;;; -*-  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.				 
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;;;  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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(defpackage "RING"
  (:use :cl)
  (:shadow "GCD" "LCM")
  (:export "PARSE"
	   "UNIT-FOR"
	   "ZEROP"
	   "ADD"
	   "SUB"
	   "UMINUS"
	   "MUL"
	   "DIV"
	   "LCM"
	   "EZGCD"
	   "GCD"
	   ))

(in-package :ring)

(defgeneric unit-for (object)
  (:method ((self number)) 1))

(defgeneric zerop (object)
  (:method ((self number)) (cl:zerop self)))

(defgeneric add (x y)
  (:method ((x number) (y number)) (+ x y))) 

(defgeneric mul (x y)
  (:method ((x number) (y number)) (* x y))) 

(defgeneric tensor-mul (x y))

(defgeneric div (x y)
  (:method ((x number) (y number)) (/ x y))) 

(defgeneric lcm (x y)
  (:method ((x integer) (y integer)) (cl:lcm x y))) 

(defgeneric ezgcd (x y)
  (:method ((x integer) (y integer)
	    &aux (c (gcd x y)))
    (values c (/ x c) (/ y c))))

(defgeneric gcd (x y)
  (:method ((x integer) (y integer))
    (cl:gcd x y)))

(defgeneric dimension (object))

(defgeneric total-degree (object &optional start end))

(defgeneric divides-p (object1 object2)
  (:method ((object1 integer) (object2 integer))
    (zerop (rem object2 object1)))
  (:documentation "Returns T if OBJECT1 divides OBJECT2"))

(defgeneric divides-lcm-p (object1 object2 object3)
  (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))

(defgeneric lcm-divides-lcm-p (object1 object2 object3 object4)
  (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))

(defmethod lcm-equal-lcm-p (object1 object2 object3 object4)
  "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise.")