source: branches/f4grobner/gb-postprocessing.lisp@ 134

;;; -*-  Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- 
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;                                                                              
;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
;;;                                                                              
;;;  This program is free software; you can redistribute it and/or modify        
;;;  it under the terms of the GNU General Public License as published by        
;;;  the Free Software Foundation; either version 2 of the License, or           
;;;  (at your option) any later version.                                         
;;;                                                                              
;;;  This program is distributed in the hope that it will be useful,             
;;;  but WITHOUT ANY WARRANTY; without even the implied warranty of              
;;;  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the               
;;;  GNU General Public License for more details.                                
;;;                                                                              
;;;  You should have received a copy of the GNU General Public License           
;;;  along with this program; if not, write to the Free Software                 
;;;  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.  
;;;                                                                              
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;


;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; Standard postprocessing of Grobner bases:
;; - reduction
;; - minimization
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defun reduction (ring plist)
  "Reduce a list of polynomials PLIST, so that non of the terms in any of
the polynomials is divisible by a leading monomial of another
polynomial.  Return the reduced list."
  (do ((q plist)
       (found t))
      ((not found)
       (mapcar #'(lambda (x) (poly-primitive-part ring x)) q))
    ;;Find p in Q such that p is reducible mod Q\{p}
    (setf found nil)
    (dolist (x q)
      (let ((q1 (remove x q)))
        (multiple-value-bind (h c div-count)
            (normal-form ring x q1 nil #| not a top reduction! |# )
          (declare (ignore c))
          (unless (zerop div-count)
            (setf found t q q1)
            (unless (poly-zerop h)
              (setf q (nconc q1 (list h))))
            (return)))))))

(defun minimization (p)
  "Returns a sublist of the polynomial list P spanning the same
monomial ideal as P but minimal, i.e. no leading monomial
of a polynomial in the sublist divides the leading monomial
of another polynomial."
  (do ((q p)
       (found t))
      ((not found) q)
    ;;Find p in Q such that lm(p) is in LM(Q\{p})
    (setf found nil
          q (dolist (x q q)
              (let ((q1 (remove x q)))
                (when (member-if #'(lambda (p) (monom-divides-p (poly-lm x) (poly-lm p))) q1)
                  (setf found t)
                  (return q1)))))))