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source: branches/f4grobner/criterion.lisp@ 224

Last change on this file since 224 was 192, checked in by Marek Rychlik, 9 years ago
File size: 3.3 KB
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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(in-package :ngrobner)
23
24;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
25;;
26;; Pair selection criteria
27;;
28;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
29
30(defun criterion-1 (pair)
31 "Returns T if the leading monomials of the two polynomials
32in G pointed to by the integers in PAIR have disjoint (relatively prime)
33monomials. This test is known as the first Buchberger criterion."
34 (declare (type pair pair))
35 (let ((f (pair-first pair))
36 (g (pair-second pair)))
37 (when (monom-rel-prime-p (poly-lm f) (poly-lm g))
38 (debug-cgb ":1")
39 (return-from criterion-1 t))))
40
41(defun criterion-2 (pair b-done partial-basis
42 &aux (f (pair-first pair)) (g (pair-second pair))
43 (place :before))
44 "Returns T if the leading monomial of some element P of
45PARTIAL-BASIS divides the LCM of the leading monomials of the two
46polynomials in the polynomial list PARTIAL-BASIS, and P paired with
47each of the polynomials pointed to by the the PAIR has already been
48treated, as indicated by the absence in the hash table B-done."
49 (declare (type pair pair) (type hash-table b-done)
50 (type poly f g))
51 ;; In the code below we assume that pairs are ordered as follows:
52 ;; if PAIR is (I J) then I appears before J in the PARTIAL-BASIS.
53 ;; We traverse the list PARTIAL-BASIS and keep track of where we
54 ;; are, so that we can produce the pairs in the correct order
55 ;; when we check whether they have been processed, i.e they
56 ;; appear in the hash table B-done
57 (dolist (h partial-basis nil)
58 (cond
59 ((eq h f)
60 #+grobner-check(assert (eq place :before))
61 (setf place :in-the-middle))
62 ((eq h g)
63 #+grobner-check(assert (eq place :in-the-middle))
64 (setf place :after))
65 ((and (monom-divides-monom-lcm-p (poly-lm h) (poly-lm f) (poly-lm g))
66 (gethash (case place
67 (:before (list h f))
68 ((:in-the-middle :after) (list f h)))
69 b-done)
70 (gethash (case place
71 ((:before :in-the-middle) (list h g))
72 (:after (list g h)))
73 b-done))
74 (debug-cgb ":2")
75 (return-from criterion-2 t)))))
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