;;; -*-  Mode: Lisp -*- 
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;;;                                                                              
;;;  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	 
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;;;  (at your option) any later version.					 
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;;;  GNU General Public License for more details.				 
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;;;  along with this program; if not, write to the Free Software 		 
;;;  Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.	 
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;;
;; Standard postprocessing of Grobner bases:
;; - reduction
;; - minimization
;;
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(defpackage "GB-POSTPROCESSING"
  (:use :cl :monomial :division :polynomial :ring-and-order)
  (:export "REDUCTION" "MINIMIZATION"))

(in-package :gb-postprocessing)

(defun reduction (ring-and-order 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."
  (declare (type ring-and-order ring-and-order))
  (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)))))))