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source: branches/f4grobner/monom.lisp@ 2294

Last change on this file since 2294 was 2294, 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 nil :exponents nil :exponent nil))
62
63(defmethod print-object ((self monom) stream)
64 (format stream "#<MONOM DIMENSION=~A EXPONENTS=~A>"
65 (slot-value self 'dimension)
66 (slot-value self 'exponents)))
67
68#|
69(defmethod initialize-instance :before ((self monom)
70 &rest
71 args
72 &key
73 &allow-other-keys)
74 (format t "MONOM::INITIALIZE-INSTANCE called with:~&ARGS: ~W.~%" args))
75|#
76
77(defmethod initialize-instance ((self monom)
78 ;;&rest args
79 &key
80 dimension
81 exponents
82 exponent
83 &allow-other-keys
84 )
85 (let* ((new-dimension (cond (dimension dimension)
86 (exponents
87 (length exponents))
88 (t
89 (error "DIMENSION or EXPONENTS must not be NIL"))))
90 (new-exponents (cond
91 ;; when exponents are supplied
92 (exponents
93 (make-array (list new-dimension) :initial-contents exponents))
94 ;; when all exponents are to be identical
95 (exponent
96 (make-array (list new-dimension) :initial-element exponent
97 :element-type 'exponent))
98 ;; otherwise, all exponents are zero
99 (t
100 (make-array (list new-dimension) :element-type 'exponent :initial-element 0)))))
101 (setf (slot-value self 'dimension) new-dimension
102 (slot-value self 'exponents) new-exponents)))
103
104
105
106;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
107;;
108;; Operations on monomials
109;;
110;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
111
112(defmethod r-dimension ((m monom))
113 (monom-dimension m))
114
115(defmethod r-elt ((m monom) index)
116 "Return the power in the monomial M of variable number INDEX."
117 (with-slots (exponents)
118 m
119 (elt exponents index)))
120
121(defmethod (setf r-elt) (new-value (m monom) index)
122 "Return the power in the monomial M of variable number INDEX."
123 (with-slots (exponents)
124 m
125 (setf (elt exponents index) new-value)))
126
127(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
128 "Return the todal degree of a monomoal M. Optinally, a range
129of variables may be specified with arguments START and END."
130 (declare (type fixnum start end))
131 (with-slots (exponents)
132 m
133 (reduce #'+ exponents :start start :end end)))
134
135
136(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
137 "Return the sugar of a monomial M. Optinally, a range
138of variables may be specified with arguments START and END."
139 (declare (type fixnum start end))
140 (r-total-degree m start end))
141
142(defmethod r* ((m1 monom) (m2 monom))
143 "Multiply monomial M1 by monomial M2."
144 (with-slots ((exponents1 exponents) dimension)
145 m1
146 (with-slots ((exponents2 exponents))
147 m2
148 (let* ((exponents (copy-seq exponents1)))
149 (map-into exponents #'+ exponents1 exponents2)
150 (make-instance 'monom :dimension dimension :exponents exponents)))))
151
152
153
154(defmethod r/ ((m1 monom) (m2 monom))
155 "Divide monomial M1 by monomial M2."
156 (with-slots ((exponents1 exponents))
157 m1
158 (with-slots ((exponents2 exponents))
159 m2
160 (let* ((exponents (copy-seq exponents1))
161 (dimension (reduce #'+ exponents)))
162 (map-into exponents #'- exponents1 exponents2)
163 (make-instance 'monom :dimension dimension :exponents exponents)))))
164
165(defmethod r-divides-p ((m1 monom) (m2 monom))
166 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
167 (with-slots ((exponents1 exponents))
168 m1
169 (with-slots ((exponents2 exponents))
170 m2
171 (every #'<= exponents1 exponents2))))
172
173
174(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
175 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
176 (every #'(lambda (x y z) (<= x (max y z)))
177 m1 m2 m3))
178
179
180(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
181 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
182 (declare (type monom m1 m2 m3 m4))
183 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
184 m1 m2 m3 m4))
185
186(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
187 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
188 (with-slots ((exponents1 exponents))
189 m1
190 (with-slots ((exponents2 exponents))
191 m2
192 (with-slots ((exponents3 exponents))
193 m3
194 (with-slots ((exponents4 exponents))
195 m4
196 (every
197 #'(lambda (x y z w) (= (max x y) (max z w)))
198 exponents1 exponents2 exponents3 exponents4))))))
199
200(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
201 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
202 (with-slots ((exponents1 exponents))
203 m1
204 (with-slots ((exponents2 exponents))
205 m2
206 (every #'>= exponents1 exponents2))))
207
208(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
209 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
210 (with-slots ((exponents1 exponents))
211 m1
212 (with-slots ((exponents2 exponents))
213 m2
214 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
215
216
217(defmethod r-equalp ((m1 monom) (m2 monom))
218 "Returns T if two monomials M1 and M2 are equal."
219 (with-slots ((exponents1 exponents))
220 m1
221 (with-slots ((exponents2 exponents))
222 m2
223 (every #'= exponents1 exponents2))))
224
225(defmethod r-lcm ((m1 monom) (m2 monom))
226 "Returns least common multiple of monomials M1 and M2."
227 (with-slots ((exponents1 exponents))
228 m1
229 (with-slots ((exponents2 exponents))
230 m2
231 (let* ((exponents (copy-seq exponents1))
232 (dimension (reduce #'+ exponents)))
233 (map-into exponents #'max exponents1 exponents2)
234 (make-instance 'monom :dimension dimension :exponents exponents)))))
235
236
237(defmethod r-gcd ((m1 monom) (m2 monom))
238 "Returns greatest common divisor of monomials M1 and M2."
239 (with-slots ((exponents1 exponents))
240 m1
241 (with-slots ((exponents2 exponents))
242 m2
243 (let* ((exponents (copy-seq exponents1))
244 (dimension (reduce #'+ exponents)))
245 (map-into exponents #'min exponents1 exponents2)
246 (make-instance 'monom :dimension dimension :exponents exponents)))))
247
248(defmethod r-depends-p ((m monom) k)
249 "Return T if the monomial M depends on variable number K."
250 (declare (type fixnum k))
251 (with-slots (exponents)
252 m
253 (plusp (elt exponents k))))
254
255(defmethod r-tensor-product ((m1 monom) (m2 monom)
256 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
257 (declare (fixnum dimension))
258 (with-slots ((exponents1 exponents))
259 m1
260 (with-slots ((exponents2 exponents))
261 m2
262 (make-instance 'monom
263 :dimension dimension
264 :exponents (concatenate 'vector exponents1 exponents2)))))
265
266(defmethod r-contract ((m monom) k)
267 "Drop the first K variables in monomial M."
268 (declare (fixnum k))
269 (with-slots (dimension exponents)
270 m
271 (setf dimension (- dimension k)
272 exponents (subseq exponents k))))
273
274(defun make-monom-variable (nvars pos &optional (power 1)
275 &aux (m (make-instance 'monom :dimension nvars)))
276 "Construct a monomial in the polynomial ring
277RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
278which represents a single variable. It assumes number of variables
279NVARS and the variable is at position POS. Optionally, the variable
280may appear raised to power POWER. "
281 (declare (type fixnum nvars pos power) (type monom m))
282 (with-slots (exponents)
283 m
284 (setf (elt exponents pos) power)
285 m))
286
287(defmethod r->list ((m monom))
288 "A human-readable representation of a monomial M as a list of exponents."
289 (coerce (monom-exponents m) 'list))
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