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source: branches/f4grobner/buchberger.lisp@ 2125

Last change on this file since 2125 was 1958, checked in by Marek Rychlik, 10 years ago

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File size: 6.7 KB
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1;;; -*- Mode: Lisp -*-
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(defpackage "BUCHBERGER"
23 (:use :cl :grobner-debug
24 :ring :polynomial :order :ring-and-order :division
25 :criterion :pair-queue :priority-queue
26 )
27 (:export "BUCHBERGER" "PARALLEL-BUCHBERGER"))
28
29(in-package :buchberger)
30
31;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
32;;
33;; Buchberger Algorithm Implementation
34;;
35;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
36
37(defun buchberger (ring-and-order f
38 &optional
39 (start 0)
40 (top-reduction-only $poly_top_reduction_only)
41 &aux
42 (ring (ro-ring ring-and-order)))
43 "An implementation of the Buchberger algorithm. Return Grobner basis
44of the ideal generated by the polynomial list F. Polynomials 0 to
45START-1 are assumed to be a Grobner basis already, so that certain
46critical pairs will not be examined. If TOP-REDUCTION-ONLY set, top
47reduction will be preformed. This function assumes that all polynomials
48in F are non-zero."
49 (declare (type ring-and-order ring-and-order) (type fixnum start))
50 (when (endp f) (return-from buchberger f)) ;cut startup costs
51 (debug-cgb "~&GROBNER BASIS - BUCHBERGER ALGORITHM")
52 (when (plusp start) (debug-cgb "~&INCREMENTAL:~d done" start))
53 #+grobner-check (when (plusp start)
54 (grobner-test ring-and-order (subseq f 0 start) (subseq f 0 start)))
55 ;;Initialize critical pairs
56 (let ((b (pair-queue-initialize (make-pair-queue)
57 f start))
58 (b-done (make-hash-table :test #'equal)))
59 (declare (type priority-queue b) (type hash-table b-done))
60 (dotimes (i (1- start))
61 (do ((j (1+ i) (1+ j))) ((>= j start))
62 (setf (gethash (list (elt f i) (elt f j)) b-done) t)))
63 (do ()
64 ((pair-queue-empty-p b)
65 #+grobner-check(grobner-test ring-and-order f f)
66 (debug-cgb "~&GROBNER END")
67 f)
68 (let ((pair (pair-queue-remove b)))
69 (declare (type pair pair))
70 (cond
71 ((criterion-1 pair) nil)
72 ((criterion-2 pair b-done f) nil)
73 (t
74 (let ((sp (normal-form ring-and-order
75 (spoly ring-and-order
76 (pair-first pair)
77 (pair-second pair))
78 f top-reduction-only)))
79 (declare (type poly sp))
80 (cond
81 ((poly-zerop sp)
82 nil)
83 (t
84 (setf sp (poly-primitive-part ring sp)
85 f (nconc f (list sp)))
86 ;; Add new critical pairs
87 (dolist (h f)
88 (pair-queue-insert b (make-pair h sp)))
89 (debug-cgb "~&Sugar: ~d Polynomials: ~d; Pairs left: ~d; Pairs done: ~d;"
90 (pair-sugar pair) (length f) (pair-queue-size b)
91 (hash-table-count b-done)))))))
92 (setf (gethash (list (pair-first pair) (pair-second pair)) b-done)
93 t)))))
94
95(defun parallel-buchberger (ring-and-order f
96 &optional
97 (start 0)
98 (top-reduction-only $poly_top_reduction_only)
99 &aux
100 (ring (ro-ring ring-and-order)))
101 "An implementation of the Buchberger algorithm. Return Grobner basis
102of the ideal generated by the polynomial list F. Polynomials 0 to
103START-1 are assumed to be a Grobner basis already, so that certain
104critical pairs will not be examined. If TOP-REDUCTION-ONLY set, top
105reduction will be preformed."
106 (declare (type ring-and-order ring-and-order)
107 (ignore top-reduction-only)
108 (type fixnum start))
109 (when (endp f) (return-from parallel-buchberger f)) ;cut startup costs
110 (debug-cgb "~&GROBNER BASIS - PARALLEL-BUCHBERGER ALGORITHM")
111 (when (plusp start) (debug-cgb "~&INCREMENTAL:~d done" start))
112 #+grobner-check (when (plusp start)
113 (grobner-test ring-and-order (subseq f 0 start) (subseq f 0 start)))
114 ;;Initialize critical pairs
115 (let ((b (pair-queue-initialize (make-pair-queue) f start))
116 (b-done (make-hash-table :test #'equal)))
117 (declare (type priority-queue b)
118 (type hash-table b-done))
119 (dotimes (i (1- start))
120 (do ((j (1+ i) (1+ j))) ((>= j start))
121 (declare (type fixnum j))
122 (setf (gethash (list (elt f i) (elt f j)) b-done) t)))
123 (do ()
124 ((pair-queue-empty-p b)
125 #+grobner-check(grobner-test ring-and-order f f)
126 (debug-cgb "~&GROBNER END")
127 f)
128 (let ((pair (pair-queue-remove b)))
129 (when (null (pair-division-data pair))
130 (setf (pair-division-data pair) (list (spoly ring-and-order
131 (pair-first pair)
132 (pair-second pair))
133 (make-poly-zero)
134 (funcall (ring-unit ring))
135 0)))
136 (cond
137 ((criterion-1 pair) nil)
138 ((criterion-2 pair b-done f) nil)
139 (t
140 (let* ((dd (pair-division-data pair))
141 (p (first dd))
142 (sp (second dd))
143 (c (third dd))
144 (division-count (fourth dd)))
145 (cond
146 ((poly-zerop p) ;normal form completed
147 (debug-cgb "~&~3T~d reduction~:p" division-count)
148 (cond
149 ((poly-zerop sp)
150 (debug-cgb " ---> 0")
151 nil)
152 (t
153 (setf sp (poly-nreverse sp)
154 sp (poly-primitive-part ring sp)
155 f (nconc f (list sp)))
156 ;; Add new critical pairs
157 (dolist (h f)
158 (pair-queue-insert b (make-pair h sp)))
159 (debug-cgb "~&Sugar: ~d Polynomials: ~d; Pairs left: ~d; Pairs done: ~d;"
160 (pair-sugar pair) (length f) (pair-queue-size b)
161 (hash-table-count b-done))))
162 (setf (gethash (list (pair-first pair) (pair-second pair))
163 b-done) t))
164 (t ;normal form not complete
165 (do ()
166 ((cond
167 ((> (poly-sugar sp) (pair-sugar pair))
168 (debug-cgb "(~a)?" (poly-sugar sp))
169 t)
170 ((poly-zerop p)
171 (debug-cgb ".")
172 t)
173 (t nil))
174 (setf (first dd) p
175 (second dd) sp
176 (third dd) c
177 (fourth dd) division-count
178 (pair-sugar pair) (poly-sugar sp))
179 (pair-queue-insert b pair))
180 (multiple-value-setq (p sp c division-count)
181 (normal-form-step ring-and-order f p sp c division-count))))))))))))
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