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source: branches/f4grobner/monom.lisp@ 2276

Last change on this file since 2276 was 2274, 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 ((self monom)
69 ;;&rest args
70 &key
71 dimension
72 exponents
73 exponent
74 &allow-other-keys
75 )
76 ;;(format t "INITIALIZE-INSTANCE called with:~&ARGS: ~W.~%" args)
77 (let* ((new-dimension (cond (dimension dimension)
78 (exponents
79 (length exponents))
80 (t
81 (error "DIMENSION or EXPONENTS must not be NIL"))))
82 (new-exponents (cond
83 ;; when exponents are supplied
84 (exponents
85 (make-array (list new-dimension) :initial-contents exponents))
86 ;; when all exponents are to be identical
87 (exponent
88 (make-array (list new-dimension) :initial-element exponent
89 :element-type 'exponent))
90 ;; otherwise, all exponents are zero
91 (t
92 (make-array (list new-dimension) :element-type 'exponent :initial-element 0)))))
93 (setf (slot-value self 'dimension) new-dimension
94 (slot-value self 'exponents) new-exponents)))
95
96
97
98;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
99;;
100;; Operations on monomials
101;;
102;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
103
104(defmethod r-dimension ((m monom))
105 (monom-dimension m))
106
107(defmethod r-elt ((m monom) index)
108 "Return the power in the monomial M of variable number INDEX."
109 (with-slots (exponents)
110 m
111 (elt exponents index)))
112
113(defmethod (setf r-elt) (new-value (m monom) index)
114 "Return the power in the monomial M of variable number INDEX."
115 (with-slots (exponents)
116 m
117 (setf (elt exponents index) new-value)))
118
119(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
120 "Return the todal degree of a monomoal M. Optinally, a range
121of variables may be specified with arguments START and END."
122 (declare (type fixnum start end))
123 (with-slots (exponents)
124 m
125 (reduce #'+ exponents :start start :end end)))
126
127
128(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
129 "Return the sugar of a monomial M. Optinally, a range
130of variables may be specified with arguments START and END."
131 (declare (type fixnum start end))
132 (r-total-degree m start end))
133
134(defmethod r* ((m1 monom) (m2 monom))
135 "Multiply monomial M1 by monomial M2."
136 (with-slots ((exponents1 exponents) dimension)
137 m1
138 (with-slots ((exponents2 exponents))
139 m2
140 (let* ((exponents (copy-seq exponents1)))
141 (map-into exponents #'+ exponents1 exponents2)
142 (make-instance 'monom :dimension dimension :exponents exponents)))))
143
144
145
146(defmethod r/ ((m1 monom) (m2 monom))
147 "Divide monomial M1 by monomial M2."
148 (with-slots ((exponents1 exponents))
149 m1
150 (with-slots ((exponents2 exponents))
151 m2
152 (let* ((exponents (copy-seq exponents1))
153 (dimension (reduce #'+ exponents)))
154 (map-into exponents #'- exponents1 exponents2)
155 (make-instance 'monom :dimension dimension :exponents exponents)))))
156
157(defmethod r-divides-p ((m1 monom) (m2 monom))
158 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
159 (with-slots ((exponents1 exponents))
160 m1
161 (with-slots ((exponents2 exponents))
162 m2
163 (every #'<= exponents1 exponents2))))
164
165
166(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
167 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
168 (every #'(lambda (x y z) (<= x (max y z)))
169 m1 m2 m3))
170
171
172(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
173 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
174 (declare (type monom m1 m2 m3 m4))
175 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
176 m1 m2 m3 m4))
177
178(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
179 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
180 (with-slots ((exponents1 exponents))
181 m1
182 (with-slots ((exponents2 exponents))
183 m2
184 (with-slots ((exponents3 exponents))
185 m3
186 (with-slots ((exponents4 exponents))
187 m4
188 (every
189 #'(lambda (x y z w) (= (max x y) (max z w)))
190 exponents1 exponents2 exponents3 exponents4))))))
191
192(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
193 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
194 (with-slots ((exponents1 exponents))
195 m1
196 (with-slots ((exponents2 exponents))
197 m2
198 (every #'>= exponents1 exponents2))))
199
200(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
201 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
202 (with-slots ((exponents1 exponents))
203 m1
204 (with-slots ((exponents2 exponents))
205 m2
206 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
207
208
209(defmethod r-equalp ((m1 monom) (m2 monom))
210 "Returns T if two monomials M1 and M2 are equal."
211 (with-slots ((exponents1 exponents))
212 m1
213 (with-slots ((exponents2 exponents))
214 m2
215 (every #'= exponents1 exponents2))))
216
217(defmethod r-lcm ((m1 monom) (m2 monom))
218 "Returns least common multiple of monomials M1 and M2."
219 (with-slots ((exponents1 exponents))
220 m1
221 (with-slots ((exponents2 exponents))
222 m2
223 (let* ((exponents (copy-seq exponents1))
224 (dimension (reduce #'+ exponents)))
225 (map-into exponents #'max exponents1 exponents2)
226 (make-instance 'monom :dimension dimension :exponents exponents)))))
227
228
229(defmethod r-gcd ((m1 monom) (m2 monom))
230 "Returns greatest common divisor of monomials M1 and M2."
231 (with-slots ((exponents1 exponents))
232 m1
233 (with-slots ((exponents2 exponents))
234 m2
235 (let* ((exponents (copy-seq exponents1))
236 (dimension (reduce #'+ exponents)))
237 (map-into exponents #'min exponents1 exponents2)
238 (make-instance 'monom :dimension dimension :exponents exponents)))))
239
240(defmethod r-depends-p ((m monom) k)
241 "Return T if the monomial M depends on variable number K."
242 (declare (type fixnum k))
243 (with-slots (exponents)
244 m
245 (plusp (elt exponents k))))
246
247(defmethod r-tensor-product ((m1 monom) (m2 monom)
248 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
249 (declare (fixnum dimension))
250 (with-slots ((exponents1 exponents))
251 m1
252 (with-slots ((exponents2 exponents))
253 m2
254 (make-instance 'monom
255 :dimension dimension
256 :exponents (concatenate 'vector exponents1 exponents2)))))
257
258(defmethod r-contract ((m monom) k)
259 "Drop the first K variables in monomial M."
260 (declare (fixnum k))
261 (with-slots (dimension exponents)
262 m
263 (setf dimension (- dimension k)
264 exponents (subseq exponents k))))
265
266(defun make-monom-variable (nvars pos &optional (power 1)
267 &aux (m (make-instance 'monom :dimension nvars)))
268 "Construct a monomial in the polynomial ring
269RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
270which represents a single variable. It assumes number of variables
271NVARS and the variable is at position POS. Optionally, the variable
272may appear raised to power POWER. "
273 (declare (type fixnum nvars pos power) (type monom m))
274 (with-slots (exponents)
275 m
276 (setf (elt exponents pos) power)
277 m))
278
279(defmethod r->list ((m monom))
280 "A human-readable representation of a monomial M as a list of exponents."
281 (coerce (monom-exponents m) 'list))
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