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source: branches/f4grobner/monom.lisp@ 2164

Last change on this file since 2164 was 2163, 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))
134 m1
135 (with-slots ((exponents2 exponents))
136 m2
137 (let* ((exponents (copy-seq exponents1))
138 (dim (reduce #'+ exponents)))
139 (map-into exponents #'+ exponents1 exponents2)
140 (make-instance 'monom :dim dim :exponents exponents)))))
141
142
143
144(defmethod r/ ((m1 monom) (m2 monom))
145 "Divide monomial M1 by monomial M2."
146 (with-slots ((exponents1 exponents))
147 m1
148 (with-slots ((exponents2 exponents))
149 m2
150 (let* ((exponents (copy-seq exponents1))
151 (dim (reduce #'+ exponents)))
152 (map-into exponents #'- exponents1 exponents2)
153 (make-instance 'monom :dim dim :exponents exponents)))))
154
155(defmethod r-divides-p ((m1 monom) (m2 monom))
156 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
157 (with-slots ((exponents1 exponents))
158 m1
159 (with-slots ((exponents2 exponents))
160 m2
161 (every #'<= exponents1 exponents2))))
162
163
164(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
165 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
166 (every #'(lambda (x y z) (<= x (max y z)))
167 m1 m2 m3))
168
169
170(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
171 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
172 (declare (type monom m1 m2 m3 m4))
173 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
174 m1 m2 m3 m4))
175
176(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
177 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
178 (with-slots (exponents1 exponents)
179 m1
180 (with-slots (exponents2 exponents)
181 m2
182 (with-slots (exponents3 exponents)
183 m3
184 (with-slots (exponents4 exponents)
185 m4
186 (every
187 #'(lambda (x y z w) (= (max x y) (max z w)))
188 exponents1 exponents2 exponents3 exponents4))))))
189
190(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
191 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
192 (with-slots (exponents1 exponents)
193 m1
194 (with-slots (exponents2 exponents)
195 m2
196 (every #'>= exponents1 exponents2))))
197
198(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
199 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
200 (with-slots (exponents1 exponents)
201 m1
202 (with-slots (exponents2 exponents)
203 m2
204 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
205
206
207(defmethod r-equalp ((m1 monom) (m2 monom))
208 "Returns T if two monomials M1 and M2 are equal."
209 (with-slots (exponents1 exponents)
210 m1
211 (with-slots (exponents2 exponents)
212 m2
213 (every #'= exponents1 exponents2))))
214
215(defmethod r-lcm ((m1 monom) (m2 monom))
216 "Returns least common multiple of monomials M1 and M2."
217 (with-slots (exponents1 exponents)
218 m1
219 (with-slots (exponents2 exponents)
220 m2
221 (let* ((exponents (copy-seq exponents1))
222 (dim (reduce #'+ exponents)))
223 (map-into exponents #'max exponents1 exponents2)
224 (make-instance 'monom :dim dim :exponents exponents)))))
225
226
227(defmethod r-gcd ((m1 monom) (m2 monom))
228 "Returns greatest common divisor of monomials M1 and M2."
229 (with-slots (exponents1 exponents)
230 m1
231 (with-slots (exponents2 exponents)
232 m2
233 (let* ((exponents (copy-seq exponents1))
234 (dim (reduce #'+ exponents)))
235 (map-into exponents #'min exponents1 exponents2)
236 (make-instance 'monom :dim dim :exponents exponents)))))
237
238(defmethod r-depends-p ((m monom) k)
239 "Return T if the monomial M depends on variable number K."
240 (declare (type fixnum k))
241 (with-slots (exponents)
242 m
243 (plusp (elt exponents k))))
244
245(defmethod r-tensor-product ((m1 monom) (m2 monom)
246 &aux (dim (+ (r-dimension m1) (r-dimension m2))))
247 (declare (fixnum dim))
248 (with-slots (exponents1 exponents)
249 m1
250 (with-slots (exponents2 exponents)
251 m2
252 (make-instance 'monom
253 :dim dim
254 :exponents (concatenate 'vector exponents1 exponents2)))))
255
256(defmethod r-contract ((m monom) k)
257 "Drop the first K variables in monomial M."
258 (declare (fixnum k))
259 (with-slots (dim exponents)
260 m
261 (setf dim (- dim k)
262 exponents (subseq exponents k))))
263
264(defun make-monom-variable (nvars pos &optional (power 1)
265 &aux (m (make-monom :dimension nvars)))
266 "Construct a monomial in the polynomial ring
267RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
268which represents a single variable. It assumes number of variables
269NVARS and the variable is at position POS. Optionally, the variable
270may appear raised to power POWER. "
271 (declare (type fixnum nvars pos power) (type monom m))
272 (with-slots (exponents)
273 m
274 (setf (elt exponents pos) power)
275 m))
276
277(defmethod r->list ((m monom))
278 "A human-readable representation of a monomial M as a list of exponents."
279 (coerce (monom-exponents m) 'list))
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