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 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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23 | ;;
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24 | ;; Pair selection criteria
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25 | ;;
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26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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27 |
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28 | (defpackage "CRITERION"
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29 | (:use :monomial :pair-queue :grobner-debug)
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30 | (:export "CRITERION-1"
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31 | "CRITERION-2"
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32 | ))
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33 |
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34 | (in-package :criterion)
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35 |
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36 | (defun criterion-1 (pair)
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37 | "Returns T if the leading monomials of the two polynomials
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38 | in G pointed to by the integers in PAIR have disjoint (relatively prime)
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39 | monomials. This test is known as the first Buchberger criterion."
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40 | (declare (type pair pair))
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41 | (let ((f (pair-first pair))
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42 | (g (pair-second pair)))
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43 | (when (monom-rel-prime-p (poly-lm f) (poly-lm g))
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44 | (debug-cgb ":1")
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45 | (return-from 'criterion-1 t))))
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46 |
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47 | (defun criterion-2 (pair b-done partial-basis
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48 | &aux (f (pair-first pair)) (g (pair-second pair))
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49 | (place :before))
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50 | "Returns T if the leading monomial of some element P of
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51 | PARTIAL-BASIS divides the LCM of the leading monomials of the two
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52 | polynomials in the polynomial list PARTIAL-BASIS, and P paired with
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53 | each of the polynomials pointed to by the the PAIR has already been
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54 | treated, as indicated by the absence in the hash table B-done."
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55 | (declare (type pair pair) (type hash-table b-done)
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56 | (type poly f g))
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57 | ;; In the code below we assume that pairs are ordered as follows:
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58 | ;; if PAIR is (I J) then I appears before J in the PARTIAL-BASIS.
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59 | ;; We traverse the list PARTIAL-BASIS and keep track of where we
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60 | ;; are, so that we can produce the pairs in the correct order
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61 | ;; when we check whether they have been processed, i.e they
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62 | ;; appear in the hash table B-done
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63 | (dolist (h partial-basis nil)
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64 | (cond
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65 | ((eq h f)
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66 | #+grobner-check(assert (eq place :before))
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67 | (setf place :in-the-middle))
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68 | ((eq h g)
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69 | #+grobner-check(assert (eq place :in-the-middle))
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70 | (setf place :after))
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71 | ((and (monom-divides-monom-lcm-p (poly-lm h) (poly-lm f) (poly-lm g))
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72 | (gethash (case place
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73 | (:before (list h f))
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74 | ((:in-the-middle :after) (list f h)))
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75 | b-done)
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76 | (gethash (case place
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77 | ((:before :in-the-middle) (list h g))
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78 | (:after (list g h)))
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79 | b-done))
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80 | (debug-cgb ":2")
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81 | (return-from 'criterion-2 t)))))
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