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source: branches/f4grobner/ring.lisp@ 3584

Last change on this file since 3584 was 3459, 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 (:shadowing-import-from
67 #+openmcl-native-threads #:ccl
68 #+cmu #:pcl
69 #+sbcl #:sb-pcl
70 #+lispworks #:hcl
71 #+allegro #:mop
72 #+clisp #:clos
73 #:class-slots #:slot-definition-name)
74 (:documentation
75 "Implements ring operations. These are all operations that are
76performed on the coefficients by the package, and thus the coefficient
77ring can be changed by merely redefining these operations."))
78
79(in-package :ring)
80
81(defclass scalar ()
82 ((coeff :initarg :coeff :accessor scalar-coeff))
83 (:default-initargs :coeff nil)
84 (:documentation "Wraps objects suitable as scalars/polynomial coefficients"))
85
86(defmethod print-object ((self scalar) stream)
87 (print-unreadable-object (self stream :type t :identity t)
88 (format stream "COEFF=~A"
89 (slot-value self 'coeff))))
90
91(defgeneric unit-element (class))
92
93(defgeneric r-zerop (object)
94 (:method ((self number)) (zerop self))
95 (:documentation "Tests whether a ring element is 0."))
96
97(defgeneric r+ (x y)
98 (:method ((x number) (y number)) (+ x y))
99 (:documentation "Adds ring elements."))
100
101(defgeneric r- (minuend &rest subtrahends)
102 (:method ((minuend number) &rest subtrahends) (apply #'- (cons minuend subtrahends)))
103 (:documentation "Subtracts ring elements."))
104
105(defgeneric r* (x y)
106 (:method (x y) (* x y))
107 (:documentation "Multiplies ring elements."))
108
109(defgeneric left-tensor-product-by (self other)
110 (:documentation "Takes a tensor product of SELF with OTHER, where
111OTHER is the left factor."))
112
113(defgeneric right-tensor-product-by (self other)
114 (:documentation "Takes a tensor product of SELF with OTHER, where
115OTHER is the right factor."))
116
117(defgeneric r/ (numerator &rest denominators)
118 (:method ((numerator number) &rest denominators) (apply #'/ (cons numerator denominators)))
119 (:documentation "Divides ring elements."))
120
121(defgeneric r-lcm (x y)
122 (:method ((x integer) (y integer)) (lcm x y))
123 (:documentation "Returns the least common multiple of ring elements."))
124
125(defgeneric r-expt (x y)
126 (:method ((x number) (y integer)) (expt x y))
127 (:method ((x t) (y integer))
128 (declare (type fixnum y))
129 (cond
130 ((minusp y) (error "r-expt: Negative exponent."))
131 ((r-zerop x) (if (zerop y) 1))
132 (t
133 (do ((k 1 (ash k 1))
134 (q x (r* q q)) ;keep squaring
135 (p 1 (if (not (zerop (logand k y))) (r* p q) p)))
136 ((> k y) p)
137 (declare (fixnum k))))))
138 (:documentation "Raises X to power Y."))
139
140(defgeneric r-ezgcd (x y)
141 (:method ((x integer) (y integer)
142 &aux (c (gcd x y)))
143 (values c (/ x c) (/ y c)))
144 (:documentation "Solves the diophantine system: X=C*X1, Y=C*X2,
145C=GCD(X,Y). It returns C, X1 and Y1. The result may be obtained by
146the Euclidean algorithm."))
147
148(defgeneric r-gcd (x y)
149 (:method ((x integer) (y integer))
150 (gcd x y))
151 (:documentation "Returns GCD(X,Y)."))
152
153(defgeneric r-dimension (object))
154(defgeneric r-exponents (object))
155
156(defgeneric r-coeff (object))
157(defgeneric (setf r-coeff) (new-value object))
158
159(defgeneric r-total-degree (object &optional start end))
160
161(defgeneric r-divides-p (object1 object2)
162 (:method ((object1 integer) (object2 integer))
163 (zerop (rem object2 object1)))
164 (:documentation "Returns T if OBJECT1 divides OBJECT2"))
165
166(defgeneric r-divides-lcm-p (object1 object2 object3)
167 (:documentation "Returns T if OBJECT divides LCM(OBJECT2, OBJECT3), NIL otherwise."))
168
169(defgeneric r-lcm-divides-lcm-p (object1 object2 object3 object4)
170 (:documentation "Returns T if LCM(OBJECT1,OBJECT2) divides LCM(OBJECT3,OBJECT4), NIL otherwise."))
171
172(defgeneric r-lcm-equal-lcm-p (object1 object2 object3 object4)
173 (:documentation "Returns T if object LCM(OBJECT1,OBJECT2) equals LCM(OBJECT3,OBJECT4), NIL otherwise."))
174
175(defgeneric r-equalp (object1 object2)
176 (:method (object1 object2) (equalp object1 object2))
177 (:method ((object1 list) (object2 list))
178 (every #'r-equalp object1 object2))
179 (:method ((object1 scalar) (object2 scalar))
180 (r-equalp (scalar-coeff object1) (scalar-coeff object2)))
181 (:documentation "Equality using deep comparison of object slots."))
182
183(defgeneric r-elt (object index)
184 (:documentation "Access a part of an object OBJECT with index INDEX."))
185
186(defgeneric (setf r-elt) (new-value object index)
187 (:documentation "A setter of a part of an object OBJECT with index INDEX."))
188
189(defgeneric r-length (object))
190
191(defgeneric r->list (object))
192(defgeneric r-sugar (object))
193(defgeneric r-rel-prime-p (object1 object2))
194(defgeneric left-contract (object k))
195(defgeneric r-divisible-by-p (object1 object2))
196(defgeneric r-depends-p (object k))
197
198(defgeneric multiply-by (self other)
199 (:method (self other) (r* self other))
200 (:documentation "Multiply object SELF and OTHER and store the result
201into SELF. It returns SELF. For instances of a class, this operation
202may be destructive."))
203
204(defgeneric divide-by (self other)
205 (:method (self other) (r/ self other))
206 (:documentation "Divided object SELF by OTHER and store the result
207into SELF. It returns SELF. For instances of a class, this operation
208may be destructive."))
209
210(defgeneric add-to (self other)
211 (:documentation "Add to object SELF another object OTHER. For
212complex objects, it may destructively modify SELF and destructively
213modify/invalidate object OTHER. For standard classes implementing this
214method, the result should be an object which is EQ to SELF. For
215built-in classes, such as NUMBER, the returned object may not be EQ to
216the original, but it will be EQL to it.")
217 (:method (self other) (r+ self other)))
218
219(defgeneric subtract-from (self other)
220 (:documentation "Subtract from an object SELF another object OTHER.
221For complex objects, it may destructively modify SELF and
222destructively modify/invalidate object OTHER. For standard classes
223implementing this method, the result should be an object which is EQ
224to SELF. For built-in classes, such as NUMBER, the returned object may
225not be EQ to the original.")
226 (:method (self other) (r- self other)))
227
228(defgeneric unary-minus (self)
229 (:method ((x number)) (- x)))
230
231(defgeneric insert-item (self item))
232(defgeneric append-item (self item))
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