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source: branches/f4grobner/ring.lisp@ 2761

Last change on this file since 2761 was 2720, checked in by Marek Rychlik, 9 years ago

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File size: 5.5 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(defpackage "RING"
23 (:use :cl)
24 (:export "R-PARSE"
25 "UNIT-ELEMENT"
26 "R-ZEROP"
27 "R+"
28 "R-"
29 "R*"
30 "R+"
31 "R/"
32 "R-EXPT"
33 "R-LCM"
34 "R-EZGCD"
35 "R-GCD"
36 "R-TOTAL-DEGREE"
37 "R-DIMENSION"
38 "R-EXPONENTS"
39 "R-COEFF"
40 "R-SUGAR"
41 "R-DIVIDES-P"
42 "R-DIVIDES-LCM-P"
43 "R-LCM-DIVIDES-LCM-P"
44 "R-LCM-EQUAL-LCM-P"
45 "R-REL-PRIME-P"
46 "R-EQUALP"
47 "R-ELT"
48 "R->LIST"
49 "R-DIVISIBLE-BY-P"
50 "R-REL-PRIME-P"
51 "R-DEPENDS-P"
52 "R-TENSOR-PRODUCT"
53 "R-CONTRACT"
54 "R-LENGTH"
55 "MULTIPLY-BY"
56 "ADD-TO"
57 "SUBTRACT-FROM"
58 "UNARY-MINUS"
59 "SCALAR"
60 "INSERT-ITEM"
61 "APPEND-ITEM")
62 (:documentation
63 "Implements ring operations. These are all operations that are
64performed on the coefficients by the package, and thus the coefficient
65ring can be changed by merely redefining these operations."))
66
67(in-package :ring)
68
69(defclass scalar ()
70 ((value :initarg :value :accessor value))
71 (:documentation "Wraps objects suitable as scalars/polynomial coefficients"))
72
73(defgeneric unit-element (class))
74
75(defgeneric r-zerop (object)
76 (:method ((self number)) (zerop self)))
77
78(defgeneric r+ (x y)
79 (:method ((x number) (y number)) (+ x y)))
80
81(defgeneric r- (x y)
82 (:method ((x number) (y number)) (- x y)))
83
84(defgeneric r* (x y)
85 (:method ((x number) (y number)) (* x y)))
86
87(defgeneric r-tensor-product (x y))
88
89(defgeneric r/ (x y)
90 (:method ((x number) (y number)) (/ x y)))
91
92(defgeneric r-lcm (x y)
93 (:method ((x integer) (y integer)) (lcm x y)))
94
95(defgeneric r-expt (x y)
96 (:method ((x integer) (y integer)) (expt x y)))
97
98(defgeneric r-ezgcd (x y)
99 (:method ((x integer) (y integer)
100 &aux (c (gcd x y)))
101 (values c (/ x c) (/ y c))))
102
103(defgeneric r-gcd (x y)
104 (:method ((x integer) (y integer))
105 (gcd x y)))
106
107(defgeneric r-dimension (object))
108(defgeneric r-exponents (object))
109
110(defgeneric r-coeff (object))
111(defgeneric (setf r-coeff) (new-value object))
112
113(defgeneric r-total-degree (object &optional start end))
114
115(defgeneric r-divides-p (object1 object2)
116 (:method ((object1 integer) (object2 integer))
117 (zerop (rem object2 object1)))
118 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
119
120(defgeneric r-divides-lcm-p (object1 object2 object3)
121 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
122
123(defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)
124 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
125
126(defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)
127 (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
128
129(defgeneric r-equalp (object1 object2)
130 (:method (object1 object2) (equalp object1 object2))
131 (:documentation "Equality using deep comparison of object slots."))
132
133(defgeneric r-elt (object index))
134
135(defgeneric (setf r-elt) (new-value object index))
136
137(defgeneric r-length (object))
138
139(defgeneric r->list (object))
140(defgeneric r-sugar (object))
141(defgeneric r-rel-prime-p (object1 object2))
142(defgeneric r-contract (object k))
143(defgeneric r-divisible-by-p (object1 object2))
144(defgeneric r-depends-p (object k))
145
146(defgeneric multiply-by (self other)
147 (:method (self other) (r* self other)))
148
149(defgeneric add-to (self other)
150 (:documentation "Add to object SELF another object OTHER. For
151complex objects, it may destructively modify SELF and destructively
152modify/invalidate object OTHER. For standard classes implementing this
153method, the result should be an object which is EQ to SELF. For
154built-in classes, such as NUMBER, the returned object may not be EQ to
155the original, but it will be EQL to it.")
156 (:method (self other) (r+ self other)))
157
158(defgeneric subtract-from (self other)
159 (:documentation "Subtract from an object SELF another object OTHER.
160For complex objects, it may destructively modify SELF and
161destructively modify/invalidate object OTHER. For standard classes
162implementing this method, the result should be an object which is EQ
163to SELF. For built-in classes, such as NUMBER, the returned object may
164not be EQ to the original.")
165 (:method (self other) (r- self other)))
166
167(defgeneric unary-minus (self)
168 (:method ((x number)) (- x)))
169
170(defgeneric insert-item (self item))
171(defgeneric append-item (self item))
172
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