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source: branches/f4grobner/monom.lisp@ 3447

Last change on this file since 3447 was 3447, 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(defpackage "MONOM"
23 (:use :cl :copy)
24 (:export "MONOM"
25 "EXPONENT"
26 "MONOM-DIMENSION"
27 "MONOM-EXPONENTS"
28 "MONOM-EQUALP"
29 "MONOM-ELT"
30 "MONOM-TOTAL-DEGREE"
31 "MONOM-SUGRAR"
32 "MONOM-MULTIPLY-BY"
33 "MONOM-DIVIDE-BY"
34 "MONOM-COPY-INSTANCE"
35 "MONOM-MULTIPLY-2"
36 "MONOM-MULTIPLY"
37 "MONOM-DIVIDES-P"
38 "MONOM-DIVIDES-LCM-P"
39 "MONOM-LCM-DIVIDES-LCM-P"
40 "MONOM-LCM-EQUAL-LCM-P"
41 "MONOM-DIVISIBLE-BY-P"
42 "MONOM-REL-PRIME-P"
43 "MONOM-LCM"
44 "MONOM-GCD"
45 "MONOM-DEPENDS-P"
46 "MONOM-LEFT-TENSOR-PRODUCT-BY"
47 "MONOM-RIGHT-TENSOR-PRODUCT-BY"
48 "MONOM-LEFT-CONTRACT"
49 "MAKE-MONOM-VARIABLE"
50 "MONOM->LIST")
51
52 (:documentation
53 "This package implements basic operations on monomials.
54DATA STRUCTURES: Conceptually, monomials can be represented as lists:
55
56 monom: (n1 n2 ... nk) where ni are non-negative integers
57
58However, lists may be implemented as other sequence types, so the
59flexibility to change the representation should be maintained in the
60code to use general operations on sequences whenever possible. The
61optimization for the actual representation should be left to
62declarations and the compiler.
63
64EXAMPLES: Suppose that variables are x and y. Then
65
66 Monom x*y^2 ---> (1 2) "))
67
68(in-package :monom)
69
70(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
71
72(deftype exponent ()
73 "Type of exponent in a monomial."
74 'fixnum)
75
76(defclass monom ()
77 ((exponents :initarg :exponents :accessor monom-exponents
78 :documentation "The powers of the variables."))
79 ;; default-initargs are not needed, they are handled by SHARED-INITIALIZE
80 ;;(:default-initargs :dimension 'foo :exponents 'bar :exponent 'baz)
81 (:documentation
82 "Implements a monomial, i.e. a product of powers
83of variables, like X*Y^2."))
84
85(defmethod print-object ((self monom) stream)
86 (print-unreadable-object (self stream :type t :identity t)
87 (with-accessors ((exponents monom-exponents))
88 self
89 (format stream "EXPONENTS=~A"
90 exponents))))
91
92(defmethod initialize-instance :after ((self monom)
93 &key
94 (dimension 0 dimension-supplied-p)
95 (exponents nil exponents-supplied-p)
96 (exponent 0)
97 &allow-other-keys
98 )
99 "The following INITIALIZE-INSTANCE method allows instance initialization
100of a MONOM in a style similar to MAKE-ARRAY, e.g.:
101
102 (MAKE-INSTANCE :EXPONENTS '(1 2 3)) --> #<MONOM EXPONENTS=#(1 2 3)>
103 (MAKE-INSTANCE :DIMENSION 3) --> #<MONOM EXPONENTS=#(0 0 0)>
104 (MAKE-INSTANCE :DIMENSION 3 :EXPONENT 7) --> #<MONOM EXPONENTS=#(7 7 7)>
105
106If both DIMENSION and EXPONENTS are supplied, they must be compatible,
107i.e. the length of EXPONENTS must be equal DIMENSION. If EXPONENTS
108is not supplied, a monom with repeated value EXPONENT is created.
109By default EXPONENT is 0, which results in a constant monomial.
110"
111 (cond
112 (exponents-supplied-p
113 (when (and dimension-supplied-p
114 (/= dimension (length exponents)))
115 (error "EXPONENTS (~A) must have supplied length DIMENSION (~A)"
116 exponents dimension))
117 (let ((dim (length exponents)))
118 (setf (slot-value self 'exponents) (make-array dim :initial-contents exponents))))
119 (dimension-supplied-p
120 ;; when all exponents are to be identical
121 (setf (slot-value self 'exponents) (make-array (list dimension)
122 :initial-element exponent
123 :element-type 'exponent)))
124 (t
125 (error "Initarg DIMENSION or EXPONENTS must be supplied."))))
126
127(defgeneric monom-dimension (m)
128 (:method ((m monom))
129 (length (monom-exponents m))))
130
131(defgeneric monom-equalp (m1 m2)
132 (:documentation "Returns T iff monomials M1 and M2 have identical EXPONENTS.")
133 (:method ((m1 monom) (m2 monom))
134 `(equalp (monom-exponents ,m1) (monom-exponents ,m2))))
135
136(defgeneric monom-elt (m index)
137 (:documentation
138 "Return the power in the monomial M of variable number INDEX.")
139 (:method ((m monom) index)
140 (with-slots (exponents)
141 m
142 (elt exponents index))))
143
144(defgeneric (setf monom-elt) (new-value m index)
145 (:documentation "Return the power in the monomial M of variable number INDEX.")
146 (:method (new-value (m monom) index)
147 (with-slots (exponents)
148 m
149 (setf (elt exponents index) new-value)))
150
151(defmethod monom-total-degree (m &optional (start 0) (end (monom-dimension m)))
152 "Return the todal degree of a monomoal M. Optinally, a range
153of variables may be specified with arguments START and END."
154 (declare (type fixnum start end))
155 (with-slots (exponents)
156 m
157 (reduce #'+ exponents :start start :end end)))
158
159
160(defmethod monom-sugar (m &optional start end)
161 (:documentation "Return the sugar of a monomial M. Optinally, a range
162of variables may be specified with arguments START and END.")
163 (:method ((m monom) &optional (start 0) (end (monom-dimension m)))
164 (declare (type fixnum start end))
165 (monom-total-degree m start end)))
166
167(defgeneric monom-multiply-by (self other)
168 (:method ((self monom) (other monom))
169 (with-slots ((exponents1 exponents))
170 self
171 (with-slots ((exponents2 exponents))
172 other
173 (unless (= (length exponents1) (length exponents2))
174 (error "Incompatible dimensions"))
175 (map-into exponents1 #'+ exponents1 exponents2)))
176 self))
177
178(defgeneric divide-by (self other)
179 (:method ((self monom) (other monom))
180 (with-slots ((exponents1 exponents))
181 self
182 (with-slots ((exponents2 exponents))
183 other
184 (unless (= (length exponents1) (length exponents2))
185 (error "divide-by: Incompatible dimensions."))
186 (unless (every #'>= exponents1 exponents2)
187 (error "divide-by: Negative power would result."))
188 (map-into exponents1 #'- exponents1 exponents2)))
189 self))
190
191(defmethod copy-instance :around (object &rest initargs &key &allow-other-keys)
192 (:documentation "An :AROUND method of COPY-INSTANCE. It replaces
193exponents with a fresh copy of the sequence.")
194 (:method ((object monom) &rest initargs &key &allow-other-keys)
195 (declare (ignore object initargs))
196 (let ((copy (call-next-method)))
197 (setf (monom-exponents copy) (copy-seq (monom-exponents copy)))
198 copy)))
199
200(defmethod monom-multiply-2 ((m1 monom) (m2 monom))
201 "Non-destructively multiply monomial M1 by M2."
202 (multiply-by (copy-instance m1) (copy-instance m2)))
203
204(defmethod monom-multiply ((numerator monom) &rest denominators)
205 "Non-destructively divide monomial NUMERATOR by product of DENOMINATORS."
206 (divide-by (copy-instance numerator) (reduce #'monom-multiply-2 denominators)))
207
208(defmethod monom-divides-p ((m1 monom) (m2 monom))
209 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
210 (with-slots ((exponents1 exponents))
211 m1
212 (with-slots ((exponents2 exponents))
213 m2
214 (every #'<= exponents1 exponents2))))
215
216
217(defmethod monom-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
218 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
219 (every #'(lambda (x y z) (<= x (max y z)))
220 m1 m2 m3))
221
222
223(defmethod monom-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
224 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
225 (declare (type monom m1 m2 m3 m4))
226 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
227 m1 m2 m3 m4))
228
229(defmethod monom-lcm-equal-lcm-p (m1 m2 m3 m4)
230 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
231 (with-slots ((exponents1 exponents))
232 m1
233 (with-slots ((exponents2 exponents))
234 m2
235 (with-slots ((exponents3 exponents))
236 m3
237 (with-slots ((exponents4 exponents))
238 m4
239 (every
240 #'(lambda (x y z w) (= (max x y) (max z w)))
241 exponents1 exponents2 exponents3 exponents4))))))
242
243(defmethod monom-divisible-by-p ((m1 monom) (m2 monom))
244 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
245 (with-slots ((exponents1 exponents))
246 m1
247 (with-slots ((exponents2 exponents))
248 m2
249 (every #'>= exponents1 exponents2))))
250
251(defmethod monom-rel-prime-p ((m1 monom) (m2 monom))
252 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
253 (with-slots ((exponents1 exponents))
254 m1
255 (with-slots ((exponents2 exponents))
256 m2
257 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
258
259
260(defmethod monom-lcm ((m1 monom) (m2 monom))
261 "Returns least common multiple of monomials M1 and M2."
262 (with-slots ((exponents1 exponents))
263 m1
264 (with-slots ((exponents2 exponents))
265 m2
266 (let* ((exponents (copy-seq exponents1)))
267 (map-into exponents #'max exponents1 exponents2)
268 (make-instance 'monom :exponents exponents)))))
269
270
271(defmethod monom-gcd ((m1 monom) (m2 monom))
272 "Returns greatest common divisor of monomials M1 and M2."
273 (with-slots ((exponents1 exponents))
274 m1
275 (with-slots ((exponents2 exponents))
276 m2
277 (let* ((exponents (copy-seq exponents1)))
278 (map-into exponents #'min exponents1 exponents2)
279 (make-instance 'monom :exponents exponents)))))
280
281(defmethod monom-depends-p ((m monom) k)
282 "Return T if the monomial M depends on variable number K."
283 (declare (type fixnum k))
284 (with-slots (exponents)
285 m
286 (plusp (elt exponents k))))
287
288(defmethod monom-left-tensor-product-by ((self monom) (other monom))
289 (with-slots ((exponents1 exponents))
290 self
291 (with-slots ((exponents2 exponents))
292 other
293 (setf exponents1 (concatenate 'vector exponents2 exponents1))))
294 self)
295
296(defmethod monom-right-tensor-product-by ((self monom) (other monom))
297 (with-slots ((exponents1 exponents))
298 self
299 (with-slots ((exponents2 exponents))
300 other
301 (setf exponents1 (concatenate 'vector exponents1 exponents2))))
302 self)
303
304(defmethod monom-left-contract ((self monom) k)
305 "Drop the first K variables in monomial M."
306 (declare (fixnum k))
307 (with-slots (exponents)
308 self
309 (setf exponents (subseq exponents k)))
310 self)
311
312(defun make-monom-variable (nvars pos &optional (power 1)
313 &aux (m (make-instance 'monom :dimension nvars)))
314 "Construct a monomial in the polynomial ring
315RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
316which represents a single variable. It assumes number of variables
317NVARS and the variable is at position POS. Optionally, the variable
318may appear raised to power POWER. "
319 (declare (type fixnum nvars pos power) (type monom m))
320 (with-slots (exponents)
321 m
322 (setf (elt exponents pos) power)
323 m))
324
325(defmethod monom->list ((m monom))
326 "A human-readable representation of a monomial M as a list of exponents."
327 (coerce (monom-exponents m) 'list))
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