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source: branches/f4grobner/buchberger.lisp@ 1307

Last change on this file since 1307 was 1302, checked in by Marek Rychlik, 10 years ago

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