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source: branches/f4grobner/ring.lisp@ 2876

Last change on this file since 2876 was 2870, checked in by Marek Rychlik, 9 years ago

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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-CLONE"
48 "R-ELT"
49 "R->LIST"
50 "R-DIVISIBLE-BY-P"
51 "R-REL-PRIME-P"
52 "R-DEPENDS-P"
53 "R-TENSOR-PRODUCT"
54 "R-CONTRACT"
55 "R-LENGTH"
56 "MULTIPLY-BY"
57 "DIVIDE-BY"
58 "ADD-TO"
59 "SUBTRACT-FROM"
60 "UNARY-MINUS"
61 "SCALAR"
62 "INSERT-ITEM"
63 "APPEND-ITEM"
64 "COPY-INSTANCE")
65 (:documentation
66 "Implements ring operations. These are all operations that are
67performed on the coefficients by the package, and thus the coefficient
68ring can be changed by merely redefining these operations."))
69
70(in-package :ring)
71
72(defclass scalar ()
73 ((value :initarg :value :accessor value))
74 (:documentation "Wraps objects suitable as scalars/polynomial coefficients"))
75
76(defgeneric unit-element (class))
77
78(defgeneric r-zerop (object)
79 (:method ((self number)) (zerop self))
80 (:documentation "Tests whether a ring element is 0."))
81
82(defgeneric r+ (x y)
83 (:method ((x number) (y number)) (+ x y))
84 (:documentation "Adds ring elements."))
85
86(defgeneric r- (x y)
87 (:method ((x number) (y number)) (- x y))
88 (:documentation "Subtracts ring elements."))
89
90(defgeneric r* (x y)
91 (:method ((x number) (y number)) (* x y))
92 (:documentation "Multiplies ring elements."))
93
94(defgeneric r-tensor-product (x y)
95 (:documentation "Takes a tensor product of two objects."))
96
97(defgeneric r/ (x y)
98 (:method ((x number) (y number)) (/ x y))
99 (:documentation "Divides ring elements."))
100
101(defgeneric r-lcm (x y)
102 (:method ((x integer) (y integer)) (lcm x y))
103 (:documentation "Returns the least common multiple of ring elements."))
104
105(defgeneric r-expt (x y)
106 (:method ((x integer) (y integer)) (expt x y))
107 (:documentation "Raises X to power Y."))
108
109(defgeneric r-ezgcd (x y)
110 (:method ((x integer) (y integer)
111 &aux (c (gcd x y)))
112 (values c (/ x c) (/ y c)))
113 (:documentation "Solves the diophantine system: X=C*X1, Y=C*X2,
114C=GCD(X,Y). It returns C, X1 and Y1. The result may be obtained by
115the Euclidean algorithm."))
116
117(defgeneric r-gcd (x y)
118 (:method ((x integer) (y integer))
119 (gcd x y))
120 (:documentation "Returns GCD(X,Y)."))
121
122(defgeneric r-dimension (object))
123(defgeneric r-exponents (object))
124
125(defgeneric r-coeff (object))
126(defgeneric (setf r-coeff) (new-value object))
127
128(defgeneric r-total-degree (object &optional start end))
129
130(defgeneric r-divides-p (object1 object2)
131 (:method ((object1 integer) (object2 integer))
132 (zerop (rem object2 object1)))
133 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
134
135(defgeneric r-divides-lcm-p (object1 object2 object3)
136 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
137
138(defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)
139 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
140
141(defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)
142 (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
143
144(defgeneric r-equalp (object1 object2)
145 (:method (object1 object2) (equalp object1 object2))
146 (:documentation "Equality using deep comparison of object slots."))
147
148(defgeneric r-elt (object index))
149
150(defgeneric (setf r-elt) (new-value object index))
151
152(defgeneric r-length (object))
153
154(defgeneric r->list (object))
155(defgeneric r-sugar (object))
156(defgeneric r-rel-prime-p (object1 object2))
157(defgeneric r-contract (object k))
158(defgeneric r-divisible-by-p (object1 object2))
159(defgeneric r-depends-p (object k))
160
161(defgeneric multiply-by (self other)
162 (:method (self other) (r* self other))
163 (:documentation "Multiply object SELF and OTHER and store the result
164into SELF. It returns SELF. For instances of a class, this operation
165may be destructive."))
166
167(defgeneric divide-by (self other)
168 (:method (self other) (r/ self other))
169 (:documentation "Divided object SELF by OTHER and store the result
170into SELF. It returns SELF. For instances of a class, this operation
171may be destructive."))
172
173(defgeneric add-to (self other)
174 (:documentation "Add to object SELF another object OTHER. For
175complex objects, it may destructively modify SELF and destructively
176modify/invalidate object OTHER. For standard classes implementing this
177method, the result should be an object which is EQ to SELF. For
178built-in classes, such as NUMBER, the returned object may not be EQ to
179the original, but it will be EQL to it.")
180 (:method (self other) (r+ self other)))
181
182(defgeneric subtract-from (self other)
183 (:documentation "Subtract from an object SELF another object OTHER.
184For complex objects, it may destructively modify SELF and
185destructively modify/invalidate object OTHER. For standard classes
186implementing this method, the result should be an object which is EQ
187to SELF. For built-in classes, such as NUMBER, the returned object may
188not be EQ to the original.")
189 (:method (self other) (r- self other)))
190
191(defgeneric unary-minus (self)
192 (:method ((x number)) (- x)))
193
194(defgeneric insert-item (self item))
195(defgeneric append-item (self item))
196
197;; Source: http://stackoverflow.com/questions/11067899/is-there-a-generic-method-for-cloning-clos-objects
198(defgeneric copy-instance (object &rest initargs &key &allow-other-keys)
199 (:documentation "Makes and returns a shallow copy of OBJECT.
200
201 An uninitialized object of the same class as OBJECT is allocated by
202 calling ALLOCATE-INSTANCE. For all slots returned by
203 CLASS-SLOTS, the returned object has the
204 same slot values and slot-unbound status as OBJECT.
205
206 REINITIALIZE-INSTANCE is called to update the copy with INITARGS.")
207 (:method ((object standard-object) &rest initargs &key &allow-other-keys)
208 (let* ((class (class-of object))
209 (copy (allocate-instance class)))
210 (dolist (slot-name (mapcar #'sb-mop:slot-definition-name (sb-mop:class-slots class)))
211 (when (slot-boundp object slot-name)
212 (setf (slot-value copy slot-name)
213 (slot-value object slot-name))))
214 (apply #'reinitialize-instance copy initargs))))
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