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source: branches/f4grobner/monom.lisp@ 2331

Last change on this file since 2331 was 2331, 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 initialize-instance ((self monom)
80 ;;&rest args
81 &key
82 dimension
83 exponents
84 exponent
85 &allow-other-keys
86 )
87 (format t "MONOM::INITIALIZE-INSTANCE called with:~&ARGS: ~W.~%" args)
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 (with-slots ((exponents1 exponents) dimension)
148 m1
149 (with-slots ((exponents2 exponents))
150 m2
151 (let* ((exponents (copy-seq exponents1)))
152 (map-into exponents #'+ exponents1 exponents2)
153 (make-instance 'monom :dimension dimension :exponents exponents)))))
154
155
156
157(defmethod r/ ((m1 monom) (m2 monom))
158 "Divide monomial M1 by monomial M2."
159 (with-slots ((exponents1 exponents) (dimension1 dimension))
160 m1
161 (with-slots ((exponents2 exponents))
162 m2
163 (let* ((exponents (copy-seq exponents1))
164 (dimension dimension1))
165 (map-into exponents #'- exponents1 exponents2)
166 (make-instance 'monom :dimension dimension :exponents exponents)))))
167
168(defmethod r-divides-p ((m1 monom) (m2 monom))
169 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
170 (with-slots ((exponents1 exponents))
171 m1
172 (with-slots ((exponents2 exponents))
173 m2
174 (every #'<= exponents1 exponents2))))
175
176
177(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
178 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
179 (every #'(lambda (x y z) (<= x (max y z)))
180 m1 m2 m3))
181
182
183(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
184 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
185 (declare (type monom m1 m2 m3 m4))
186 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
187 m1 m2 m3 m4))
188
189(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
190 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
191 (with-slots ((exponents1 exponents))
192 m1
193 (with-slots ((exponents2 exponents))
194 m2
195 (with-slots ((exponents3 exponents))
196 m3
197 (with-slots ((exponents4 exponents))
198 m4
199 (every
200 #'(lambda (x y z w) (= (max x y) (max z w)))
201 exponents1 exponents2 exponents3 exponents4))))))
202
203(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
204 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
205 (with-slots ((exponents1 exponents))
206 m1
207 (with-slots ((exponents2 exponents))
208 m2
209 (every #'>= exponents1 exponents2))))
210
211(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
212 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
213 (with-slots ((exponents1 exponents))
214 m1
215 (with-slots ((exponents2 exponents))
216 m2
217 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
218
219
220(defmethod r-equalp ((m1 monom) (m2 monom))
221 "Returns T if two monomials M1 and M2 are equal."
222 (with-slots ((exponents1 exponents))
223 m1
224 (with-slots ((exponents2 exponents))
225 m2
226 (every #'= exponents1 exponents2))))
227
228(defmethod r-lcm ((m1 monom) (m2 monom))
229 "Returns least common multiple of monomials M1 and M2."
230 (with-slots ((exponents1 exponents) (dimension1 dimension))
231 m1
232 (with-slots ((exponents2 exponents))
233 m2
234 (let* ((exponents (copy-seq exponents1))
235 (dimension dimension1))
236 (map-into exponents #'max exponents1 exponents2)
237 (make-instance 'monom :dimension dimension :exponents exponents)))))
238
239
240(defmethod r-gcd ((m1 monom) (m2 monom))
241 "Returns greatest common divisor of monomials M1 and M2."
242 (with-slots ((exponents1 exponents) (dimension1 dimension))
243 m1
244 (with-slots ((exponents2 exponents))
245 m2
246 (let* ((exponents (copy-seq exponents1))
247 (dimension dimension1))
248 (map-into exponents #'min exponents1 exponents2)
249 (make-instance 'monom :dimension dimension :exponents exponents)))))
250
251(defmethod r-depends-p ((m monom) k)
252 "Return T if the monomial M depends on variable number K."
253 (declare (type fixnum k))
254 (with-slots (exponents)
255 m
256 (plusp (elt exponents k))))
257
258(defmethod r-tensor-product ((m1 monom) (m2 monom))
259 (with-slots ((exponents1 exponents) (dimension1 dimension))
260 m1
261 (with-slots ((exponents2 exponents) (dimension2 dimension))
262 m2
263 (make-instance 'monom
264 :dimension (+ dimension1 dimension2)
265 :exponents (concatenate 'vector exponents1 exponents2)))))
266
267(defmethod r-contract ((m monom) k)
268 "Drop the first K variables in monomial M."
269 (declare (fixnum k))
270 (with-slots (dimension exponents)
271 m
272 (setf dimension (- dimension k)
273 exponents (subseq exponents k))))
274
275(defun make-monom-variable (nvars pos &optional (power 1)
276 &aux (m (make-instance 'monom :dimension nvars)))
277 "Construct a monomial in the polynomial ring
278RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
279which represents a single variable. It assumes number of variables
280NVARS and the variable is at position POS. Optionally, the variable
281may appear raised to power POWER. "
282 (declare (type fixnum nvars pos power) (type monom m))
283 (with-slots (exponents)
284 m
285 (setf (elt exponents pos) power)
286 m))
287
288(defmethod r->list ((m monom))
289 "A human-readable representation of a monomial M as a list of exponents."
290 (coerce (monom-exponents m) 'list))
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