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Last change on this file since 3297 was 3297, 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(defpackage "MONOM"
23 (:use :cl :ring)
24 (:export "MONOM"
25 "EXPONENT"
26 "MONOM-DIMENSION"
27 "MONOM-EXPONENTS"
28 "MAKE-MONOM-VARIABLE")
29 (:documentation
30 "This package implements basic operations on monomials.
31DATA STRUCTURES: Conceptually, monomials can be represented as lists:
32
33 monom: (n1 n2 ... nk) where ni are non-negative integers
34
35However, lists may be implemented as other sequence types, so the
36flexibility to change the representation should be maintained in the
37code to use general operations on sequences whenever possible. The
38optimization for the actual representation should be left to
39declarations and the compiler.
40
41EXAMPLES: Suppose that variables are x and y. Then
42
43 Monom x*y^2 ---> (1 2) "))
44
45(in-package :monom)
46
47(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
48
49(deftype exponent ()
50 "Type of exponent in a monomial."
51 'fixnum)
52
53(defclass monom ()
54 ((dimension :initarg :dimension :accessor monom-dimension
55 :documentation "The number of variables.")
56 (exponents :initarg :exponents :accessor monom-exponents
57 :documentation "The powers of the variables."))
58 ;; default-initargs are not needed, they are handled by SHARED-INITIALIZE
59 ;;(:default-initargs :dimension 'foo :exponents 'bar :exponent 'baz)
60 (:documentation
61 "Implements a monomial, i.e. a product of powers
62of variables, like X*Y^2."))
63
64(defmethod print-object ((self monom) stream)
65 (print-unreadable-object (self stream :type t :identity t)
66 (with-accessors ((dimension monom-dimension) (exponents monom-exponents))
67 self
68 (format stream "DIMENSION=~A EXPONENTS=~A"
69 dimension exponents))))
70
71;; SHARED-INITIALIZE allows instance initialization in a style similar to MAKE-ARRAY, e.g.
72;;
73;; (MAKE-INSTANCE :EXPONENTS '(1 2 3)) --> #<MONOM DIMENSION=3 EXPONENTS=#(1 2 3)>
74;; (MAKE-INSTANCE :DIMENSION 3) --> #<MONOM DIMENSION=3 EXPONENTS=#(0 0 0)>
75;; (MAKE-INSTANCE :DIMENSION 3 :EXPONENT 7) --> #<MONOM DIMENSION=3 EXPONENTS=#(7 7 7)>
76;;
77(defmethod initialize-instance :after ((self monom) slot-names
78 &key
79 (dimension 0 dimension-supplied-p)
80 (exponents nil exponents-supplied-p)
81 (exponent 0 exponent-supplied-p)
82 &allow-other-keys
83 )
84 (when (and dimension-supplied-p (slot-accessible-p 'dimension))
85 (setf (slot-value self 'dimension) dimension))
86
87 (when (and exponents-supplied-p (slot-accessible-p 'exponents))
88 (let ((dim (length exponents)))
89 (when (and dimension-supplied-p (/= dimension dim))
90 (error "EXPONENTS must have length DIMENSION"))
91 (setf (slot-value self 'dimension) dim
92 (slot-value self 'exponents) (make-array dim :initial-contents exponents))
93 (setf (slot-value self 'dimension) (length exponents))))
94
95 ;; when all exponents are to be identical
96 (when (and exponent-supplied-p (slot-accessible-p 'exponents))
97 (unless (slot-boundp self 'dimension)
98 (error "Slot DIMENSION is unbound, but must be known if EXPONENT is supplied."))
99 (let ((dim (slot-value self 'dimension)))
100 (setf (slot-value self 'exponents)
101 (make-array (list dim) :initial-element exponent
102 :element-type 'exponent))))))
103
104(defmethod r-equalp ((m1 monom) (m2 monom))
105 "Returns T iff monomials M1 and M2 have identical
106EXPONENTS."
107 (equalp (monom-exponents m1) (monom-exponents m2)))
108
109(defmethod r-coeff ((m monom))
110 "A MONOM can be treated as a special case of TERM,
111where the coefficient is 1."
112 1)
113
114(defmethod r-elt ((m monom) index)
115 "Return the power in the monomial M of variable number INDEX."
116 (with-slots (exponents)
117 m
118 (elt exponents index)))
119
120(defmethod (setf r-elt) (new-value (m monom) index)
121 "Return the power in the monomial M of variable number INDEX."
122 (with-slots (exponents)
123 m
124 (setf (elt exponents index) new-value)))
125
126(defmethod r-total-degree ((m monom) &optional (start 0) (end (monom-dimension m)))
127 "Return the todal degree of a monomoal M. Optinally, a range
128of variables may be specified with arguments START and END."
129 (declare (type fixnum start end))
130 (with-slots (exponents)
131 m
132 (reduce #'+ exponents :start start :end end)))
133
134
135(defmethod r-sugar ((m monom) &aux (start 0) (end (monom-dimension m)))
136 "Return the sugar of a monomial M. Optinally, a range
137of variables may be specified with arguments START and END."
138 (declare (type fixnum start end))
139 (r-total-degree m start end))
140
141(defmethod multiply-by ((self monom) (other monom))
142 (with-slots ((exponents1 exponents) (dimension1 dimension))
143 self
144 (with-slots ((exponents2 exponents) (dimension2 dimension))
145 other
146 (unless (= dimension1 dimension2)
147 (error "Incompatible dimensions: ~A and ~A.~%" dimension1 dimension2))
148 (map-into exponents1 #'+ exponents1 exponents2)))
149 self)
150
151(defmethod divide-by ((self monom) (other monom))
152 (with-slots ((exponents1 exponents) (dimension1 dimension))
153 self
154 (with-slots ((exponents2 exponents) (dimension2 dimension))
155 other
156 (unless (= dimension1 dimension2)
157 (error "Incompatible dimensions: ~A and ~A.~%" dimension1 dimension2))
158 (map-into exponents1 #'- exponents1 exponents2)))
159 self)
160
161(defmethod copy-instance :around ((object monom) &rest initargs &key &allow-other-keys)
162 "An :AROUNT method for COPY-INSTANCE. The primary method is a shallow copy,
163 while for monomials we typically need a fresh copy of the
164 exponents."
165 (declare (ignore object initargs))
166 (let ((copy (call-next-method)))
167 (setf (monom-exponents copy) (copy-seq (monom-exponents copy)))
168 copy))
169
170(defmethod r* ((m1 monom) (m2 monom))
171 "Non-destructively multiply monomial M1 by M2."
172 (multiply-by (copy-instance m1) (copy-instance m2)))
173
174(defmethod r/ ((m1 monom) (m2 monom))
175 "Non-destructively divide monomial M1 by monomial M2."
176 (divide-by (copy-instance m1) (copy-instance m2)))
177
178(defmethod r-divides-p ((m1 monom) (m2 monom))
179 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
180 (with-slots ((exponents1 exponents))
181 m1
182 (with-slots ((exponents2 exponents))
183 m2
184 (every #'<= exponents1 exponents2))))
185
186
187(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
188 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
189 (every #'(lambda (x y z) (<= x (max y z)))
190 m1 m2 m3))
191
192
193(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
194 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
195 (declare (type monom m1 m2 m3 m4))
196 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
197 m1 m2 m3 m4))
198
199(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
200 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
201 (with-slots ((exponents1 exponents))
202 m1
203 (with-slots ((exponents2 exponents))
204 m2
205 (with-slots ((exponents3 exponents))
206 m3
207 (with-slots ((exponents4 exponents))
208 m4
209 (every
210 #'(lambda (x y z w) (= (max x y) (max z w)))
211 exponents1 exponents2 exponents3 exponents4))))))
212
213(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
214 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
215 (with-slots ((exponents1 exponents))
216 m1
217 (with-slots ((exponents2 exponents))
218 m2
219 (every #'>= exponents1 exponents2))))
220
221(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
222 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
223 (with-slots ((exponents1 exponents))
224 m1
225 (with-slots ((exponents2 exponents))
226 m2
227 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
228
229
230(defmethod r-lcm ((m1 monom) (m2 monom))
231 "Returns least common multiple of monomials M1 and M2."
232 (with-slots ((exponents1 exponents) (dimension1 dimension))
233 m1
234 (with-slots ((exponents2 exponents))
235 m2
236 (let* ((exponents (copy-seq exponents1))
237 (dimension dimension1))
238 (map-into exponents #'max exponents1 exponents2)
239 (make-instance 'monom :dimension dimension :exponents exponents)))))
240
241
242(defmethod r-gcd ((m1 monom) (m2 monom))
243 "Returns greatest common divisor of monomials M1 and M2."
244 (with-slots ((exponents1 exponents) (dimension1 dimension))
245 m1
246 (with-slots ((exponents2 exponents))
247 m2
248 (let* ((exponents (copy-seq exponents1))
249 (dimension dimension1))
250 (map-into exponents #'min exponents1 exponents2)
251 (make-instance 'monom :dimension dimension :exponents exponents)))))
252
253(defmethod r-depends-p ((m monom) k)
254 "Return T if the monomial M depends on variable number K."
255 (declare (type fixnum k))
256 (with-slots (exponents)
257 m
258 (plusp (elt exponents k))))
259
260(defmethod left-tensor-product-by ((self monom) (other monom))
261 (with-slots ((exponents1 exponents) (dimension1 dimension))
262 self
263 (with-slots ((exponents2 exponents) (dimension2 dimension))
264 other
265 (setf dimension1 (+ dimension1 dimension2)
266 exponents1 (concatenate 'vector exponents2 exponents1))))
267 self)
268
269(defmethod right-tensor-product-by ((self monom) (other monom))
270 (with-slots ((exponents1 exponents) (dimension1 dimension))
271 self
272 (with-slots ((exponents2 exponents) (dimension2 dimension))
273 other
274 (setf dimension1 (+ dimension1 dimension2)
275 exponents1 (concatenate 'vector exponents1 exponents2))))
276 self)
277
278(defmethod left-contract ((self monom) k)
279 "Drop the first K variables in monomial M."
280 (declare (fixnum k))
281 (with-slots (dimension exponents)
282 self
283 (setf dimension (- dimension k)
284 exponents (subseq exponents k)))
285 self)
286
287(defun make-monom-variable (nvars pos &optional (power 1)
288 &aux (m (make-instance 'monom :dimension nvars)))
289 "Construct a monomial in the polynomial ring
290RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
291which represents a single variable. It assumes number of variables
292NVARS and the variable is at position POS. Optionally, the variable
293may appear raised to power POWER. "
294 (declare (type fixnum nvars pos power) (type monom m))
295 (with-slots (exponents)
296 m
297 (setf (elt exponents pos) power)
298 m))
299
300(defmethod r->list ((m monom))
301 "A human-readable representation of a monomial M as a list of exponents."
302 (coerce (monom-exponents m) 'list))
303
304(defmethod r-dimension ((self monom))
305 (monom-dimension self))
306
307(defmethod r-exponents ((self monom))
308 (monom-exponents self))
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