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source: branches/f4grobner/monom.lisp@ 2281

Last change on this file since 2281 was 2281, 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(defmethod initialize-instance :before ((self monom)
69 &rest
70 args
71 &key
72 &allow-other-keys)
73 (format t "INITIALIZE-INSTANCE called with:~&ARGS: ~W.~%" args))
74
75(defmethod initialize-instance :after ((self monom)
76 ;;&rest args
77 &key
78 dimension
79 exponents
80 exponent
81 &allow-other-keys
82 )
83 (let* ((new-dimension (cond (dimension dimension)
84 (exponents
85 (length exponents))
86 (t
87 (error "DIMENSION or EXPONENTS must not be NIL"))))
88 (new-exponents (cond
89 ;; when exponents are supplied
90 (exponents
91 (make-array (list new-dimension) :initial-contents exponents))
92 ;; when all exponents are to be identical
93 (exponent
94 (make-array (list new-dimension) :initial-element exponent
95 :element-type 'exponent))
96 ;; otherwise, all exponents are zero
97 (t
98 (make-array (list new-dimension) :element-type 'exponent :initial-element 0)))))
99 (setf (slot-value self 'dimension) new-dimension
100 (slot-value self 'exponents) new-exponents)
101 (call-next-method)))
102
103
104
105;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
106;;
107;; Operations on monomials
108;;
109;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
110
111(defmethod r-dimension ((m monom))
112 (monom-dimension m))
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 (r-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 (r-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 r* ((m1 monom) (m2 monom))
142 "Multiply monomial M1 by monomial M2."
143 (with-slots ((exponents1 exponents) dimension)
144 m1
145 (with-slots ((exponents2 exponents))
146 m2
147 (let* ((exponents (copy-seq exponents1)))
148 (map-into exponents #'+ exponents1 exponents2)
149 (make-instance 'monom :dimension dimension :exponents exponents)))))
150
151
152
153(defmethod r/ ((m1 monom) (m2 monom))
154 "Divide monomial M1 by monomial M2."
155 (with-slots ((exponents1 exponents))
156 m1
157 (with-slots ((exponents2 exponents))
158 m2
159 (let* ((exponents (copy-seq exponents1))
160 (dimension (reduce #'+ exponents)))
161 (map-into exponents #'- exponents1 exponents2)
162 (make-instance 'monom :dimension dimension :exponents exponents)))))
163
164(defmethod r-divides-p ((m1 monom) (m2 monom))
165 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
166 (with-slots ((exponents1 exponents))
167 m1
168 (with-slots ((exponents2 exponents))
169 m2
170 (every #'<= exponents1 exponents2))))
171
172
173(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
174 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
175 (every #'(lambda (x y z) (<= x (max y z)))
176 m1 m2 m3))
177
178
179(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
180 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
181 (declare (type monom m1 m2 m3 m4))
182 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
183 m1 m2 m3 m4))
184
185(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
186 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
187 (with-slots ((exponents1 exponents))
188 m1
189 (with-slots ((exponents2 exponents))
190 m2
191 (with-slots ((exponents3 exponents))
192 m3
193 (with-slots ((exponents4 exponents))
194 m4
195 (every
196 #'(lambda (x y z w) (= (max x y) (max z w)))
197 exponents1 exponents2 exponents3 exponents4))))))
198
199(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
200 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
201 (with-slots ((exponents1 exponents))
202 m1
203 (with-slots ((exponents2 exponents))
204 m2
205 (every #'>= exponents1 exponents2))))
206
207(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
208 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
209 (with-slots ((exponents1 exponents))
210 m1
211 (with-slots ((exponents2 exponents))
212 m2
213 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
214
215
216(defmethod r-equalp ((m1 monom) (m2 monom))
217 "Returns T if two monomials M1 and M2 are equal."
218 (with-slots ((exponents1 exponents))
219 m1
220 (with-slots ((exponents2 exponents))
221 m2
222 (every #'= exponents1 exponents2))))
223
224(defmethod r-lcm ((m1 monom) (m2 monom))
225 "Returns least common multiple of monomials M1 and M2."
226 (with-slots ((exponents1 exponents))
227 m1
228 (with-slots ((exponents2 exponents))
229 m2
230 (let* ((exponents (copy-seq exponents1))
231 (dimension (reduce #'+ exponents)))
232 (map-into exponents #'max exponents1 exponents2)
233 (make-instance 'monom :dimension dimension :exponents exponents)))))
234
235
236(defmethod r-gcd ((m1 monom) (m2 monom))
237 "Returns greatest common divisor of monomials M1 and M2."
238 (with-slots ((exponents1 exponents))
239 m1
240 (with-slots ((exponents2 exponents))
241 m2
242 (let* ((exponents (copy-seq exponents1))
243 (dimension (reduce #'+ exponents)))
244 (map-into exponents #'min exponents1 exponents2)
245 (make-instance 'monom :dimension dimension :exponents exponents)))))
246
247(defmethod r-depends-p ((m monom) k)
248 "Return T if the monomial M depends on variable number K."
249 (declare (type fixnum k))
250 (with-slots (exponents)
251 m
252 (plusp (elt exponents k))))
253
254(defmethod r-tensor-product ((m1 monom) (m2 monom)
255 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
256 (declare (fixnum dimension))
257 (with-slots ((exponents1 exponents))
258 m1
259 (with-slots ((exponents2 exponents))
260 m2
261 (make-instance 'monom
262 :dimension dimension
263 :exponents (concatenate 'vector exponents1 exponents2)))))
264
265(defmethod r-contract ((m monom) k)
266 "Drop the first K variables in monomial M."
267 (declare (fixnum k))
268 (with-slots (dimension exponents)
269 m
270 (setf dimension (- dimension k)
271 exponents (subseq exponents k))))
272
273(defun make-monom-variable (nvars pos &optional (power 1)
274 &aux (m (make-instance 'monom :dimension nvars)))
275 "Construct a monomial in the polynomial ring
276RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
277which represents a single variable. It assumes number of variables
278NVARS and the variable is at position POS. Optionally, the variable
279may appear raised to power POWER. "
280 (declare (type fixnum nvars pos power) (type monom m))
281 (with-slots (exponents)
282 m
283 (setf (elt exponents pos) power)
284 m))
285
286(defmethod r->list ((m monom))
287 "A human-readable representation of a monomial M as a list of exponents."
288 (coerce (monom-exponents m) 'list))
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