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source: branches/f4grobner/ring.lisp@ 2092

Last change on this file since 2092 was 2091, checked in by Marek Rychlik, 9 years ago

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File size: 4.2 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 (: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#|
55
56(defstruct (ring)
57 "Defines a RING structure, whose fields
58are common ring operations necessary to implement
59Groebner bases."
60 (parse #'identity :type function)
61 (unit #'identity :type function)
62 (zerop #'identity :type function)
63 (add #'identity :type function)
64 (sub #'identity :type function)
65 (uminus #'identity :type function)
66 (mul #'identity :type function)
67 (div #'identity :type function)
68 (lcm #'identity :type function)
69 (ezgcd #'identity :type function)
70 (gcd #'identity :type function))
71
72(defparameter +ring-of-integers+
73 (make-ring
74 :parse #'identity
75 :unit #'(lambda () 1)
76 :zerop #'zerop
77 :add #'+
78 :sub #'-
79 :uminus #'-
80 :mul #'*
81 :div #'/
82 :lcm #'lcm
83 :ezgcd #'(lambda (x y &aux (c (gcd x y))) (values c (/ x c) (/ y c)))
84 :gcd #'gcd
85 )
86 "The ring of integers.")
87|#
88
89(defgeneric ring-parse (object)
90 (:method ((object t)) object))
91
92(defgeneric ring-unit-for (object)
93 (:method ((self number)) 1))
94
95(defgeneric ring-zerop (object)
96 (:method ((self number)) (zerop self)))
97
98(defgeneric ring-add (x y)
99 (:method ((x number) (y number)) (+ x y)))
100
101(defgeneric ring-mul (x y)
102 (:method ((x number) (y number)) (* x y)))
103
104(defgeneric ring-tensor-mul (x y))
105
106(defgeneric ring-div (x y)
107 (:method ((x number) (y number)) (/ x y)))
108
109(defgeneric ring-lcm (x y)
110 (:method ((x integer) (y integer)) (lcm x y)))
111
112(defgeneric ring-ezgcd (x y)
113 (:method ((x integer) (y integer)
114 &aux (c (gcd x y)))
115 (values c (/ x c) (/ y c))))
116
117(defgeneric ring-gcd (x y)
118 (:method ((x integer) (y integer))
119 (gcd x y)))
120
121(defgeneric dimension (object))
122
123(defgeneric total-degree (object &optional start end))
124
125(defgeneric divides-p (object1 object2)
126 (:method ((object1 integer) (object2 integer))
127 (zerop (rem object2 object1)))
128 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
129
130(defgeneric divides-lcm-p (object1 object2 object3)
131 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
132
133(defgeneric lcm-divides-lcm-p (object1 object2 object3 object4)
134 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
135
136(defun lcm-equal-lcm-p (object1 object2 object3 object4)
137 "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."
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