;;; -*-  Mode: Lisp -*- 
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;;;                                                                              
;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>		 
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;;
;; Standard postprocessing of Grobner bases:
;; - reduction
;; - minimization
;;
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(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))))))