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source: branches/f4grobner/monom.lisp@ 2241

Last change on this file since 2241 was 2241, 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 0 :exponents nil))
62
63(defmethod print-object ((m monom) stream)
64 (princ (slot-value m 'exponents) stream))
65
66(defmethod initialize-instance :after ((self monom) &rest args &key &allow-other-keys)
67 (format t "INITIALIZE-INSTANCE called with args ~W.~%" args))
68
69
70 #|
71 (let ((new-dimension (cond (dimension-suppied-p dimension)
72 (exponents-supplied-p
73 (length exponents))
74 (t
75 (error "You must provide DIMENSION or EXPONENTS"))))
76 (new-exponents (cond
77 ;; when exponents are supplied
78 (exponents-supplied-p
79 (make-array (list dimension) :initial-contents exponents
80 :element-type 'exponent))
81 ;; when all exponents are to be identical
82 (exponent-supplied-p
83 (make-array (list dimension) :initial-element exponent
84 :element-type 'exponent))
85 ;; otherwise, all exponents are zero
86 (t
87 (make-array (list dimension) :element-type 'exponent :initial-element 0)))))
88 |#
89
90
91
92;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
93;;
94;; Operations on monomials
95;;
96;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
97
98(defmethod r-dimension ((m monom))
99 (monom-dimension m))
100
101(defmethod r-elt ((m monom) index)
102 "Return the power in the monomial M of variable number INDEX."
103 (with-slots (exponents)
104 m
105 (elt exponents index)))
106
107(defmethod (setf r-elt) (new-value (m monom) index)
108 "Return the power in the monomial M of variable number INDEX."
109 (with-slots (exponents)
110 m
111 (setf (elt exponents index) new-value)))
112
113(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
114 "Return the todal degree of a monomoal M. Optinally, a range
115of variables may be specified with arguments START and END."
116 (declare (type fixnum start end))
117 (with-slots (exponents)
118 m
119 (reduce #'+ exponents :start start :end end)))
120
121
122(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
123 "Return the sugar of a monomial M. Optinally, a range
124of variables may be specified with arguments START and END."
125 (declare (type fixnum start end))
126 (r-total-degree m start end))
127
128(defmethod r* ((m1 monom) (m2 monom))
129 "Multiply monomial M1 by monomial M2."
130 (with-slots ((exponents1 exponents) dimension)
131 m1
132 (with-slots ((exponents2 exponents))
133 m2
134 (let* ((exponents (copy-seq exponents1)))
135 (map-into exponents #'+ exponents1 exponents2)
136 (make-instance 'monom :dimension dimension :exponents exponents)))))
137
138
139
140(defmethod r/ ((m1 monom) (m2 monom))
141 "Divide monomial M1 by monomial M2."
142 (with-slots ((exponents1 exponents))
143 m1
144 (with-slots ((exponents2 exponents))
145 m2
146 (let* ((exponents (copy-seq exponents1))
147 (dimension (reduce #'+ exponents)))
148 (map-into exponents #'- exponents1 exponents2)
149 (make-instance 'monom :dimension dimension :exponents exponents)))))
150
151(defmethod r-divides-p ((m1 monom) (m2 monom))
152 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
153 (with-slots ((exponents1 exponents))
154 m1
155 (with-slots ((exponents2 exponents))
156 m2
157 (every #'<= exponents1 exponents2))))
158
159
160(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
161 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
162 (every #'(lambda (x y z) (<= x (max y z)))
163 m1 m2 m3))
164
165
166(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
167 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
168 (declare (type monom m1 m2 m3 m4))
169 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
170 m1 m2 m3 m4))
171
172(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
173 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
174 (with-slots ((exponents1 exponents))
175 m1
176 (with-slots ((exponents2 exponents))
177 m2
178 (with-slots ((exponents3 exponents))
179 m3
180 (with-slots ((exponents4 exponents))
181 m4
182 (every
183 #'(lambda (x y z w) (= (max x y) (max z w)))
184 exponents1 exponents2 exponents3 exponents4))))))
185
186(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
187 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
188 (with-slots ((exponents1 exponents))
189 m1
190 (with-slots ((exponents2 exponents))
191 m2
192 (every #'>= exponents1 exponents2))))
193
194(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
195 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
196 (with-slots ((exponents1 exponents))
197 m1
198 (with-slots ((exponents2 exponents))
199 m2
200 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
201
202
203(defmethod r-equalp ((m1 monom) (m2 monom))
204 "Returns T if two monomials M1 and M2 are equal."
205 (with-slots ((exponents1 exponents))
206 m1
207 (with-slots ((exponents2 exponents))
208 m2
209 (every #'= exponents1 exponents2))))
210
211(defmethod r-lcm ((m1 monom) (m2 monom))
212 "Returns least common multiple of monomials M1 and M2."
213 (with-slots ((exponents1 exponents))
214 m1
215 (with-slots ((exponents2 exponents))
216 m2
217 (let* ((exponents (copy-seq exponents1))
218 (dimension (reduce #'+ exponents)))
219 (map-into exponents #'max exponents1 exponents2)
220 (make-instance 'monom :dimension dimension :exponents exponents)))))
221
222
223(defmethod r-gcd ((m1 monom) (m2 monom))
224 "Returns greatest common divisor 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 #'min exponents1 exponents2)
232 (make-instance 'monom :dimension dimension :exponents exponents)))))
233
234(defmethod r-depends-p ((m monom) k)
235 "Return T if the monomial M depends on variable number K."
236 (declare (type fixnum k))
237 (with-slots (exponents)
238 m
239 (plusp (elt exponents k))))
240
241(defmethod r-tensor-product ((m1 monom) (m2 monom)
242 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
243 (declare (fixnum dimension))
244 (with-slots ((exponents1 exponents))
245 m1
246 (with-slots ((exponents2 exponents))
247 m2
248 (make-instance 'monom
249 :dimension dimension
250 :exponents (concatenate 'vector exponents1 exponents2)))))
251
252(defmethod r-contract ((m monom) k)
253 "Drop the first K variables in monomial M."
254 (declare (fixnum k))
255 (with-slots (dimension exponents)
256 m
257 (setf dimension (- dimension k)
258 exponents (subseq exponents k))))
259
260(defun make-monom-variable (nvars pos &optional (power 1)
261 &aux (m (make-instance 'monom :dimension nvars)))
262 "Construct a monomial in the polynomial ring
263RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
264which represents a single variable. It assumes number of variables
265NVARS and the variable is at position POS. Optionally, the variable
266may appear raised to power POWER. "
267 (declare (type fixnum nvars pos power) (type monom m))
268 (with-slots (exponents)
269 m
270 (setf (elt exponents pos) power)
271 m))
272
273(defmethod r->list ((m monom))
274 "A human-readable representation of a monomial M as a list of exponents."
275 (coerce (monom-exponents m) 'list))
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