;;; -*-  Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*- 
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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	 
;;;  the Free Software Foundation; either version 2 of the License, or		 
;;;  (at your option) any later version.					 
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;;;  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.	 
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;;
;; Coefficient ring operations
;;
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;;
;; These are ALL operations that are performed on the coefficients by
;; the package, and thus the coefficient ring can be changed by merely
;; redefining these operations.
;;
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(defstruct (ring)
  (parse #'identity :type function)
  (unit #'identity :type function)
  (zerop #'identity :type function)
  (add #'identity :type function)
  (sub #'identity :type function)
  (uminus #'identity :type function)
  (mul #'identity :type function)
  (div #'identity :type function)
  (lcm #'identity :type function)
  (ezgcd #'identity :type function)
  (gcd #'identity :type function))

(defparameter *ring-of-integers*
    (make-ring
     :parse #'identity
     :unit #'(lambda () 1)
     :zerop #'zerop
     :add #'+
     :sub #'-
     :uminus #'-
     :mul #'*
     :div #'/
     :lcm #'lcm
     :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
     :gcd #'gcd)
  "The ring of integers.")

(defvar *expression-ring* *ring-of-integers*
  "The ring of coefficients, over which all polynomials are assumed to
  be defined.")