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source: branches/f4grobner/monom.lisp@ 2472

Last change on this file since 2472 was 2414, 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-VARIABLE"))
46
47(in-package :monom)
48
49(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
50
51(deftype exponent ()
52 "Type of exponent in a monomial."
53 'fixnum)
54
55(defclass monom ()
56 ((dimension :initarg :dimension :accessor r-dimension)
57 (exponents :initarg :exponents :accessor r-exponents))
58 (:default-initargs :dimension nil :exponents nil :exponent nil))
59
60(defmethod print-object ((self monom) stream)
61 (format stream "#<MONOM DIMENSION=~A EXPONENTS=~A>"
62 (r-dimension self)
63 (r-exponents self)))
64
65(defmethod shared-initialize :after ((self monom) slot-names
66 &key
67 dimension
68 exponents
69 exponent
70 &allow-other-keys
71 )
72 (if (eq slot-names t) (setf slot-names '(dimension exponents)))
73 (dolist (slot-name slot-names)
74 (case slot-name
75 (dimension
76 (cond (dimension
77 (setf (slot-value self 'dimension) dimension))
78 (exponents
79 (setf (slot-value self 'dimension) (length exponents)))
80 (t
81 (error "DIMENSION or EXPONENTS must not be NIL"))))
82 (exponents
83 (cond
84 ;; when exponents are supplied
85 (exponents
86 (let ((dim (length exponents)))
87 (when (and dimension (/= dimension dim))
88 (error "EXPONENTS must have length DIMENSION"))
89 (setf (slot-value self 'dimension) dim
90 (slot-value self 'exponents) (make-array dim :initial-contents exponents))))
91 ;; when all exponents are to be identical
92 (t
93 (let ((dim (slot-value self 'dimension)))
94 (setf (slot-value self 'exponents)
95 (make-array (list dim) :initial-element (or exponent 0)
96 :element-type 'exponent)))))))))
97
98;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
99;;
100;; Operations on monomials
101;;
102;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
103
104(defmethod r-coeff ((m monom))
105 "A MONOM can be treated as a special case of TERM,
106where the coefficient is 1."
107 1)
108
109(defmethod r-elt ((m monom) index)
110 "Return the power in the monomial M of variable number INDEX."
111 (with-slots (exponents)
112 m
113 (elt exponents index)))
114
115(defmethod (setf r-elt) (new-value (m monom) index)
116 "Return the power in the monomial M of variable number INDEX."
117 (with-slots (exponents)
118 m
119 (setf (elt exponents index) new-value)))
120
121(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
122 "Return the todal degree of a monomoal M. Optinally, a range
123of variables may be specified with arguments START and END."
124 (declare (type fixnum start end))
125 (with-slots (exponents)
126 m
127 (reduce #'+ exponents :start start :end end)))
128
129
130(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
131 "Return the sugar of a monomial M. Optinally, a range
132of variables may be specified with arguments START and END."
133 (declare (type fixnum start end))
134 (r-total-degree m start end))
135
136(defmethod r* ((m1 monom) (m2 monom))
137 "Multiply monomial M1 by monomial M2."
138 (with-slots ((exponents1 exponents) dimension)
139 m1
140 (with-slots ((exponents2 exponents))
141 m2
142 (let* ((exponents (copy-seq exponents1)))
143 (map-into exponents #'+ exponents1 exponents2)
144 (make-instance 'monom :dimension dimension :exponents exponents)))))
145
146
147(defmethod r/ ((m1 monom) (m2 monom))
148 "Divide monomial M1 by monomial M2."
149 (with-slots ((exponents1 exponents) (dimension1 dimension))
150 m1
151 (with-slots ((exponents2 exponents))
152 m2
153 (let* ((exponents (copy-seq exponents1))
154 (dimension dimension1))
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) (dimension1 dimension))
221 m1
222 (with-slots ((exponents2 exponents))
223 m2
224 (let* ((exponents (copy-seq exponents1))
225 (dimension dimension1))
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) (dimension1 dimension))
233 m1
234 (with-slots ((exponents2 exponents))
235 m2
236 (let* ((exponents (copy-seq exponents1))
237 (dimension dimension1))
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 (with-slots ((exponents1 exponents) (dimension1 dimension))
250 m1
251 (with-slots ((exponents2 exponents) (dimension2 dimension))
252 m2
253 (make-instance 'monom
254 :dimension (+ dimension1 dimension2)
255 :exponents (concatenate 'vector exponents1 exponents2)))))
256
257(defmethod r-contract ((m monom) k)
258 "Drop the first K variables in monomial M."
259 (declare (fixnum k))
260 (with-slots (dimension exponents)
261 m
262 (setf dimension (- dimension k)
263 exponents (subseq exponents k))))
264
265(defun make-monom-variable (nvars pos &optional (power 1)
266 &aux (m (make-instance 'monom :dimension nvars)))
267 "Construct a monomial in the polynomial ring
268RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
269which represents a single variable. It assumes number of variables
270NVARS and the variable is at position POS. Optionally, the variable
271may appear raised to power POWER. "
272 (declare (type fixnum nvars pos power) (type monom m))
273 (with-slots (exponents)
274 m
275 (setf (elt exponents pos) power)
276 m))
277
278(defmethod r->list ((m monom))
279 "A human-readable representation of a monomial M as a list of exponents."
280 (coerce (r-exponents m) 'list))
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