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source: branches/f4grobner/monom.lisp@ 2277

Last change on this file since 2277 was 2277, 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 (call-next-method)))
96
97
98
99;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
100;;
101;; Operations on monomials
102;;
103;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
104
105(defmethod r-dimension ((m monom))
106 (monom-dimension m))
107
108(defmethod r-elt ((m monom) index)
109 "Return the power in the monomial M of variable number INDEX."
110 (with-slots (exponents)
111 m
112 (elt exponents index)))
113
114(defmethod (setf r-elt) (new-value (m monom) index)
115 "Return the power in the monomial M of variable number INDEX."
116 (with-slots (exponents)
117 m
118 (setf (elt exponents index) new-value)))
119
120(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
121 "Return the todal degree of a monomoal M. Optinally, a range
122of variables may be specified with arguments START and END."
123 (declare (type fixnum start end))
124 (with-slots (exponents)
125 m
126 (reduce #'+ exponents :start start :end end)))
127
128
129(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
130 "Return the sugar of a monomial M. Optinally, a range
131of variables may be specified with arguments START and END."
132 (declare (type fixnum start end))
133 (r-total-degree m start end))
134
135(defmethod r* ((m1 monom) (m2 monom))
136 "Multiply monomial M1 by monomial M2."
137 (with-slots ((exponents1 exponents) dimension)
138 m1
139 (with-slots ((exponents2 exponents))
140 m2
141 (let* ((exponents (copy-seq exponents1)))
142 (map-into exponents #'+ exponents1 exponents2)
143 (make-instance 'monom :dimension dimension :exponents exponents)))))
144
145
146
147(defmethod r/ ((m1 monom) (m2 monom))
148 "Divide monomial M1 by monomial M2."
149 (with-slots ((exponents1 exponents))
150 m1
151 (with-slots ((exponents2 exponents))
152 m2
153 (let* ((exponents (copy-seq exponents1))
154 (dimension (reduce #'+ exponents)))
155 (map-into exponents #'- exponents1 exponents2)
156 (make-instance 'monom :dimension dimension :exponents exponents)))))
157
158(defmethod r-divides-p ((m1 monom) (m2 monom))
159 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
160 (with-slots ((exponents1 exponents))
161 m1
162 (with-slots ((exponents2 exponents))
163 m2
164 (every #'<= exponents1 exponents2))))
165
166
167(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
168 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
169 (every #'(lambda (x y z) (<= x (max y z)))
170 m1 m2 m3))
171
172
173(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
174 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
175 (declare (type monom m1 m2 m3 m4))
176 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
177 m1 m2 m3 m4))
178
179(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
180 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
181 (with-slots ((exponents1 exponents))
182 m1
183 (with-slots ((exponents2 exponents))
184 m2
185 (with-slots ((exponents3 exponents))
186 m3
187 (with-slots ((exponents4 exponents))
188 m4
189 (every
190 #'(lambda (x y z w) (= (max x y) (max z w)))
191 exponents1 exponents2 exponents3 exponents4))))))
192
193(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
194 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
195 (with-slots ((exponents1 exponents))
196 m1
197 (with-slots ((exponents2 exponents))
198 m2
199 (every #'>= exponents1 exponents2))))
200
201(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
202 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
203 (with-slots ((exponents1 exponents))
204 m1
205 (with-slots ((exponents2 exponents))
206 m2
207 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
208
209
210(defmethod r-equalp ((m1 monom) (m2 monom))
211 "Returns T if two monomials M1 and M2 are equal."
212 (with-slots ((exponents1 exponents))
213 m1
214 (with-slots ((exponents2 exponents))
215 m2
216 (every #'= exponents1 exponents2))))
217
218(defmethod r-lcm ((m1 monom) (m2 monom))
219 "Returns least common multiple of monomials M1 and M2."
220 (with-slots ((exponents1 exponents))
221 m1
222 (with-slots ((exponents2 exponents))
223 m2
224 (let* ((exponents (copy-seq exponents1))
225 (dimension (reduce #'+ exponents)))
226 (map-into exponents #'max exponents1 exponents2)
227 (make-instance 'monom :dimension dimension :exponents exponents)))))
228
229
230(defmethod r-gcd ((m1 monom) (m2 monom))
231 "Returns greatest common divisor of monomials M1 and M2."
232 (with-slots ((exponents1 exponents))
233 m1
234 (with-slots ((exponents2 exponents))
235 m2
236 (let* ((exponents (copy-seq exponents1))
237 (dimension (reduce #'+ exponents)))
238 (map-into exponents #'min exponents1 exponents2)
239 (make-instance 'monom :dimension dimension :exponents exponents)))))
240
241(defmethod r-depends-p ((m monom) k)
242 "Return T if the monomial M depends on variable number K."
243 (declare (type fixnum k))
244 (with-slots (exponents)
245 m
246 (plusp (elt exponents k))))
247
248(defmethod r-tensor-product ((m1 monom) (m2 monom)
249 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
250 (declare (fixnum dimension))
251 (with-slots ((exponents1 exponents))
252 m1
253 (with-slots ((exponents2 exponents))
254 m2
255 (make-instance 'monom
256 :dimension dimension
257 :exponents (concatenate 'vector exponents1 exponents2)))))
258
259(defmethod r-contract ((m monom) k)
260 "Drop the first K variables in monomial M."
261 (declare (fixnum k))
262 (with-slots (dimension exponents)
263 m
264 (setf dimension (- dimension k)
265 exponents (subseq exponents k))))
266
267(defun make-monom-variable (nvars pos &optional (power 1)
268 &aux (m (make-instance 'monom :dimension nvars)))
269 "Construct a monomial in the polynomial ring
270RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
271which represents a single variable. It assumes number of variables
272NVARS and the variable is at position POS. Optionally, the variable
273may appear raised to power POWER. "
274 (declare (type fixnum nvars pos power) (type monom m))
275 (with-slots (exponents)
276 m
277 (setf (elt exponents pos) power)
278 m))
279
280(defmethod r->list ((m monom))
281 "A human-readable representation of a monomial M as a list of exponents."
282 (coerce (monom-exponents m) 'list))
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