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68 | (defun make-pair-queue ()
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69 | "Constructs a priority queue for critical pairs."
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70 | (make-priority-queue
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71 | :element-type 'pair
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72 | :element-key #'(lambda (pair) (funcall *pair-key-function* (pair-first pair) (pair-second pair)))
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73 | :test *pair-order*))
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74 |
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75 | (defun pair-queue-initialize (pq f start
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76 | &aux
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77 | (s (1- (length f)))
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78 | (b (nconc (makelist (make-pair (elt f i) (elt f j))
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79 | (i 0 (1- start)) (j start s))
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80 | (makelist (make-pair (elt f i) (elt f j))
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81 | (i start (1- s)) (j (1+ i) s)))))
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82 | "Initializes the priority for critical pairs. F is the initial list of polynomials.
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83 | START is the first position beyond the elements which form a partial
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84 | grobner basis, i.e. satisfy the Buchberger criterion."
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85 | (declare (type priority-queue pq) (type fixnum start))
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86 | (dolist (pair b pq)
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87 | (priority-queue-insert pq pair)))
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88 |
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89 | (defun pair-queue-insert (b pair)
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90 | (priority-queue-insert b pair))
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91 |
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92 | (defun pair-queue-remove (b)
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93 | (priority-queue-remove b))
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94 |
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95 | (defun pair-queue-size (b)
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96 | (priority-queue-size b))
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97 |
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98 | (defun pair-queue-empty-p (b)
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99 | (priority-queue-empty-p b))
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