| 1 | ;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
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| 2 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 3 | ;;;
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| 4 | ;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
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| 5 | ;;;
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| 6 | ;;; This program is free software; you can redistribute it and/or modify
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| 7 | ;;; it under the terms of the GNU General Public License as published by
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| 8 | ;;; the Free Software Foundation; either version 2 of the License, or
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| 9 | ;;; (at your option) any later version.
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| 10 | ;;;
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| 11 | ;;; This program is distributed in the hope that it will be useful,
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| 12 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 13 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 14 | ;;; GNU General Public License for more details.
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| 15 | ;;;
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| 16 | ;;; You should have received a copy of the GNU General Public License
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| 17 | ;;; along with this program; if not, write to the Free Software
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| 18 | ;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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| 19 | ;;;
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| 20 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 21 |
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| 22 | (in-package :ngrobner)
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| 23 |
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| 24 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 25 | ;;
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| 26 | ;; Standard postprocessing of Grobner bases:
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| 27 | ;; - reduction
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| 28 | ;; - minimization
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| 29 | ;;
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| 30 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 31 |
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| 32 | (defun reduction (ring plist)
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| 33 | "Reduce a list of polynomials PLIST, so that non of the terms in any of
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| 34 | the polynomials is divisible by a leading monomial of another
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| 35 | polynomial. Return the reduced list."
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| 36 | (do ((q plist)
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| 37 | (found t))
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| 38 | ((not found)
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| 39 | (mapcar #'(lambda (x) (poly-primitive-part ring x)) q))
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| 40 | ;;Find p in Q such that p is reducible mod Q\{p}
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| 41 | (setf found nil)
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| 42 | (dolist (x q)
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| 43 | (let ((q1 (remove x q)))
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| 44 | (multiple-value-bind (h c div-count)
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| 45 | (normal-form ring x q1 nil #| not a top reduction! |# )
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| 46 | (declare (ignore c))
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| 47 | (unless (zerop div-count)
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| 48 | (setf found t q q1)
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| 49 | (unless (poly-zerop h)
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| 50 | (setf q (nconc q1 (list h))))
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| 51 | (return)))))))
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| 52 |
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| 53 | (defun minimization (p)
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| 54 | "Returns a sublist of the polynomial list P spanning the same
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| 55 | monomial ideal as P but minimal, i.e. no leading monomial
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| 56 | of a polynomial in the sublist divides the leading monomial
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| 57 | of another polynomial."
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| 58 | (do ((q p)
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| 59 | (found t))
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| 60 | ((not found) q)
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| 61 | ;;Find p in Q such that lm(p) is in LM(Q\{p})
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| 62 | (setf found nil
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| 63 | q (dolist (x q q)
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| 64 | (let ((q1 (remove x q)))
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| 65 | (when (member-if #'(lambda (p) (monom-divides-p (poly-lm x) (poly-lm p))) q1)
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| 66 | (setf found t)
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| 67 | (return q1)))))))
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