source: branches/f4grobner/gb-postprocessing.lisp@ 2217

;;; -*-  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))))))