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source: branches/f4grobner/ring.lisp@ 476

Last change on this file since 476 was 425, checked in by Marek Rychlik, 10 years ago

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File size: 2.9 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 "*EXPRESSION-RING*"
51 ))
52
53(in-package :ring)
54
55(defstruct (ring)
56 "Defines a RING structure, whose fields
57are common ring operations necessary to implement
58Groebner bases."
59 (parse #'identity :type function)
60 (unit #'identity :type function)
61 (zerop #'identity :type function)
62 (add #'identity :type function)
63 (sub #'identity :type function)
64 (uminus #'identity :type function)
65 (mul #'identity :type function)
66 (div #'identity :type function)
67 (lcm #'identity :type function)
68 (ezgcd #'identity :type function)
69 (gcd #'identity :type function))
70
71(defparameter *ring-of-integers*
72 (make-ring
73 :parse #'identity
74 :unit #'(lambda () 1)
75 :zerop #'zerop
76 :add #'+
77 :sub #'-
78 :uminus #'-
79 :mul #'*
80 :div #'/
81 :lcm #'lcm
82 :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
83 :gcd #'gcd)
84 "The ring of integers.")
85
86(defvar *expression-ring* *ring-of-integers*
87 "The ring of coefficients, over which all polynomials are assumed to
88 be defined.")
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