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source: branches/f4grobner/monom.lisp@ 2179

Last change on this file since 2179 was 2171, 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 ((dim :initarg :dim :accessor monom-dimension)
60 (exponents :initarg :exponents :accessor monom-exponents))
61 (:default-initargs :dim 0 :exponents nil))
62
63(defmethod print-object ((m monom) stream)
64 (princ (slot-value m 'exponents) stream))
65
66;; If a monomial is redefined as structure with slot EXPONENTS, the function
67;; below can be the BOA constructor.
68(defun make-monom (&key
69 (dimension nil dimension-suppied-p)
70 (initial-exponents nil initial-exponents-supplied-p)
71 (initial-exponent nil initial-exponent-supplied-p)
72 &aux
73 (dim (cond (dimension-suppied-p dimension)
74 (initial-exponents-supplied-p (length initial-exponents))
75 (t (error "You must provide DIMENSION or INITIAL-EXPONENTS"))))
76 (exponents (cond
77 ;; when exponents are supplied
78 (initial-exponents-supplied-p
79 (make-array (list dim) :initial-contents initial-exponents
80 :element-type 'exponent))
81 ;; when all exponents are to be identical
82 (initial-exponent-supplied-p
83 (make-array (list dim) :initial-element initial-exponent
84 :element-type 'exponent))
85 ;; otherwise, all exponents are zero
86 (t
87 (make-array (list dim) :element-type 'exponent :initial-element 0)))))
88 "A constructor (factory) of monomials. If DIMENSION is given, a sequence of
89DIMENSION elements of type EXPONENT is constructed, where individual
90elements are the value of INITIAL-EXPONENT, which defaults to 0.
91Alternatively, all elements may be specified as a list
92INITIAL-EXPONENTS."
93 (make-instance 'monom :dim dim :exponents exponents))
94
95;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
96;;
97;; Operations on monomials
98;;
99;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
100
101(defmethod r-dimension ((m monom))
102 (monom-dimension m))
103
104(defmethod r-elt ((m monom) index)
105 "Return the power in the monomial M of variable number INDEX."
106 (with-slots (exponents)
107 m
108 (elt exponents index)))
109
110(defmethod (setf r-elt) (new-value (m monom) index)
111 "Return the power in the monomial M of variable number INDEX."
112 (with-slots (exponents)
113 m
114 (setf (elt exponents index) new-value)))
115
116(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
117 "Return the todal degree of a monomoal M. Optinally, a range
118of variables may be specified with arguments START and END."
119 (declare (type fixnum start end))
120 (with-slots (exponents)
121 m
122 (reduce #'+ exponents :start start :end end)))
123
124
125(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
126 "Return the sugar of a monomial M. Optinally, a range
127of variables may be specified with arguments START and END."
128 (declare (type fixnum start end))
129 (r-total-degree m start end))
130
131(defmethod r* ((m1 monom) (m2 monom))
132 "Multiply monomial M1 by monomial M2."
133 (with-slots ((exponents1 exponents) dim)
134 m1
135 (with-slots ((exponents2 exponents))
136 m2
137 (let* ((exponents (copy-seq exponents1)))
138 (map-into exponents #'+ exponents1 exponents2)
139 (make-instance 'monom :dim dim :exponents exponents)))))
140
141
142
143(defmethod r/ ((m1 monom) (m2 monom))
144 "Divide monomial M1 by monomial M2."
145 (with-slots ((exponents1 exponents))
146 m1
147 (with-slots ((exponents2 exponents))
148 m2
149 (let* ((exponents (copy-seq exponents1))
150 (dim (reduce #'+ exponents)))
151 (map-into exponents #'- exponents1 exponents2)
152 (make-instance 'monom :dim dim :exponents exponents)))))
153
154(defmethod r-divides-p ((m1 monom) (m2 monom))
155 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
156 (with-slots ((exponents1 exponents))
157 m1
158 (with-slots ((exponents2 exponents))
159 m2
160 (every #'<= exponents1 exponents2))))
161
162
163(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
164 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
165 (every #'(lambda (x y z) (<= x (max y z)))
166 m1 m2 m3))
167
168
169(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
170 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
171 (declare (type monom m1 m2 m3 m4))
172 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
173 m1 m2 m3 m4))
174
175(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
176 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
177 (with-slots ((exponents1 exponents))
178 m1
179 (with-slots ((exponents2 exponents))
180 m2
181 (with-slots ((exponents3 exponents))
182 m3
183 (with-slots ((exponents4 exponents))
184 m4
185 (every
186 #'(lambda (x y z w) (= (max x y) (max z w)))
187 exponents1 exponents2 exponents3 exponents4))))))
188
189(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
190 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
191 (with-slots ((exponents1 exponents))
192 m1
193 (with-slots ((exponents2 exponents))
194 m2
195 (every #'>= exponents1 exponents2))))
196
197(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
198 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
199 (with-slots ((exponents1 exponents))
200 m1
201 (with-slots ((exponents2 exponents))
202 m2
203 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
204
205
206(defmethod r-equalp ((m1 monom) (m2 monom))
207 "Returns T if two monomials M1 and M2 are equal."
208 (with-slots ((exponents1 exponents))
209 m1
210 (with-slots ((exponents2 exponents))
211 m2
212 (every #'= exponents1 exponents2))))
213
214(defmethod r-lcm ((m1 monom) (m2 monom))
215 "Returns least common multiple of monomials M1 and M2."
216 (with-slots ((exponents1 exponents))
217 m1
218 (with-slots ((exponents2 exponents))
219 m2
220 (let* ((exponents (copy-seq exponents1))
221 (dim (reduce #'+ exponents)))
222 (map-into exponents #'max exponents1 exponents2)
223 (make-instance 'monom :dim dim :exponents exponents)))))
224
225
226(defmethod r-gcd ((m1 monom) (m2 monom))
227 "Returns greatest common divisor of monomials M1 and M2."
228 (with-slots ((exponents1 exponents))
229 m1
230 (with-slots ((exponents2 exponents))
231 m2
232 (let* ((exponents (copy-seq exponents1))
233 (dim (reduce #'+ exponents)))
234 (map-into exponents #'min exponents1 exponents2)
235 (make-instance 'monom :dim dim :exponents exponents)))))
236
237(defmethod r-depends-p ((m monom) k)
238 "Return T if the monomial M depends on variable number K."
239 (declare (type fixnum k))
240 (with-slots (exponents)
241 m
242 (plusp (elt exponents k))))
243
244(defmethod r-tensor-product ((m1 monom) (m2 monom)
245 &aux (dim (+ (r-dimension m1) (r-dimension m2))))
246 (declare (fixnum dim))
247 (with-slots ((exponents1 exponents))
248 m1
249 (with-slots ((exponents2 exponents))
250 m2
251 (make-instance 'monom
252 :dim dim
253 :exponents (concatenate 'vector exponents1 exponents2)))))
254
255(defmethod r-contract ((m monom) k)
256 "Drop the first K variables in monomial M."
257 (declare (fixnum k))
258 (with-slots (dim exponents)
259 m
260 (setf dim (- dim k)
261 exponents (subseq exponents k))))
262
263(defun make-monom-variable (nvars pos &optional (power 1)
264 &aux (m (make-monom :dimension nvars)))
265 "Construct a monomial in the polynomial ring
266RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
267which represents a single variable. It assumes number of variables
268NVARS and the variable is at position POS. Optionally, the variable
269may appear raised to power POWER. "
270 (declare (type fixnum nvars pos power) (type monom m))
271 (with-slots (exponents)
272 m
273 (setf (elt exponents pos) power)
274 m))
275
276(defmethod r->list ((m monom))
277 "A human-readable representation of a monomial M as a list of exponents."
278 (coerce (monom-exponents m) 'list))
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