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source: branches/f4grobner/monom.lisp@ 2353

Last change on this file since 2353 was 2351, 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 "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 (let* ((new-dimension (cond (dimension dimension)
89 (exponents
90 (length exponents))
91 (t
92 (error "DIMENSION or EXPONENTS must not be NIL"))))
93 (new-exponents (cond
94 ;; when exponents are supplied
95 (exponents
96 (make-array (list new-dimension) :initial-contents exponents))
97 ;; when all exponents are to be identical
98 (exponent
99 (make-array (list new-dimension) :initial-element exponent
100 :element-type 'exponent))
101 ;; otherwise, all exponents are zero
102 (t
103 (make-array (list new-dimension) :element-type 'exponent :initial-element 0)))))
104 (setf (slot-value self 'dimension) new-dimension
105 (slot-value self 'exponents) new-exponents)))
106
107
108
109;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
110;;
111;; Operations on monomials
112;;
113;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
114
115(defmethod r-dimension ((m monom))
116 (monom-dimension m))
117
118(defmethod r-elt ((m monom) index)
119 "Return the power in the monomial M of variable number INDEX."
120 (with-slots (exponents)
121 m
122 (elt exponents index)))
123
124(defmethod (setf r-elt) (new-value (m monom) index)
125 "Return the power in the monomial M of variable number INDEX."
126 (with-slots (exponents)
127 m
128 (setf (elt exponents index) new-value)))
129
130(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
131 "Return the todal degree of a monomoal M. Optinally, a range
132of variables may be specified with arguments START and END."
133 (declare (type fixnum start end))
134 (with-slots (exponents)
135 m
136 (reduce #'+ exponents :start start :end end)))
137
138
139(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
140 "Return the sugar of a monomial M. Optinally, a range
141of variables may be specified with arguments START and END."
142 (declare (type fixnum start end))
143 (r-total-degree m start end))
144
145(defmethod r* ((m1 monom) (m2 monom))
146 "Multiply monomial M1 by monomial M2."
147 (format t "MONOM::R* called with:~& M1: ~A~& M2: ~A~%" m1 m2)
148 (with-slots ((exponents1 exponents) dimension)
149 m1
150 (with-slots ((exponents2 exponents))
151 m2
152 (let* ((exponents (copy-seq exponents1)))
153 (map-into exponents #'+ exponents1 exponents2)
154 (make-instance 'monom :dimension dimension :exponents exponents)))))
155
156
157
158(defmethod r/ ((m1 monom) (m2 monom))
159 "Divide monomial M1 by monomial M2."
160 (with-slots ((exponents1 exponents) (dimension1 dimension))
161 m1
162 (with-slots ((exponents2 exponents))
163 m2
164 (let* ((exponents (copy-seq exponents1))
165 (dimension dimension1))
166 (map-into exponents #'- exponents1 exponents2)
167 (make-instance 'monom :dimension dimension :exponents exponents)))))
168
169(defmethod r-divides-p ((m1 monom) (m2 monom))
170 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
171 (with-slots ((exponents1 exponents))
172 m1
173 (with-slots ((exponents2 exponents))
174 m2
175 (every #'<= exponents1 exponents2))))
176
177
178(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
179 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
180 (every #'(lambda (x y z) (<= x (max y z)))
181 m1 m2 m3))
182
183
184(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
185 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
186 (declare (type monom m1 m2 m3 m4))
187 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
188 m1 m2 m3 m4))
189
190(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
191 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
192 (with-slots ((exponents1 exponents))
193 m1
194 (with-slots ((exponents2 exponents))
195 m2
196 (with-slots ((exponents3 exponents))
197 m3
198 (with-slots ((exponents4 exponents))
199 m4
200 (every
201 #'(lambda (x y z w) (= (max x y) (max z w)))
202 exponents1 exponents2 exponents3 exponents4))))))
203
204(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
205 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
206 (with-slots ((exponents1 exponents))
207 m1
208 (with-slots ((exponents2 exponents))
209 m2
210 (every #'>= exponents1 exponents2))))
211
212(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
213 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
214 (with-slots ((exponents1 exponents))
215 m1
216 (with-slots ((exponents2 exponents))
217 m2
218 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
219
220
221(defmethod r-equalp ((m1 monom) (m2 monom))
222 "Returns T if two monomials M1 and M2 are equal."
223 (with-slots ((exponents1 exponents))
224 m1
225 (with-slots ((exponents2 exponents))
226 m2
227 (every #'= exponents1 exponents2))))
228
229(defmethod r-lcm ((m1 monom) (m2 monom))
230 "Returns least common multiple of monomials M1 and M2."
231 (with-slots ((exponents1 exponents) (dimension1 dimension))
232 m1
233 (with-slots ((exponents2 exponents))
234 m2
235 (let* ((exponents (copy-seq exponents1))
236 (dimension dimension1))
237 (map-into exponents #'max exponents1 exponents2)
238 (make-instance 'monom :dimension dimension :exponents exponents)))))
239
240
241(defmethod r-gcd ((m1 monom) (m2 monom))
242 "Returns greatest common divisor of monomials M1 and M2."
243 (with-slots ((exponents1 exponents) (dimension1 dimension))
244 m1
245 (with-slots ((exponents2 exponents))
246 m2
247 (let* ((exponents (copy-seq exponents1))
248 (dimension dimension1))
249 (map-into exponents #'min exponents1 exponents2)
250 (make-instance 'monom :dimension dimension :exponents exponents)))))
251
252(defmethod r-depends-p ((m monom) k)
253 "Return T if the monomial M depends on variable number K."
254 (declare (type fixnum k))
255 (with-slots (exponents)
256 m
257 (plusp (elt exponents k))))
258
259(defmethod r-tensor-product ((m1 monom) (m2 monom))
260 (with-slots ((exponents1 exponents) (dimension1 dimension))
261 m1
262 (with-slots ((exponents2 exponents) (dimension2 dimension))
263 m2
264 (make-instance 'monom
265 :dimension (+ dimension1 dimension2)
266 :exponents (concatenate 'vector exponents1 exponents2)))))
267
268(defmethod r-contract ((m monom) k)
269 "Drop the first K variables in monomial M."
270 (declare (fixnum k))
271 (with-slots (dimension exponents)
272 m
273 (setf dimension (- dimension k)
274 exponents (subseq exponents k))))
275
276(defun make-monom-variable (nvars pos &optional (power 1)
277 &aux (m (make-instance 'monom :dimension nvars)))
278 "Construct a monomial in the polynomial ring
279RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
280which represents a single variable. It assumes number of variables
281NVARS and the variable is at position POS. Optionally, the variable
282may appear raised to power POWER. "
283 (declare (type fixnum nvars pos power) (type monom m))
284 (with-slots (exponents)
285 m
286 (setf (elt exponents pos) power)
287 m))
288
289(defmethod r->list ((m monom))
290 "A human-readable representation of a monomial M as a list of exponents."
291 (coerce (monom-exponents m) 'list))
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