source: branches/f4grobner/gb-postprocessing.lisp

;;; -*-  Mode: Lisp -*- 
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;                                                                              
;;;  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
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defpackage "GB-POSTPROCESSING"
  (:use :cl :monom :division :polynomial :ring :ring-and-order)
  (:export "REDUCTION" "MINIMIZATION"))

(in-package :gb-postprocessing)

(defun reduction (ring-and-order plist
                  &aux
                    (ring (ro-ring ring-and-order)))
  "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."
  (declare (type ring-and-order ring-and-order))
  (do ((q plist)
       (found t)
       p q1)
      ((not found)
       (mapcar #'(lambda (x) (poly-primitive-part ring x)) q))
    ;; 1) Find p in Q such that p is reducible mod Q\{p}
    ;; 2) Replace p with remainder from division by Q\{p}, if
    ;;    non-zero, else set Q to Q\{p}
    (setf found nil)
    (dolist (x q)
      (setf q1 (remove x q))
      (unless q1 (return))
      (multiple-value-bind (h c div-count)
          (normal-form ring-and-order x q1 nil #| not a top reduction! |#)
        (declare (ignore c))
        (when (plusp div-count)
          (setf found t
                p h)
          (return))))
    (when found
      (if (poly-zerop p)
          (setf q q1)
          (setf q (cons p q1))))))


(defun minimization (plist)
  "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 plist)
       (found t))
      ((not found) q)
    ;;1) Find p in Q such that lm(p) is in LM(Q\{p})
    ;;2) Set Q <- Q\{p}
    (setf found nil)
    ;; NOTE: Below we rely on the fact that NIL is not of type POLY
    (let ((x (find-if 
              #'(lambda (y) 
                  (find-if #'(lambda (p) 
                               (monom-divides-p 
                                (poly-lm p) 
                                (poly-lm y)))
                           (remove y q)))
              q)))
      (when x
        (setf found t
              q (delete x q))))))