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source: branches/f4grobner/criterion.lisp@ 477

Last change on this file since 477 was 477, checked in by Marek Rychlik, 9 years ago

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1;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
24;; Pair selection criteria
25;;
26;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
27
28(defpackage "CRITERION"
29 (:use :monomial :pair-queue :grobner-debug)
30 (:export "CRITERION-1"
31 "CRITERION-2"))
32
33(in-package :criterion)
34
35(defun criterion-1 (pair)
36 "Returns T if the leading monomials of the two polynomials
37in G pointed to by the integers in PAIR have disjoint (relatively prime)
38monomials. This test is known as the first Buchberger criterion."
39 (declare (type pair pair))
40 (let ((f (pair-first pair))
41 (g (pair-second pair)))
42 (when (monom-rel-prime-p (poly-lm f) (poly-lm g))
43 (debug-cgb ":1")
44 (return-from criterion-1 t))))
45
46(defun criterion-2 (pair b-done partial-basis
47 &aux (f (pair-first pair)) (g (pair-second pair))
48 (place :before))
49 "Returns T if the leading monomial of some element P of
50PARTIAL-BASIS divides the LCM of the leading monomials of the two
51polynomials in the polynomial list PARTIAL-BASIS, and P paired with
52each of the polynomials pointed to by the the PAIR has already been
53treated, as indicated by the absence in the hash table B-done."
54 (declare (type pair pair) (type hash-table b-done)
55 (type poly f g))
56 ;; In the code below we assume that pairs are ordered as follows:
57 ;; if PAIR is (I J) then I appears before J in the PARTIAL-BASIS.
58 ;; We traverse the list PARTIAL-BASIS and keep track of where we
59 ;; are, so that we can produce the pairs in the correct order
60 ;; when we check whether they have been processed, i.e they
61 ;; appear in the hash table B-done
62 (dolist (h partial-basis nil)
63 (cond
64 ((eq h f)
65 #+grobner-check(assert (eq place :before))
66 (setf place :in-the-middle))
67 ((eq h g)
68 #+grobner-check(assert (eq place :in-the-middle))
69 (setf place :after))
70 ((and (monom-divides-monom-lcm-p (poly-lm h) (poly-lm f) (poly-lm g))
71 (gethash (case place
72 (:before (list h f))
73 ((:in-the-middle :after) (list f h)))
74 b-done)
75 (gethash (case place
76 ((:before :in-the-middle) (list h g))
77 (:after (list g h)))
78 b-done))
79 (debug-cgb ":2")
80 (return-from criterion-2 t)))))
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