source: branches/f4grobner/ring.lisp@ 2098

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

(in-package :ring)

(defgeneric parse (object)
  (:method ((object t)) object))

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

(defgeneric zerop (object)
  (:method ((self number)) (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)) (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))
    (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.")