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source: branches/f4grobner/criterion.lisp@ 75

Last change on this file since 75 was 74, checked in by Marek Rychlik, 9 years ago

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[74]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
[62]23;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
24;;
25;; Pair selection criteria
26;;
27;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
28
29(defun criterion-1 (pair)
30 "Returns T if the leading monomials of the two polynomials
31in G pointed to by the integers in PAIR have disjoint (relatively prime)
32monomials. This test is known as the first Buchberger criterion."
33 (declare (type pair pair))
34 (let ((f (pair-first pair))
35 (g (pair-second pair)))
36 (when (monom-rel-prime-p (poly-lm f) (poly-lm g))
37 (debug-cgb ":1")
38 (return-from criterion-1 t))))
39
40(defun criterion-2 (pair b-done partial-basis
41 &aux (f (pair-first pair)) (g (pair-second pair))
42 (place :before))
43 "Returns T if the leading monomial of some element P of
44PARTIAL-BASIS divides the LCM of the leading monomials of the two
45polynomials in the polynomial list PARTIAL-BASIS, and P paired with
46each of the polynomials pointed to by the the PAIR has already been
47treated, as indicated by the absence in the hash table B-done."
48 (declare (type pair pair) (type hash-table b-done)
49 (type poly f g))
50 ;; In the code below we assume that pairs are ordered as follows:
51 ;; if PAIR is (I J) then I appears before J in the PARTIAL-BASIS.
52 ;; We traverse the list PARTIAL-BASIS and keep track of where we
53 ;; are, so that we can produce the pairs in the correct order
54 ;; when we check whether they have been processed, i.e they
55 ;; appear in the hash table B-done
56 (dolist (h partial-basis nil)
57 (cond
58 ((eq h f)
59 #+grobner-check(assert (eq place :before))
60 (setf place :in-the-middle))
61 ((eq h g)
62 #+grobner-check(assert (eq place :in-the-middle))
63 (setf place :after))
64 ((and (monom-divides-monom-lcm-p (poly-lm h) (poly-lm f) (poly-lm g))
65 (gethash (case place
66 (:before (list h f))
67 ((:in-the-middle :after) (list f h)))
68 b-done)
69 (gethash (case place
70 ((:before :in-the-middle) (list h g))
71 (:after (list g h)))
72 b-done))
73 (debug-cgb ":2")
74 (return-from criterion-2 t)))))
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