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source: branches/f4grobner/monom.lisp@ 2222

Last change on this file since 2222 was 2222, 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 "MAKE-MONOM"
46 "MONOM-DIMENSION"
47 "MONOM-EXPONENTS"
48 "MAKE-MONOM-VARIABLE"))
49
50(in-package :monom)
51
52(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
53
54(deftype exponent ()
55 "Type of exponent in a monomial."
56 'fixnum)
57
58(defclass monom ()
59 ((dimension :initarg :dimension :accessor monom-dimension)
60 (exponents :initarg :exponents :accessor monom-exponents))
61 (:default-initargs :dimension 0 :exponents nil :exponent 0))
62
63(defmethod print-object ((m monom) stream)
64 (princ (slot-value m 'exponents) stream))
65
66#|
67(defmethod initialize-instance :after ((self monom) &rest args &key)
68 (format t "INITIALIZE-INSTANCE-INSTANCE called with SELF ~A, args ~A.~%"
69 self args)
70 (call-next-method))
71|#
72
73
74(defmethod make-instance :around ((self monom)
75 &key
76 (dimension nil dimension-suppied-p)
77 (exponents nil exponents-supplied-p)
78 (exponent nil exponent-supplied-p))
79 "A constructor (factory) of monomials. If DIMENSION is given, a
80sequence of DIMENSION elements of type EXPONENT is constructed, where
81individual elements are the value of EXPONENT, which defaults
82to 0. Alternatively, all elements may be specified as a list
83EXPONENTS."
84 (format t "MAKE-INSTANCE called with DIMENSION ~A(~A), EXPONENTS ~A(~A), EXPONENT ~A(~A).~%"
85 dimension dimension-suppied-p
86 exponents exponents-supplied-p
87 exponent exponent-supplied-p)
88 (call-next-method :dimension dimension :exponents exponents))
89
90 #|
91 (let ((new-dimension (cond (dimension-suppied-p dimension)
92 (exponents-supplied-p
93 (length exponents))
94 (t
95 (error "You must provide DIMENSION or EXPONENTS"))))
96 (new-exponents (cond
97 ;; when exponents are supplied
98 (exponents-supplied-p
99 (make-array (list dimension) :initial-contents exponents
100 :element-type 'exponent))
101 ;; when all exponents are to be identical
102 (exponent-supplied-p
103 (make-array (list dimension) :initial-element exponent
104 :element-type 'exponent))
105 ;; otherwise, all exponents are zero
106 (t
107 (make-array (list dimension) :element-type 'exponent :initial-element 0)))))
108 |#
109
110
111;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
112;;
113;; Operations on monomials
114;;
115;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
116
117(defmethod r-dimension ((m monom))
118 (monom-dimension m))
119
120(defmethod r-elt ((m monom) index)
121 "Return the power in the monomial M of variable number INDEX."
122 (with-slots (exponents)
123 m
124 (elt exponents index)))
125
126(defmethod (setf r-elt) (new-value (m monom) index)
127 "Return the power in the monomial M of variable number INDEX."
128 (with-slots (exponents)
129 m
130 (setf (elt exponents index) new-value)))
131
132(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
133 "Return the todal degree of a monomoal M. Optinally, a range
134of variables may be specified with arguments START and END."
135 (declare (type fixnum start end))
136 (with-slots (exponents)
137 m
138 (reduce #'+ exponents :start start :end end)))
139
140
141(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
142 "Return the sugar of a monomial M. Optinally, a range
143of variables may be specified with arguments START and END."
144 (declare (type fixnum start end))
145 (r-total-degree m start end))
146
147(defmethod r* ((m1 monom) (m2 monom))
148 "Multiply monomial M1 by monomial M2."
149 (with-slots ((exponents1 exponents) dimension)
150 m1
151 (with-slots ((exponents2 exponents))
152 m2
153 (let* ((exponents (copy-seq exponents1)))
154 (map-into exponents #'+ exponents1 exponents2)
155 (make-instance 'monom :dimension dimension :exponents exponents)))))
156
157
158
159(defmethod r/ ((m1 monom) (m2 monom))
160 "Divide monomial M1 by monomial M2."
161 (with-slots ((exponents1 exponents))
162 m1
163 (with-slots ((exponents2 exponents))
164 m2
165 (let* ((exponents (copy-seq exponents1))
166 (dimension (reduce #'+ exponents)))
167 (map-into exponents #'- exponents1 exponents2)
168 (make-instance 'monom :dimension dimension :exponents exponents)))))
169
170(defmethod r-divides-p ((m1 monom) (m2 monom))
171 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
172 (with-slots ((exponents1 exponents))
173 m1
174 (with-slots ((exponents2 exponents))
175 m2
176 (every #'<= exponents1 exponents2))))
177
178
179(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
180 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
181 (every #'(lambda (x y z) (<= x (max y z)))
182 m1 m2 m3))
183
184
185(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
186 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
187 (declare (type monom m1 m2 m3 m4))
188 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
189 m1 m2 m3 m4))
190
191(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
192 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
193 (with-slots ((exponents1 exponents))
194 m1
195 (with-slots ((exponents2 exponents))
196 m2
197 (with-slots ((exponents3 exponents))
198 m3
199 (with-slots ((exponents4 exponents))
200 m4
201 (every
202 #'(lambda (x y z w) (= (max x y) (max z w)))
203 exponents1 exponents2 exponents3 exponents4))))))
204
205(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
206 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
207 (with-slots ((exponents1 exponents))
208 m1
209 (with-slots ((exponents2 exponents))
210 m2
211 (every #'>= exponents1 exponents2))))
212
213(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
214 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
215 (with-slots ((exponents1 exponents))
216 m1
217 (with-slots ((exponents2 exponents))
218 m2
219 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
220
221
222(defmethod r-equalp ((m1 monom) (m2 monom))
223 "Returns T if two monomials M1 and M2 are equal."
224 (with-slots ((exponents1 exponents))
225 m1
226 (with-slots ((exponents2 exponents))
227 m2
228 (every #'= exponents1 exponents2))))
229
230(defmethod r-lcm ((m1 monom) (m2 monom))
231 "Returns least common multiple of monomials M1 and M2."
232 (with-slots ((exponents1 exponents))
233 m1
234 (with-slots ((exponents2 exponents))
235 m2
236 (let* ((exponents (copy-seq exponents1))
237 (dimension (reduce #'+ exponents)))
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))
245 m1
246 (with-slots ((exponents2 exponents))
247 m2
248 (let* ((exponents (copy-seq exponents1))
249 (dimension (reduce #'+ exponents)))
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 r-tensor-product ((m1 monom) (m2 monom)
261 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
262 (declare (fixnum dimension))
263 (with-slots ((exponents1 exponents))
264 m1
265 (with-slots ((exponents2 exponents))
266 m2
267 (make-instance 'monom
268 :dimension dimension
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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