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source: branches/f4grobner/buchberger.lisp@ 1110

Last change on this file since 1110 was 580, checked in by Marek Rychlik, 10 years ago

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