source: branches/f4grobner/ring.lisp@ 2063

;;; -*-  mode: lisp; package: maxima; syntax: common-lisp; base: 10 -*- 
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;;                                                                              
;;;  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.                                
;;;                                                                              
;;;  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.  
;;;                                                                              
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; coefficient ring operations
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;
;; 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.
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

(defpackage "RING"
  (:use :cl)
  (:export "RING"
           "RING-PARSE"
           "RING-UNIT"
           "RING-ZEROP"
           "RING-ADD"
           "RING-SUB"
           "RING-UMINUS"
           "RING-MUL"
           "RING-DIV"
           "RING-LCM"
           "RING-EZGCD"
           "RING-GCD"
           "MAKE-RING"
           "+RING-OF-INTEGERS+"
           ))

(in-package :ring)

#|

(defstruct (ring)
  "Defines a RING structure, whose fields
are common ring operations necessary to implement
Groebner bases."
  (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.")
|#

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

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

(defgeneric ring-zerop (object)
  (:method ((self number)) (zerop self)))

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

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

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

(defgeneric ring-lcm (x y)
  (:method ((x integer) (y integer)) (lcm x y))) 

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

(defgeneric ring-gcd (x y)
  (:method ((x integer) (y integer))
    (gcd x y)))

(defgeneric ring-dimension (object))

(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."))