close Warning: Can't synchronize with repository "(default)" (The repository directory has changed, you should resynchronize the repository with: trac-admin $ENV repository resync '(default)'). Look in the Trac log for more information.

source: branches/f4grobner/ring.lisp@ 4352

Last change on this file since 4352 was 4352, checked in by Marek Rychlik, 8 years ago

* empty log message *

File size: 3.8 KB
Line 
1;;; -*- Mode: Lisp -*-
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(defpackage "RING"
23 (:use :cl :copy)
24 (:export "RING"
25 "FIELD"
26 "ADD-TO"
27 "SUBTRACT-FROM"
28 "MULTIPLY-BY"
29 "DIVIDE-BY"
30 "UNARY-MINUS"
31 "UNARY-INVERSE"
32 "UNIVERSAL-GCD"
33 "UNIVERSAL-EZGCD"
34 "UNIVERSAL-EQUALP"
35 "UNIVERSAL-ZEROP"
36 "MAKE-ZERO-FOR"
37 "MAKE-UNIT-FOR"
38 "->SEXP"
39 "RATIONAL-FIELD"
40 "RATIONAL-FIELD-VALUE"
41 "MAKE-ZERO-FOR"
42 "MAKE-UNIT-FOR"
43 "INTEGER-RING"
44 "INTEGER-RING-VALUE"
45 )
46 (:documentation "Defines an abstract ring class and ring operations.")
47 )
48
49(in-package "RING")
50
51(defclass ring () () (:documentation "An abstract ring."))
52(defclass field (ring) () (:documentation "An abstract ring."))
53
54(defgeneric multiply-by (self other)
55 (:documentation "Multiply SELF by OTHER."))
56
57(defgeneric divide-by (self other)
58 (:documentation "Divide SELF by OTHER."))
59
60(defgeneric add-to (self other)
61 (:documentation "Add OTHER to SELF."))
62
63(defgeneric subtract-from (self other)
64 (:documentation "Subtract OTHER from SELF."))
65
66(defgeneric unary-minus (self)
67 (:documentation "Changes SELF to its negative."))
68
69(defgeneric unary-inverse (self)
70 (:documentation "Changes SELF to the unary inverse of SELF."))
71
72(defgeneric universal-gcd (object other)
73 (:documentation "Returns GCD(OBJECT, OTHER)"))
74
75(defgeneric universal-ezgcd (x y)
76 (:documentation "Solves the diophantine system: X=C*X1, Y=C*X2,
77C=GCD(X,Y). It returns three values: C, X1 and Y1. The result may be obtained by
78the Euclidean algorithm."))
79
80(defgeneric universal-equalp (self other)
81 (:documentation "Return T if objects SELF and OTHER are equal, NIL otherwise.")
82 (:method ((object1 cons) (object2 cons)) (every #'universal-equalp object1 object2))
83 (:method ((self number) (other number)) (= self other)))
84
85(defgeneric universal-zerop (self)
86 (:documentation "Return T if SELF is a zero in the ring it belongs to."))
87
88(defgeneric ->sexp (self &optional vars)
89 (:documentation "Convert SELF to an S-expression."))
90
91(defgeneric make-zero-for (self)
92 (:documentation "Create a zero in the ring of SELF. A fresh instance
93should be returned upon every call."))
94
95(defgeneric make-unit-for (self)
96 (:documentation "Create a unit in the ring of SELF. A fresh instance
97should be returned upon every call."))
98
99(defgeneric multiply (factor &rest more-factors)
100 (:documentation "Successively multiplies factor FACTOR by the remaining arguments
101MORE-FACTORS, using MULTIPLY-BY to multiply two factors. FACTOR must not be destructively modified.
102Instead, a copy of factor should be made and returned as the value of this function.")
103 (:method ((factor t) &rest more-factors)
104 (reduce #'multiply-by more-factors :initial-value (copy-instance factor))))
105
Note: See TracBrowser for help on using the repository browser.