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source: branches/f4grobner/monom.lisp@ 2295

Last change on this file since 2295 was 2295, checked in by Marek Rychlik, 10 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 "MONOM::INITIALIZE-INSTANCE called with:~&ARGS: ~W.~%" args))
74
75(defmethod initialize-instance ((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
102
103
104;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
105;;
106;; Operations on monomials
107;;
108;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
109
110(defmethod r-dimension ((m monom))
111 (monom-dimension m))
112
113(defmethod r-elt ((m monom) index)
114 "Return the power in the monomial M of variable number INDEX."
115 (with-slots (exponents)
116 m
117 (elt exponents index)))
118
119(defmethod (setf r-elt) (new-value (m monom) index)
120 "Return the power in the monomial M of variable number INDEX."
121 (with-slots (exponents)
122 m
123 (setf (elt exponents index) new-value)))
124
125(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
126 "Return the todal degree of a monomoal M. Optinally, a range
127of variables may be specified with arguments START and END."
128 (declare (type fixnum start end))
129 (with-slots (exponents)
130 m
131 (reduce #'+ exponents :start start :end end)))
132
133
134(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
135 "Return the sugar of a monomial M. Optinally, a range
136of variables may be specified with arguments START and END."
137 (declare (type fixnum start end))
138 (r-total-degree m start end))
139
140(defmethod r* ((m1 monom) (m2 monom))
141 "Multiply monomial M1 by monomial M2."
142 (with-slots ((exponents1 exponents) dimension)
143 m1
144 (with-slots ((exponents2 exponents))
145 m2
146 (let* ((exponents (copy-seq exponents1)))
147 (map-into exponents #'+ exponents1 exponents2)
148 (make-instance 'monom :dimension dimension :exponents exponents)))))
149
150
151
152(defmethod r/ ((m1 monom) (m2 monom))
153 "Divide monomial M1 by monomial M2."
154 (with-slots ((exponents1 exponents))
155 m1
156 (with-slots ((exponents2 exponents))
157 m2
158 (let* ((exponents (copy-seq exponents1))
159 (dimension (reduce #'+ exponents)))
160 (map-into exponents #'- exponents1 exponents2)
161 (make-instance 'monom :dimension dimension :exponents exponents)))))
162
163(defmethod r-divides-p ((m1 monom) (m2 monom))
164 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
165 (with-slots ((exponents1 exponents))
166 m1
167 (with-slots ((exponents2 exponents))
168 m2
169 (every #'<= exponents1 exponents2))))
170
171
172(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
173 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
174 (every #'(lambda (x y z) (<= x (max y z)))
175 m1 m2 m3))
176
177
178(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
179 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
180 (declare (type monom m1 m2 m3 m4))
181 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
182 m1 m2 m3 m4))
183
184(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
185 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
186 (with-slots ((exponents1 exponents))
187 m1
188 (with-slots ((exponents2 exponents))
189 m2
190 (with-slots ((exponents3 exponents))
191 m3
192 (with-slots ((exponents4 exponents))
193 m4
194 (every
195 #'(lambda (x y z w) (= (max x y) (max z w)))
196 exponents1 exponents2 exponents3 exponents4))))))
197
198(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
199 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
200 (with-slots ((exponents1 exponents))
201 m1
202 (with-slots ((exponents2 exponents))
203 m2
204 (every #'>= exponents1 exponents2))))
205
206(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
207 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
208 (with-slots ((exponents1 exponents))
209 m1
210 (with-slots ((exponents2 exponents))
211 m2
212 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
213
214
215(defmethod r-equalp ((m1 monom) (m2 monom))
216 "Returns T if two monomials M1 and M2 are equal."
217 (with-slots ((exponents1 exponents))
218 m1
219 (with-slots ((exponents2 exponents))
220 m2
221 (every #'= exponents1 exponents2))))
222
223(defmethod r-lcm ((m1 monom) (m2 monom))
224 "Returns least common multiple of monomials M1 and M2."
225 (with-slots ((exponents1 exponents))
226 m1
227 (with-slots ((exponents2 exponents))
228 m2
229 (let* ((exponents (copy-seq exponents1))
230 (dimension (reduce #'+ exponents)))
231 (map-into exponents #'max exponents1 exponents2)
232 (make-instance 'monom :dimension dimension :exponents exponents)))))
233
234
235(defmethod r-gcd ((m1 monom) (m2 monom))
236 "Returns greatest common divisor of monomials M1 and M2."
237 (with-slots ((exponents1 exponents))
238 m1
239 (with-slots ((exponents2 exponents))
240 m2
241 (let* ((exponents (copy-seq exponents1))
242 (dimension (reduce #'+ exponents)))
243 (map-into exponents #'min exponents1 exponents2)
244 (make-instance 'monom :dimension dimension :exponents exponents)))))
245
246(defmethod r-depends-p ((m monom) k)
247 "Return T if the monomial M depends on variable number K."
248 (declare (type fixnum k))
249 (with-slots (exponents)
250 m
251 (plusp (elt exponents k))))
252
253(defmethod r-tensor-product ((m1 monom) (m2 monom)
254 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
255 (declare (fixnum dimension))
256 (with-slots ((exponents1 exponents))
257 m1
258 (with-slots ((exponents2 exponents))
259 m2
260 (make-instance 'monom
261 :dimension dimension
262 :exponents (concatenate 'vector exponents1 exponents2)))))
263
264(defmethod r-contract ((m monom) k)
265 "Drop the first K variables in monomial M."
266 (declare (fixnum k))
267 (with-slots (dimension exponents)
268 m
269 (setf dimension (- dimension k)
270 exponents (subseq exponents k))))
271
272(defun make-monom-variable (nvars pos &optional (power 1)
273 &aux (m (make-instance 'monom :dimension nvars)))
274 "Construct a monomial in the polynomial ring
275RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
276which represents a single variable. It assumes number of variables
277NVARS and the variable is at position POS. Optionally, the variable
278may appear raised to power POWER. "
279 (declare (type fixnum nvars pos power) (type monom m))
280 (with-slots (exponents)
281 m
282 (setf (elt exponents pos) power)
283 m))
284
285(defmethod r->list ((m monom))
286 "A human-readable representation of a monomial M as a list of exponents."
287 (coerce (monom-exponents m) 'list))
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