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source: branches/f4grobner/gb-postprocessing.lisp@ 1437

Last change on this file since 1437 was 1359, checked in by Marek Rychlik, 9 years ago

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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 :monomial :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 ((not found)
46 (mapcar #'(lambda (x) (poly-primitive-part ring x)) q))
47 ;;Find p in Q such that p is reducible mod Q\{p}
48 (setf found nil)
49 (dolist (x q)
50 (let ((q1 (remove x q)))
51 (multiple-value-bind (h c div-count)
52 (normal-form ring-and-order x q1 nil #| not a top reduction! |# )
53 (declare (ignore c))
54 (unless (zerop div-count)
55 (setf found t q q1)
56 (unless (poly-zerop h)
57 (setf q (nconc q1 (list h))))
58 (return)))))))
59
60(defun minimization (plist)
61 "Returns a sublist of the polynomial list P spanning the same
62monomial ideal as P but minimal, i.e. no leading monomial
63of a polynomial in the sublist divides the leading monomial
64of another polynomial."
65 (do ((q plist)
66 (found t))
67 ((not found) q)
68 ;;1) Find p in Q such that lm(p) is in LM(Q\{p})
69 ;;2) Set Q <- Q\{p}
70 (setf found nil)
71 ;; NOTE: Below we rely on the fact that NIL is not of type POLY
72 (let ((x (find-if
73 #'(lambda (y)
74 (find-if #'(lambda (p)
75 (monom-divides-p
76 (poly-lm p)
77 (poly-lm y)))
78 (remove y q)))
79 q)))
80 (when x
81 (setf found t
82 q (delete x q))))))
83
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