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source: branches/f4grobner/buchberger.lisp@ 521

Last change on this file since 521 was 493, 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 :ring :polynomial :order :grobner-debug :division :criterion :pair-queue :priority-queue)
24 (:export "BUCHBERGER" "PARALLEL-BUCHBERGER"))
25
26(in-package :buchberger)
27
28;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
29;;
30;; Buchberger Algorithm Implementation
31;;
32;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
33
34(defun buchberger (ring f start &optional (top-reduction-only $poly_top_reduction_only))
35 "An implementation of the Buchberger algorithm. Return Grobner basis
36of the ideal generated by the polynomial list F. Polynomials 0 to
37START-1 are assumed to be a Grobner basis already, so that certain
38critical pairs will not be examined. If TOP-REDUCTION-ONLY set, top
39reduction will be preformed. This function assumes that all polynomials
40in F are non-zero."
41 (declare (type fixnum start))
42 (when (endp f) (return-from buchberger f)) ;cut startup costs
43 (debug-cgb "~&GROBNER BASIS - BUCHBERGER ALGORITHM")
44 (when (plusp start) (debug-cgb "~&INCREMENTAL:~d done" start))
45 #+grobner-check (when (plusp start)
46 (grobner-test ring (subseq f 0 start) (subseq f 0 start)))
47 ;;Initialize critical pairs
48 (let ((b (pair-queue-initialize (make-pair-queue)
49 f start))
50 (b-done (make-hash-table :test #'equal)))
51 (declare (type priority-queue b) (type hash-table b-done))
52 (dotimes (i (1- start))
53 (do ((j (1+ i) (1+ j))) ((>= j start))
54 (setf (gethash (list (elt f i) (elt f j)) b-done) t)))
55 (do ()
56 ((pair-queue-empty-p b)
57 #+grobner-check(grobner-test ring f f)
58 (debug-cgb "~&GROBNER END")
59 f)
60 (let ((pair (pair-queue-remove b)))
61 (declare (type pair pair))
62 (cond
63 ((criterion-1 pair) nil)
64 ((criterion-2 pair b-done f) nil)
65 (t
66 (let ((sp (normal-form ring (spoly ring (pair-first pair)
67 (pair-second pair))
68 f top-reduction-only)))
69 (declare (type poly sp))
70 (cond
71 ((poly-zerop sp)
72 nil)
73 (t
74 (setf sp (poly-primitive-part ring sp)
75 f (nconc f (list sp)))
76 ;; Add new critical pairs
77 (dolist (h f)
78 (pair-queue-insert b (make-pair h sp)))
79 (debug-cgb "~&Sugar: ~d Polynomials: ~d; Pairs left: ~d; Pairs done: ~d;"
80 (pair-sugar pair) (length f) (pair-queue-size b)
81 (hash-table-count b-done)))))))
82 (setf (gethash (list (pair-first pair) (pair-second pair)) b-done)
83 t)))))
84
85(defun parallel-buchberger (ring f start &optional (top-reduction-only $poly_top_reduction_only))
86 "An implementation of the Buchberger algorithm. Return Grobner basis
87of the ideal generated by the polynomial list F. Polynomials 0 to
88START-1 are assumed to be a Grobner basis already, so that certain
89critical pairs will not be examined. If TOP-REDUCTION-ONLY set, top
90reduction will be preformed."
91 (declare (ignore top-reduction-only)
92 (type fixnum start))
93 (when (endp f) (return-from parallel-buchberger f)) ;cut startup costs
94 (debug-cgb "~&GROBNER BASIS - PARALLEL-BUCHBERGER ALGORITHM")
95 (when (plusp start) (debug-cgb "~&INCREMENTAL:~d done" start))
96 #+grobner-check (when (plusp start)
97 (grobner-test ring (subseq f 0 start) (subseq f 0 start)))
98 ;;Initialize critical pairs
99 (let ((b (pair-queue-initialize (make-pair-queue) f start))
100 (b-done (make-hash-table :test #'equal)))
101 (declare (type priority-queue b)
102 (type hash-table b-done))
103 (dotimes (i (1- start))
104 (do ((j (1+ i) (1+ j))) ((>= j start))
105 (declare (type fixnum j))
106 (setf (gethash (list (elt f i) (elt f j)) b-done) t)))
107 (do ()
108 ((pair-queue-empty-p b)
109 #+grobner-check(grobner-test ring f f)
110 (debug-cgb "~&GROBNER END")
111 f)
112 (let ((pair (pair-queue-remove b)))
113 (when (null (pair-division-data pair))
114 (setf (pair-division-data pair) (list (spoly ring
115 (pair-first pair)
116 (pair-second pair))
117 (make-poly-zero)
118 (funcall (ring-unit ring))
119 0)))
120 (cond
121 ((criterion-1 pair) nil)
122 ((criterion-2 pair b-done f) nil)
123 (t
124 (let* ((dd (pair-division-data pair))
125 (p (first dd))
126 (sp (second dd))
127 (c (third dd))
128 (division-count (fourth dd)))
129 (cond
130 ((poly-zerop p) ;normal form completed
131 (debug-cgb "~&~3T~d reduction~:p" division-count)
132 (cond
133 ((poly-zerop sp)
134 (debug-cgb " ---> 0")
135 nil)
136 (t
137 (setf sp (poly-nreverse sp)
138 sp (poly-primitive-part ring sp)
139 f (nconc f (list sp)))
140 ;; Add new critical pairs
141 (dolist (h f)
142 (pair-queue-insert b (make-pair h sp)))
143 (debug-cgb "~&Sugar: ~d Polynomials: ~d; Pairs left: ~d; Pairs done: ~d;"
144 (pair-sugar pair) (length f) (pair-queue-size b)
145 (hash-table-count b-done))))
146 (setf (gethash (list (pair-first pair) (pair-second pair))
147 b-done) t))
148 (t ;normal form not complete
149 (do ()
150 ((cond
151 ((> (poly-sugar sp) (pair-sugar pair))
152 (debug-cgb "(~a)?" (poly-sugar sp))
153 t)
154 ((poly-zerop p)
155 (debug-cgb ".")
156 t)
157 (t nil))
158 (setf (first dd) p
159 (second dd) sp
160 (third dd) c
161 (fourth dd) division-count
162 (pair-sugar pair) (poly-sugar sp))
163 (pair-queue-insert b pair))
164 (multiple-value-setq (p sp c division-count)
165 (normal-form-step ring f p sp c division-count))))))))))))
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