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source: branches/f4grobner/ring.lisp@ 1926

Last change on this file since 1926 was 1677, checked in by Marek Rychlik, 9 years ago

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File size: 2.7 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(defpackage "RING"
35 (:use :cl)
36 (:export "RING"
37 "RING-PARSE"
38 "RING-UNIT"
39 "RING-ZEROP"
40 "RING-ADD"
41 "RING-SUB"
42 "RING-UMINUS"
43 "RING-MUL"
44 "RING-DIV"
45 "RING-LCM"
46 "RING-EZGCD"
47 "RING-GCD"
48 "MAKE-RING"
49 "+RING-OF-INTEGERS+"
50 ))
51
52(in-package :ring)
53
54(defstruct (ring)
55 "Defines a RING structure, whose fields
56are common ring operations necessary to implement
57Groebner bases."
58 (parse #'identity :type function)
59 (unit #'identity :type function)
60 (zerop #'identity :type function)
61 (add #'identity :type function)
62 (sub #'identity :type function)
63 (uminus #'identity :type function)
64 (mul #'identity :type function)
65 (div #'identity :type function)
66 (lcm #'identity :type function)
67 (ezgcd #'identity :type function)
68 (gcd #'identity :type function))
69
70(defparameter +ring-of-integers+
71 (make-ring
72 :parse #'identity
73 :unit #'(lambda () 1)
74 :zerop #'zerop
75 :add #'+
76 :sub #'-
77 :uminus #'-
78 :mul #'*
79 :div #'/
80 :lcm #'lcm
81 :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
82 :gcd #'gcd
83 )
84 "The ring of integers.")
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