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source: branches/f4grobner/ring.lisp@ 410

Last change on this file since 410 was 409, checked in by Marek Rychlik, 9 years ago

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1;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
24;; Coefficient ring operations
25;;
26;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
27;;
28;; These are ALL operations that are performed on the coefficients by
29;; the package, and thus the coefficient ring can be changed by merely
30;; redefining these operations.
31;;
32;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
33
34(defpackage "RING"
35 (:use :cl)
36 (:export "MAKE-RING"
37 "*RING-OF-INTEGERS*"
38 "*EXPRESSION-RING*"
39 ))
40
41(defstruct (ring)
42 "Defines a RING structure, whose fields
43are common ring operations necessary to implement
44Groebner bases."
45 (parse #'identity :type function)
46 (unit #'identity :type function)
47 (zerop #'identity :type function)
48 (add #'identity :type function)
49 (sub #'identity :type function)
50 (uminus #'identity :type function)
51 (mul #'identity :type function)
52 (div #'identity :type function)
53 (lcm #'identity :type function)
54 (ezgcd #'identity :type function)
55 (gcd #'identity :type function))
56
57(defparameter *ring-of-integers*
58 (make-ring
59 :parse #'identity
60 :unit #'(lambda () 1)
61 :zerop #'zerop
62 :add #'+
63 :sub #'-
64 :uminus #'-
65 :mul #'*
66 :div #'/
67 :lcm #'lcm
68 :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
69 :gcd #'gcd)
70 "The ring of integers.")
71
72(defvar *expression-ring* *ring-of-integers*
73 "The ring of coefficients, over which all polynomials are assumed to
74 be defined.")
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