source: branches/f4grobner/ring.lisp@ 448

;;; -*-  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        
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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 "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*"
           "*EXPRESSION-RING*"
           ))

(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.")

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