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source: branches/f4grobner/monom.lisp@ 2357

Last change on this file since 2357 was 2357, checked in by Marek Rychlik, 9 years ago

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1;;; -*- Mode: Lisp -*-
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;; This package implements BASIC OPERATIONS ON MONOMIALS
24;;----------------------------------------------------------------
25;; DATA STRUCTURES: Conceptually, monomials can be represented as lists:
26;;
27;; monom: (n1 n2 ... nk) where ni are non-negative integers
28;;
29;; However, lists may be implemented as other sequence types,
30;; so the flexibility to change the representation should be
31;; maintained in the code to use general operations on sequences
32;; whenever possible. The optimization for the actual representation
33;; should be left to declarations and the compiler.
34;;----------------------------------------------------------------
35;; EXAMPLES: Suppose that variables are x and y. Then
36;;
37;; Monom x*y^2 ---> (1 2)
38;;
39;;----------------------------------------------------------------
40
41(defpackage "MONOM"
42 (:use :cl :ring)
43 (:export "MONOM"
44 "EXPONENT"
45 "MONOM-DIMENSION"
46 "MONOM-EXPONENTS"
47 "MAKE-MONOM-VARIABLE"))
48
49(in-package :monom)
50
51(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
52
53(deftype exponent ()
54 "Type of exponent in a monomial."
55 'fixnum)
56
57(defclass monom ()
58 ((dimension :initarg :dimension :accessor monom-dimension)
59 (exponents :initarg :exponents :accessor monom-exponents))
60 (:default-initargs :dimension nil :exponents nil :exponent nil))
61
62(defmethod print-object ((self monom) stream)
63 (format stream "#<MONOM DIMENSION=~A EXPONENTS=~A>"
64 (slot-value self 'dimension)
65 (slot-value self 'exponents)))
66
67#|
68;; Debug calls to initialize-instance
69(defmethod initialize-instance :around ((self monom)
70 &rest
71 args
72 &key
73 &allow-other-keys)
74 (format t "MONOM::INITIALIZE-INSTANCE called with:~&ARGS: ~W.~%" args)
75 (call-next-method)
76 )
77|#
78
79(defmethod shared-initialize :after ((self monom) slot-names
80 ;;&rest initargs
81 &key
82 dimension
83 exponents
84 exponent
85 &allow-other-keys
86 )
87 ;;(format t "MONOM::SHARED-INITIALIZE called with:~&SLOT-NAMES: ~W~&INITARGS: ~W.~%" slot-names initargs)
88 (if (eq slot-names t) (setf slot-names '(dimension exponents)))
89 (dolist (slot-name slot-names)
90 (case slot-name
91 (dimension
92 (cond (dimension
93 (setf (slot-value self 'dimension) dimension))
94 (exponents
95 (setf (slot-value self 'dimension) (length exponents)))
96 (t
97 (error "DIMENSION or EXPONENTS must not be NIL"))))
98 (exponents
99 (cond
100 ;; when exponents are supplied
101 (exponents
102 (let ((dim (length exponents)))
103 (setf (slot-value self 'dimension) dim
104 (slot-value self 'exponents) (make-array dim :initial-contents exponents))))
105 ;; when all exponents are to be identical
106 (t
107 (let ((dim (slot-value self 'dimension)))
108 (setf (slot-value self 'exponents)
109 (make-array (list dim) :initial-element (or exponent 0)
110 :element-type 'exponent)))))))))
111
112;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
113;;
114;; Operations on monomials
115;;
116;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
117
118(defmethod r-dimension ((m monom))
119 (monom-dimension m))
120
121(defmethod r-elt ((m monom) index)
122 "Return the power in the monomial M of variable number INDEX."
123 (with-slots (exponents)
124 m
125 (elt exponents index)))
126
127(defmethod (setf r-elt) (new-value (m monom) index)
128 "Return the power in the monomial M of variable number INDEX."
129 (with-slots (exponents)
130 m
131 (setf (elt exponents index) new-value)))
132
133(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
134 "Return the todal degree of a monomoal M. Optinally, a range
135of variables may be specified with arguments START and END."
136 (declare (type fixnum start end))
137 (with-slots (exponents)
138 m
139 (reduce #'+ exponents :start start :end end)))
140
141
142(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
143 "Return the sugar of a monomial M. Optinally, a range
144of variables may be specified with arguments START and END."
145 (declare (type fixnum start end))
146 (r-total-degree m start end))
147
148(defmethod r* ((m1 monom) (m2 monom))
149 "Multiply monomial M1 by monomial M2."
150 (format t "MONOM::R* called with:~& M1: ~A~& M2: ~A~%" m1 m2)
151 (with-slots ((exponents1 exponents) dimension)
152 m1
153 (with-slots ((exponents2 exponents))
154 m2
155 (let* ((exponents (copy-seq exponents1)))
156 (map-into exponents #'+ exponents1 exponents2)
157 (make-instance 'monom :dimension dimension :exponents exponents)))))
158
159
160
161(defmethod r/ ((m1 monom) (m2 monom))
162 "Divide monomial M1 by monomial M2."
163 (with-slots ((exponents1 exponents) (dimension1 dimension))
164 m1
165 (with-slots ((exponents2 exponents))
166 m2
167 (let* ((exponents (copy-seq exponents1))
168 (dimension dimension1))
169 (map-into exponents #'- exponents1 exponents2)
170 (make-instance 'monom :dimension dimension :exponents exponents)))))
171
172(defmethod r-divides-p ((m1 monom) (m2 monom))
173 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
174 (with-slots ((exponents1 exponents))
175 m1
176 (with-slots ((exponents2 exponents))
177 m2
178 (every #'<= exponents1 exponents2))))
179
180
181(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
182 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
183 (every #'(lambda (x y z) (<= x (max y z)))
184 m1 m2 m3))
185
186
187(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
188 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
189 (declare (type monom m1 m2 m3 m4))
190 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
191 m1 m2 m3 m4))
192
193(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
194 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
195 (with-slots ((exponents1 exponents))
196 m1
197 (with-slots ((exponents2 exponents))
198 m2
199 (with-slots ((exponents3 exponents))
200 m3
201 (with-slots ((exponents4 exponents))
202 m4
203 (every
204 #'(lambda (x y z w) (= (max x y) (max z w)))
205 exponents1 exponents2 exponents3 exponents4))))))
206
207(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
208 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
209 (with-slots ((exponents1 exponents))
210 m1
211 (with-slots ((exponents2 exponents))
212 m2
213 (every #'>= exponents1 exponents2))))
214
215(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
216 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
217 (with-slots ((exponents1 exponents))
218 m1
219 (with-slots ((exponents2 exponents))
220 m2
221 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
222
223
224(defmethod r-equalp ((m1 monom) (m2 monom))
225 "Returns T if two monomials M1 and M2 are equal."
226 (with-slots ((exponents1 exponents))
227 m1
228 (with-slots ((exponents2 exponents))
229 m2
230 (every #'= exponents1 exponents2))))
231
232(defmethod r-lcm ((m1 monom) (m2 monom))
233 "Returns least common multiple of monomials M1 and M2."
234 (with-slots ((exponents1 exponents) (dimension1 dimension))
235 m1
236 (with-slots ((exponents2 exponents))
237 m2
238 (let* ((exponents (copy-seq exponents1))
239 (dimension dimension1))
240 (map-into exponents #'max exponents1 exponents2)
241 (make-instance 'monom :dimension dimension :exponents exponents)))))
242
243
244(defmethod r-gcd ((m1 monom) (m2 monom))
245 "Returns greatest common divisor of monomials M1 and M2."
246 (with-slots ((exponents1 exponents) (dimension1 dimension))
247 m1
248 (with-slots ((exponents2 exponents))
249 m2
250 (let* ((exponents (copy-seq exponents1))
251 (dimension dimension1))
252 (map-into exponents #'min exponents1 exponents2)
253 (make-instance 'monom :dimension dimension :exponents exponents)))))
254
255(defmethod r-depends-p ((m monom) k)
256 "Return T if the monomial M depends on variable number K."
257 (declare (type fixnum k))
258 (with-slots (exponents)
259 m
260 (plusp (elt exponents k))))
261
262(defmethod r-tensor-product ((m1 monom) (m2 monom))
263 (with-slots ((exponents1 exponents) (dimension1 dimension))
264 m1
265 (with-slots ((exponents2 exponents) (dimension2 dimension))
266 m2
267 (make-instance 'monom
268 :dimension (+ dimension1 dimension2)
269 :exponents (concatenate 'vector exponents1 exponents2)))))
270
271(defmethod r-contract ((m monom) k)
272 "Drop the first K variables in monomial M."
273 (declare (fixnum k))
274 (with-slots (dimension exponents)
275 m
276 (setf dimension (- dimension k)
277 exponents (subseq exponents k))))
278
279(defun make-monom-variable (nvars pos &optional (power 1)
280 &aux (m (make-instance 'monom :dimension nvars)))
281 "Construct a monomial in the polynomial ring
282RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
283which represents a single variable. It assumes number of variables
284NVARS and the variable is at position POS. Optionally, the variable
285may appear raised to power POWER. "
286 (declare (type fixnum nvars pos power) (type monom m))
287 (with-slots (exponents)
288 m
289 (setf (elt exponents pos) power)
290 m))
291
292(defmethod r->list ((m monom))
293 "A human-readable representation of a monomial M as a list of exponents."
294 (coerce (monom-exponents m) 'list))
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