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source: branches/f4grobner/gebauer-moeller.lisp@ 194

Last change on this file since 194 was 192, checked in by Marek Rychlik, 9 years ago
File size: 4.9 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;; An implementation of the algorithm of Gebauer and Moeller, as
27;; described in the book of Becker-Weispfenning, p. 232
28;;
29;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
30
31(defun gebauer-moeller (ring f start &optional (top-reduction-only $poly_top_reduction_only))
32 "Compute Grobner basis by using the algorithm of Gebauer and
33Moeller. This algorithm is described as BUCHBERGERNEW2 in the book by
34Becker-Weispfenning entitled ``Grobner Bases''. This function assumes
35that all polynomials in F are non-zero."
36 (declare (ignore top-reduction-only)
37 (type fixnum start))
38 (cond
39 ((endp f) (return-from gebauer-moeller nil))
40 ((endp (cdr f))
41 (return-from gebauer-moeller (list (poly-primitive-part ring (car f))))))
42 (debug-cgb "~&GROBNER BASIS - GEBAUER MOELLER ALGORITHM")
43 (when (plusp start) (debug-cgb "~&INCREMENTAL:~d done" start))
44 #+grobner-check (when (plusp start)
45 (grobner-test ring (subseq f 0 start) (subseq f 0 start)))
46 (let ((b (make-pair-queue))
47 (g (subseq f 0 start))
48 (f1 (subseq f start)))
49 (do () ((endp f1))
50 (multiple-value-setq (g b)
51 (gebauer-moeller-update g b (poly-primitive-part ring (pop f1)))))
52 (do () ((pair-queue-empty-p b))
53 (let* ((pair (pair-queue-remove b))
54 (g1 (pair-first pair))
55 (g2 (pair-second pair))
56 (h (normal-form ring (spoly ring g1 g2)
57 g
58 nil #| Always fully reduce! |#
59 )))
60 (unless (poly-zerop h)
61 (setf h (poly-primitive-part ring h))
62 (multiple-value-setq (g b)
63 (gebauer-moeller-update g b h))
64 (debug-cgb "~&Sugar: ~d Polynomials: ~d; Pairs left: ~d~%"
65 (pair-sugar pair) (length g) (pair-queue-size b))
66 )))
67 #+grobner-check(grobner-test ring g f)
68 (debug-cgb "~&GROBNER END")
69 g))
70
71(defun gebauer-moeller-update (g b h
72 &aux
73 c d e
74 (b-new (make-pair-queue))
75 g-new)
76 "An implementation of the auxillary UPDATE algorithm used by the
77Gebauer-Moeller algorithm. G is a list of polynomials, B is a list of
78critical pairs and H is a new polynomial which possibly will be added
79to G. The naming conventions used are very close to the one used in
80the book of Becker-Weispfenning."
81 (declare
82 #+allegro (dynamic-extent b)
83 (type poly h)
84 (type priority-queue b))
85 (setf c g d nil)
86 (do () ((endp c))
87 (let ((g1 (pop c)))
88 (declare (type poly g1))
89 (when (or (monom-rel-prime-p (poly-lm h) (poly-lm g1))
90 (and
91 (notany #'(lambda (g2) (monom-lcm-divides-monom-lcm-p
92 (poly-lm h) (poly-lm g2)
93 (poly-lm h) (poly-lm g1)))
94 c)
95 (notany #'(lambda (g2) (monom-lcm-divides-monom-lcm-p
96 (poly-lm h) (poly-lm g2)
97 (poly-lm h) (poly-lm g1)))
98 d)))
99 (push g1 d))))
100 (setf e nil)
101 (do () ((endp d))
102 (let ((g1 (pop d)))
103 (declare (type poly g1))
104 (unless (monom-rel-prime-p (poly-lm h) (poly-lm g1))
105 (push g1 e))))
106 (do () ((pair-queue-empty-p b))
107 (let* ((pair (pair-queue-remove b))
108 (g1 (pair-first pair))
109 (g2 (pair-second pair)))
110 (declare (type pair pair)
111 (type poly g1 g2))
112 (when (or (not (monom-divides-monom-lcm-p
113 (poly-lm h)
114 (poly-lm g1) (poly-lm g2)))
115 (monom-lcm-equal-monom-lcm-p
116 (poly-lm g1) (poly-lm h)
117 (poly-lm g1) (poly-lm g2))
118 (monom-lcm-equal-monom-lcm-p
119 (poly-lm h) (poly-lm g2)
120 (poly-lm g1) (poly-lm g2)))
121 (pair-queue-insert b-new (make-pair g1 g2)))))
122 (dolist (g3 e)
123 (pair-queue-insert b-new (make-pair h g3)))
124 (setf g-new nil)
125 (do () ((endp g))
126 (let ((g1 (pop g)))
127 (declare (type poly g1))
128 (unless (monom-divides-p (poly-lm h) (poly-lm g1))
129 (push g1 g-new))))
130 (push h g-new)
131 (values g-new b-new))
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