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source: branches/f4grobner/ring.lisp@ 2101

Last change on this file since 2101 was 2101, checked in by Marek Rychlik, 9 years ago

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File size: 3.2 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 (:shadow "GCD" "LCM")
37 (:export "PARSE"
38 "UNIT-FOR"
39 "ZEROP"
40 "ADD"
41 "SUB"
42 "UMINUS"
43 "MUL"
44 "DIV"
45 "LCM"
46 "EZGCD"
47 "GCD"
48 ))
49
50(in-package :ring)
51
52(defgeneric unit-for (object)
53 (:method ((self number)) 1))
54
55(defgeneric zerop (object)
56 (:method ((self number)) (cl:zerop self)))
57
58(defgeneric add (x y)
59 (:method ((x number) (y number)) (+ x y)))
60
61(defgeneric mul (x y)
62 (:method ((x number) (y number)) (* x y)))
63
64(defgeneric tensor-mul (x y))
65
66(defgeneric div (x y)
67 (:method ((x number) (y number)) (/ x y)))
68
69(defgeneric lcm (x y)
70 (:method ((x integer) (y integer)) (cl:lcm x y)))
71
72(defgeneric ezgcd (x y)
73 (:method ((x integer) (y integer)
74 &aux (c (gcd x y)))
75 (values c (/ x c) (/ y c))))
76
77(defgeneric gcd (x y)
78 (:method ((x integer) (y integer))
79 (cl:gcd x y)))
80
81(defgeneric dimension (object))
82
83(defgeneric total-degree (object &optional start end))
84
85(defgeneric divides-p (object1 object2)
86 (:method ((object1 integer) (object2 integer))
87 (zerop (rem object2 object1)))
88 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
89
90(defgeneric divides-lcm-p (object1 object2 object3)
91 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
92
93(defgeneric lcm-divides-lcm-p (object1 object2 object3 object4)
94 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
95
96(defmethod lcm-equal-lcm-p (object1 object2 object3 object4)
97 "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise.")
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