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source: branches/f4grobner/buchberger.lisp@ 485

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