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source: branches/f4grobner/gb-postprocessing.lisp@ 300

Last change on this file since 300 was 192, checked in by Marek Rychlik, 9 years ago
File size: 2.7 KB
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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(in-package :ngrobner)
23
24;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
25;;
26;; Standard postprocessing of Grobner bases:
27;; - reduction
28;; - minimization
29;;
30;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
31
32(defun reduction (ring plist)
33 "Reduce a list of polynomials PLIST, so that non of the terms in any of
34the polynomials is divisible by a leading monomial of another
35polynomial. Return the reduced list."
36 (do ((q plist)
37 (found t))
38 ((not found)
39 (mapcar #'(lambda (x) (poly-primitive-part ring x)) q))
40 ;;Find p in Q such that p is reducible mod Q\{p}
41 (setf found nil)
42 (dolist (x q)
43 (let ((q1 (remove x q)))
44 (multiple-value-bind (h c div-count)
45 (normal-form ring x q1 nil #| not a top reduction! |# )
46 (declare (ignore c))
47 (unless (zerop div-count)
48 (setf found t q q1)
49 (unless (poly-zerop h)
50 (setf q (nconc q1 (list h))))
51 (return)))))))
52
53(defun minimization (p)
54 "Returns a sublist of the polynomial list P spanning the same
55monomial ideal as P but minimal, i.e. no leading monomial
56of a polynomial in the sublist divides the leading monomial
57of another polynomial."
58 (do ((q p)
59 (found t))
60 ((not found) q)
61 ;;Find p in Q such that lm(p) is in LM(Q\{p})
62 (setf found nil
63 q (dolist (x q q)
64 (let ((q1 (remove x q)))
65 (when (member-if #'(lambda (p) (monom-divides-p (poly-lm x) (poly-lm p))) q1)
66 (setf found t)
67 (return q1)))))))
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