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source: branches/f4grobner/ring.lisp@ 3436

Last change on this file since 3436 was 3424, 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 "LEFT-TENSOR-PRODUCT-BY"
54 "RIGHT-TENSOR-PRODUCT-BY"
55 "LEFT-CONTRACT"
56 "R-LENGTH"
57 "MULTIPLY-BY"
58 "DIVIDE-BY"
59 "ADD-TO"
60 "SUBTRACT-FROM"
61 "UNARY-MINUS"
62 "SCALAR"
63 "SCALAR-COEFF"
64 "INSERT-ITEM"
65 "APPEND-ITEM"
66 "COPY-INSTANCE")
67 (:shadowing-import-from
68 #+openmcl-native-threads #:ccl
69 #+cmu #:pcl
70 #+sbcl #:sb-pcl
71 #+lispworks #:hcl
72 #+allegro #:mop
73 #+clisp #:clos
74 #:class-slots #:slot-definition-name)
75 (:documentation
76 "Implements ring operations. These are all operations that are
77performed on the coefficients by the package, and thus the coefficient
78ring can be changed by merely redefining these operations."))
79
80(in-package :ring)
81
82(defclass scalar ()
83 ((coeff :initarg :coeff :accessor scalar-coeff))
84 (:default-initargs :coeff nil)
85 (:documentation "Wraps objects suitable as scalars/polynomial coefficients"))
86
87(defmethod print-object ((self scalar) stream)
88 (print-unreadable-object (self stream :type t :identity t)
89 (format stream "COEFF=~A"
90 (slot-value self 'coeff))))
91
92(defgeneric unit-element (class))
93
94(defgeneric r-zerop (object)
95 (:method ((self number)) (zerop self))
96 (:documentation "Tests whether a ring element is 0."))
97
98(defgeneric r+ (x y)
99 (:method ((x number) (y number)) (+ x y))
100 (:documentation "Adds ring elements."))
101
102(defgeneric r- (minuend &rest subtrahends)
103 (:method ((minuend number) &rest subtrahends) (apply #'- (cons minuend subtrahends)))
104 (:documentation "Subtracts ring elements."))
105
106(defgeneric r* (x y)
107 (:method (x y) (* x y))
108 (:documentation "Multiplies ring elements."))
109
110(defgeneric left-tensor-product-by (self other)
111 (:documentation "Takes a tensor product of SELF with OTHER, where
112OTHER is the left factor."))
113
114(defgeneric right-tensor-product-by (self other)
115 (:documentation "Takes a tensor product of SELF with OTHER, where
116OTHER is the right factor."))
117
118(defgeneric r/ (numerator &rest denominators)
119 (:method ((numerator number) &rest denominators) (apply #'/ (cons numerator denominators)))
120 (:documentation "Divides ring elements."))
121
122(defgeneric r-lcm (x y)
123 (:method ((x integer) (y integer)) (lcm x y))
124 (:documentation "Returns the least common multiple of ring elements."))
125
126(defgeneric r-expt (x y)
127 (:method ((x number) (y integer)) (expt x y))
128 (:method ((x t) (y integer))
129 (declare (type fixnum y))
130 (cond
131 ((minusp y) (error "r-expt: Negative exponent."))
132 ((r-zerop x) (if (zerop y) 1))
133 (t
134 (do ((k 1 (ash k 1))
135 (q x (r* q q)) ;keep squaring
136 (p 1 (if (not (zerop (logand k y))) (r* p q) p)))
137 ((> k y) p)
138 (declare (fixnum k))))))
139 (:documentation "Raises X to power Y."))
140
141(defgeneric r-ezgcd (x y)
142 (:method ((x integer) (y integer)
143 &aux (c (gcd x y)))
144 (values c (/ x c) (/ y c)))
145 (:documentation "Solves the diophantine system: X=C*X1, Y=C*X2,
146C=GCD(X,Y). It returns C, X1 and Y1. The result may be obtained by
147the Euclidean algorithm."))
148
149(defgeneric r-gcd (x y)
150 (:method ((x integer) (y integer))
151 (gcd x y))
152 (:documentation "Returns GCD(X,Y)."))
153
154(defgeneric r-dimension (object))
155(defgeneric r-exponents (object))
156
157(defgeneric r-coeff (object))
158(defgeneric (setf r-coeff) (new-value object))
159
160(defgeneric r-total-degree (object &optional start end))
161
162(defgeneric r-divides-p (object1 object2)
163 (:method ((object1 integer) (object2 integer))
164 (zerop (rem object2 object1)))
165 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
166
167(defgeneric r-divides-lcm-p (object1 object2 object3)
168 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
169
170(defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)
171 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
172
173(defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)
174 (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
175
176(defgeneric r-equalp (object1 object2)
177 (:method (object1 object2) (equalp object1 object2))
178 (:method ((object1 list) (object2 list))
179 (every #'r-equalp object1 object2))
180 (:method ((object1 scalar) (object2 scalar))
181 (r-equalp (scalar-coeff object1) (scalar-coeff object2)))
182 (:documentation "Equality using deep comparison of object slots."))
183
184(defgeneric r-elt (object index)
185 (:documentation "Access a part of an object OBJECT with index INDEX."))
186
187(defgeneric (setf r-elt) (new-value object index)
188 (:documentation "A setter of a part of an object OBJECT with index INDEX."))
189
190(defgeneric r-length (object))
191
192(defgeneric r->list (object))
193(defgeneric r-sugar (object))
194(defgeneric r-rel-prime-p (object1 object2))
195(defgeneric left-contract (object k))
196(defgeneric r-divisible-by-p (object1 object2))
197(defgeneric r-depends-p (object k))
198
199(defgeneric multiply-by (self other)
200 (:method (self other) (r* self other))
201 (:documentation "Multiply object SELF and OTHER and store the result
202into SELF. It returns SELF. For instances of a class, this operation
203may be destructive."))
204
205(defgeneric divide-by (self other)
206 (:method (self other) (r/ self other))
207 (:documentation "Divided object SELF by OTHER and store the result
208into SELF. It returns SELF. For instances of a class, this operation
209may be destructive."))
210
211(defgeneric add-to (self other)
212 (:documentation "Add to object SELF another object OTHER. For
213complex objects, it may destructively modify SELF and destructively
214modify/invalidate object OTHER. For standard classes implementing this
215method, the result should be an object which is EQ to SELF. For
216built-in classes, such as NUMBER, the returned object may not be EQ to
217the original, but it will be EQL to it.")
218 (:method (self other) (r+ self other)))
219
220(defgeneric subtract-from (self other)
221 (:documentation "Subtract from an object SELF another object OTHER.
222For complex objects, it may destructively modify SELF and
223destructively modify/invalidate object OTHER. For standard classes
224implementing this method, the result should be an object which is EQ
225to SELF. For built-in classes, such as NUMBER, the returned object may
226not be EQ to the original.")
227 (:method (self other) (r- self other)))
228
229(defgeneric unary-minus (self)
230 (:method ((x number)) (- x)))
231
232(defgeneric insert-item (self item))
233(defgeneric append-item (self item))
234
235;; Source: http://stackoverflow.com/questions/11067899/is-there-a-generic-method-for-cloning-clos-objects
236;; NOTE: This is a shallow copy. Add an around method for classes which need deep copy of the slots.
237(defgeneric copy-instance (object &rest initargs &key &allow-other-keys)
238 (:documentation "Makes and returns a shallow copy of OBJECT.
239
240 An uninitialized object of the same class as OBJECT is allocated by
241 calling ALLOCATE-INSTANCE. For all slots returned by
242 CLASS-SLOTS, the returned object has the
243 same slot values and slot-unbound status as OBJECT.
244
245 REINITIALIZE-INSTANCE is called to update the copy with INITARGS.")
246 (:method ((object standard-object) &rest initargs &key &allow-other-keys)
247 (let* ((class (class-of object))
248 (copy (allocate-instance class)))
249 (dolist (slot-name (mapcar #'slot-definition-name (class-slots class)))
250 (when (slot-boundp object slot-name)
251 (setf (slot-value copy slot-name)
252 (slot-value object slot-name))))
253 (apply #'reinitialize-instance copy initargs))))
254
255#|
256;; A stripped-down version of shallow copy
257;; Source: http://stackoverflow.com/questions/11067899/is-there-a-generic-method-for-cloning-clos-objects
258(defun shallow-copy-object (original)
259 (let* ((class (class-of original))
260 (copy (allocate-instance class)))
261 (dolist (slot (mapcar #'slot-definition-name (class-slots class)))
262 (when (slot-boundp original slot)
263 (setf (slot-value copy slot)
264 (slot-value original slot))))
265 copy))
266|#
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