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source: branches/f4grobner/monom.lisp@ 2354

Last change on this file since 2354 was 2354, 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 "MONOM-DIMENSION"
46 "MONOM-EXPONENTS"
47 "MAKE-MONOM-VARIABLE"))
48
49(in-package :monom)
50
51(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
52
53(deftype exponent ()
54 "Type of exponent in a monomial."
55 'fixnum)
56
57(defclass monom ()
58 ((dimension :initarg :dimension :accessor monom-dimension)
59 (exponents :initarg :exponents :accessor monom-exponents))
60 (:default-initargs :dimension nil :exponents nil :exponent nil))
61
62(defmethod print-object ((self monom) stream)
63 (format stream "#<MONOM DIMENSION=~A EXPONENTS=~A>"
64 (slot-value self 'dimension)
65 (slot-value self 'exponents)))
66
67#|
68;; Debug calls to initialize-instance
69(defmethod initialize-instance :around ((self monom)
70 &rest
71 args
72 &key
73 &allow-other-keys)
74 (format t "MONOM::INITIALIZE-INSTANCE called with:~&ARGS: ~W.~%" args)
75 (call-next-method)
76 )
77|#
78
79(defmethod shared-initialize :after ((self monom) slot-names
80 ;;&rest initargs
81 &key
82 dimension
83 exponents
84 exponent
85 &allow-other-keys
86 )
87 ;;(format t "MONOM::SHARED-INITIALIZE called with:~&SLOT-NAMES: ~W~&INITARGS: ~W.~%" slot-names initargs)
88 (if (eq slot-names t) (setf slot-names '(dimension exponents)))
89 (dolist (slot-name slot-names)
90 (ecase slot-name
91 (dimension
92 (cond (dimension (setf (slot-value self 'dimension)) dimension)
93 (exponents
94 (setf (slot-value self 'dimension) (length exponents)))
95 (t
96 (error "DIMENSION or EXPONENTS must not be NIL"))))
97 (exponents
98 (cond
99 ;; when exponents are supplied
100 (exponents
101 (setf (slot-value self 'exponents)
102 (make-array (slot-value self 'dimension) :initial-contents exponents)))
103 ;; when all exponents are to be identical
104 (exponent
105 (setf (slot-value self 'exponents)
106 (make-array (list new-dimension) :initial-element exponent
107 :element-type 'exponent)))
108 ;; otherwise, all exponents are zero
109 (t
110 (setf (slot-value self 'exponents)
111 (make-array (list new-dimension) :element-type 'exponent :initial-element 0))))))))
112
113
114
115
116;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
117;;
118;; Operations on monomials
119;;
120;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
121
122(defmethod r-dimension ((m monom))
123 (monom-dimension m))
124
125(defmethod r-elt ((m monom) index)
126 "Return the power in the monomial M of variable number INDEX."
127 (with-slots (exponents)
128 m
129 (elt exponents index)))
130
131(defmethod (setf r-elt) (new-value (m monom) index)
132 "Return the power in the monomial M of variable number INDEX."
133 (with-slots (exponents)
134 m
135 (setf (elt exponents index) new-value)))
136
137(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
138 "Return the todal degree of a monomoal M. Optinally, a range
139of variables may be specified with arguments START and END."
140 (declare (type fixnum start end))
141 (with-slots (exponents)
142 m
143 (reduce #'+ exponents :start start :end end)))
144
145
146(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
147 "Return the sugar of a monomial M. Optinally, a range
148of variables may be specified with arguments START and END."
149 (declare (type fixnum start end))
150 (r-total-degree m start end))
151
152(defmethod r* ((m1 monom) (m2 monom))
153 "Multiply monomial M1 by monomial M2."
154 (format t "MONOM::R* called with:~& M1: ~A~& M2: ~A~%" m1 m2)
155 (with-slots ((exponents1 exponents) dimension)
156 m1
157 (with-slots ((exponents2 exponents))
158 m2
159 (let* ((exponents (copy-seq exponents1)))
160 (map-into exponents #'+ exponents1 exponents2)
161 (make-instance 'monom :dimension dimension :exponents exponents)))))
162
163
164
165(defmethod r/ ((m1 monom) (m2 monom))
166 "Divide monomial M1 by monomial M2."
167 (with-slots ((exponents1 exponents) (dimension1 dimension))
168 m1
169 (with-slots ((exponents2 exponents))
170 m2
171 (let* ((exponents (copy-seq exponents1))
172 (dimension dimension1))
173 (map-into exponents #'- exponents1 exponents2)
174 (make-instance 'monom :dimension dimension :exponents exponents)))))
175
176(defmethod r-divides-p ((m1 monom) (m2 monom))
177 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
178 (with-slots ((exponents1 exponents))
179 m1
180 (with-slots ((exponents2 exponents))
181 m2
182 (every #'<= exponents1 exponents2))))
183
184
185(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
186 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
187 (every #'(lambda (x y z) (<= x (max y z)))
188 m1 m2 m3))
189
190
191(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
192 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
193 (declare (type monom m1 m2 m3 m4))
194 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
195 m1 m2 m3 m4))
196
197(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
198 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
199 (with-slots ((exponents1 exponents))
200 m1
201 (with-slots ((exponents2 exponents))
202 m2
203 (with-slots ((exponents3 exponents))
204 m3
205 (with-slots ((exponents4 exponents))
206 m4
207 (every
208 #'(lambda (x y z w) (= (max x y) (max z w)))
209 exponents1 exponents2 exponents3 exponents4))))))
210
211(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
212 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
213 (with-slots ((exponents1 exponents))
214 m1
215 (with-slots ((exponents2 exponents))
216 m2
217 (every #'>= exponents1 exponents2))))
218
219(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
220 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
221 (with-slots ((exponents1 exponents))
222 m1
223 (with-slots ((exponents2 exponents))
224 m2
225 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
226
227
228(defmethod r-equalp ((m1 monom) (m2 monom))
229 "Returns T if two monomials M1 and M2 are equal."
230 (with-slots ((exponents1 exponents))
231 m1
232 (with-slots ((exponents2 exponents))
233 m2
234 (every #'= exponents1 exponents2))))
235
236(defmethod r-lcm ((m1 monom) (m2 monom))
237 "Returns least common multiple of monomials M1 and M2."
238 (with-slots ((exponents1 exponents) (dimension1 dimension))
239 m1
240 (with-slots ((exponents2 exponents))
241 m2
242 (let* ((exponents (copy-seq exponents1))
243 (dimension dimension1))
244 (map-into exponents #'max exponents1 exponents2)
245 (make-instance 'monom :dimension dimension :exponents exponents)))))
246
247
248(defmethod r-gcd ((m1 monom) (m2 monom))
249 "Returns greatest common divisor of monomials M1 and M2."
250 (with-slots ((exponents1 exponents) (dimension1 dimension))
251 m1
252 (with-slots ((exponents2 exponents))
253 m2
254 (let* ((exponents (copy-seq exponents1))
255 (dimension dimension1))
256 (map-into exponents #'min exponents1 exponents2)
257 (make-instance 'monom :dimension dimension :exponents exponents)))))
258
259(defmethod r-depends-p ((m monom) k)
260 "Return T if the monomial M depends on variable number K."
261 (declare (type fixnum k))
262 (with-slots (exponents)
263 m
264 (plusp (elt exponents k))))
265
266(defmethod r-tensor-product ((m1 monom) (m2 monom))
267 (with-slots ((exponents1 exponents) (dimension1 dimension))
268 m1
269 (with-slots ((exponents2 exponents) (dimension2 dimension))
270 m2
271 (make-instance 'monom
272 :dimension (+ dimension1 dimension2)
273 :exponents (concatenate 'vector exponents1 exponents2)))))
274
275(defmethod r-contract ((m monom) k)
276 "Drop the first K variables in monomial M."
277 (declare (fixnum k))
278 (with-slots (dimension exponents)
279 m
280 (setf dimension (- dimension k)
281 exponents (subseq exponents k))))
282
283(defun make-monom-variable (nvars pos &optional (power 1)
284 &aux (m (make-instance 'monom :dimension nvars)))
285 "Construct a monomial in the polynomial ring
286RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
287which represents a single variable. It assumes number of variables
288NVARS and the variable is at position POS. Optionally, the variable
289may appear raised to power POWER. "
290 (declare (type fixnum nvars pos power) (type monom m))
291 (with-slots (exponents)
292 m
293 (setf (elt exponents pos) power)
294 m))
295
296(defmethod r->list ((m monom))
297 "A human-readable representation of a monomial M as a list of exponents."
298 (coerce (monom-exponents m) 'list))
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