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source: branches/f4grobner/monom.lisp@ 2410

Last change on this file since 2410 was 2405, 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
148(defmethod r/ ((m1 monom) (m2 monom))
149 "Divide monomial M1 by monomial M2."
150 (with-slots ((exponents1 exponents) (dimension1 dimension))
151 m1
152 (with-slots ((exponents2 exponents))
153 m2
154 (let* ((exponents (copy-seq exponents1))
155 (dimension dimension1))
156 (map-into exponents #'- exponents1 exponents2)
157 (make-instance 'monom :dimension dimension :exponents exponents)))))
158
159(defmethod r-divides-p ((m1 monom) (m2 monom))
160 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
161 (with-slots ((exponents1 exponents))
162 m1
163 (with-slots ((exponents2 exponents))
164 m2
165 (every #'<= exponents1 exponents2))))
166
167
168(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
169 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
170 (every #'(lambda (x y z) (<= x (max y z)))
171 m1 m2 m3))
172
173
174(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
175 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
176 (declare (type monom m1 m2 m3 m4))
177 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
178 m1 m2 m3 m4))
179
180(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
181 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
182 (with-slots ((exponents1 exponents))
183 m1
184 (with-slots ((exponents2 exponents))
185 m2
186 (with-slots ((exponents3 exponents))
187 m3
188 (with-slots ((exponents4 exponents))
189 m4
190 (every
191 #'(lambda (x y z w) (= (max x y) (max z w)))
192 exponents1 exponents2 exponents3 exponents4))))))
193
194(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
195 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
196 (with-slots ((exponents1 exponents))
197 m1
198 (with-slots ((exponents2 exponents))
199 m2
200 (every #'>= exponents1 exponents2))))
201
202(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
203 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
204 (with-slots ((exponents1 exponents))
205 m1
206 (with-slots ((exponents2 exponents))
207 m2
208 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
209
210
211(defmethod r-equalp ((m1 monom) (m2 monom))
212 "Returns T if two monomials M1 and M2 are equal."
213 (with-slots ((exponents1 exponents))
214 m1
215 (with-slots ((exponents2 exponents))
216 m2
217 (every #'= exponents1 exponents2))))
218
219(defmethod r-lcm ((m1 monom) (m2 monom))
220 "Returns least common multiple of monomials M1 and M2."
221 (with-slots ((exponents1 exponents) (dimension1 dimension))
222 m1
223 (with-slots ((exponents2 exponents))
224 m2
225 (let* ((exponents (copy-seq exponents1))
226 (dimension dimension1))
227 (map-into exponents #'max exponents1 exponents2)
228 (make-instance 'monom :dimension dimension :exponents exponents)))))
229
230
231(defmethod r-gcd ((m1 monom) (m2 monom))
232 "Returns greatest common divisor of monomials M1 and M2."
233 (with-slots ((exponents1 exponents) (dimension1 dimension))
234 m1
235 (with-slots ((exponents2 exponents))
236 m2
237 (let* ((exponents (copy-seq exponents1))
238 (dimension dimension1))
239 (map-into exponents #'min exponents1 exponents2)
240 (make-instance 'monom :dimension dimension :exponents exponents)))))
241
242(defmethod r-depends-p ((m monom) k)
243 "Return T if the monomial M depends on variable number K."
244 (declare (type fixnum k))
245 (with-slots (exponents)
246 m
247 (plusp (elt exponents k))))
248
249(defmethod r-tensor-product ((m1 monom) (m2 monom))
250 (with-slots ((exponents1 exponents) (dimension1 dimension))
251 m1
252 (with-slots ((exponents2 exponents) (dimension2 dimension))
253 m2
254 (make-instance 'monom
255 :dimension (+ dimension1 dimension2)
256 :exponents (concatenate 'vector exponents1 exponents2)))))
257
258(defmethod r-contract ((m monom) k)
259 "Drop the first K variables in monomial M."
260 (declare (fixnum k))
261 (with-slots (dimension exponents)
262 m
263 (setf dimension (- dimension k)
264 exponents (subseq exponents k))))
265
266(defun make-monom-variable (nvars pos &optional (power 1)
267 &aux (m (make-instance 'monom :dimension nvars)))
268 "Construct a monomial in the polynomial ring
269RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
270which represents a single variable. It assumes number of variables
271NVARS and the variable is at position POS. Optionally, the variable
272may appear raised to power POWER. "
273 (declare (type fixnum nvars pos power) (type monom m))
274 (with-slots (exponents)
275 m
276 (setf (elt exponents pos) power)
277 m))
278
279(defmethod r->list ((m monom))
280 "A human-readable representation of a monomial M as a list of exponents."
281 (coerce (r-exponents m) 'list))
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