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source: branches/f4grobner/gb-postprocessing.lisp@ 3248

Last change on this file since 3248 was 1615, checked in by Marek Rychlik, 9 years ago

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File size: 3.2 KB
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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;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
24;; Standard postprocessing of Grobner bases:
25;; - reduction
26;; - minimization
27;;
28;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
29
30(defpackage "GB-POSTPROCESSING"
31 (:use :cl :monom :division :polynomial :ring :ring-and-order)
32 (:export "REDUCTION" "MINIMIZATION"))
33
34(in-package :gb-postprocessing)
35
36(defun reduction (ring-and-order plist
37 &aux
38 (ring (ro-ring ring-and-order)))
39 "Reduce a list of polynomials PLIST, so that non of the terms in any of
40the polynomials is divisible by a leading monomial of another
41polynomial. Return the reduced list."
42 (declare (type ring-and-order ring-and-order))
43 (do ((q plist)
44 (found t)
45 p q1)
46 ((not found)
47 (mapcar #'(lambda (x) (poly-primitive-part ring x)) q))
48 ;; 1) Find p in Q such that p is reducible mod Q\{p}
49 ;; 2) Replace p with remainder from division by Q\{p}, if
50 ;; non-zero, else set Q to Q\{p}
51 (setf found nil)
52 (dolist (x q)
53 (setf q1 (remove x q))
54 (unless q1 (return))
55 (multiple-value-bind (h c div-count)
56 (normal-form ring-and-order x q1 nil #| not a top reduction! |#)
57 (declare (ignore c))
58 (when (plusp div-count)
59 (setf found t
60 p h)
61 (return))))
62 (when found
63 (if (poly-zerop p)
64 (setf q q1)
65 (setf q (cons p q1))))))
66
67
68(defun minimization (plist)
69 "Returns a sublist of the polynomial list P spanning the same
70monomial ideal as P but minimal, i.e. no leading monomial
71of a polynomial in the sublist divides the leading monomial
72of another polynomial."
73 (do ((q plist)
74 (found t))
75 ((not found) q)
76 ;;1) Find p in Q such that lm(p) is in LM(Q\{p})
77 ;;2) Set Q <- Q\{p}
78 (setf found nil)
79 ;; NOTE: Below we rely on the fact that NIL is not of type POLY
80 (let ((x (find-if
81 #'(lambda (y)
82 (find-if #'(lambda (p)
83 (monom-divides-p
84 (poly-lm p)
85 (poly-lm y)))
86 (remove y q)))
87 q)))
88 (when x
89 (setf found t
90 q (delete x q))))))
91
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