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source: branches/f4grobner/ring.lisp@ 404

Last change on this file since 404 was 404, checked in by Marek Rychlik, 9 years ago

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File size: 2.5 KB
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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(defstruct (ring)
35 (parse #'identity :type function)
36 (unit #'identity :type function)
37 (zerop #'identity :type function)
38 (add #'identity :type function)
39 (sub #'identity :type function)
40 (uminus #'identity :type function)
41 (mul #'identity :type function)
42 (div #'identity :type function)
43 (lcm #'identity :type function)
44 (ezgcd #'identity :type function)
45 (gcd #'identity :type function))
46
47(defparameter *ring-of-integers*
48 (make-ring
49 :parse #'identity
50 :unit #'(lambda () 1)
51 :zerop #'zerop
52 :add #'+
53 :sub #'-
54 :uminus #'-
55 :mul #'*
56 :div #'/
57 :lcm #'lcm
58 :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
59 :gcd #'gcd)
60 "The ring of integers.")
61
62(defvar *expression-ring* *ring-of-integers*
63 "The ring of coefficients, over which all polynomials are assumed to
64 be defined.")
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