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source: branches/f4grobner/monom.lisp@ 3444

Last change on this file since 3444 was 3443, 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)
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 &aux (start 0) (end (monom-dimension m)))
161 "Return the sugar of a monomial M. Optinally, a range
162of variables may be specified with arguments START and END."
163 (declare (type fixnum start end))
164 (monom-total-degree m start end))
165
166(defmethod monom-multiply-by ((self monom) (other monom))
167 (with-slots ((exponents1 exponents))
168 self
169 (with-slots ((exponents2 exponents))
170 other
171 (unless (= (length exponents1) (length exponents2))
172 (error "Incompatible dimensions"))
173 (map-into exponents1 #'+ exponents1 exponents2)))
174 self)
175
176(defmethod divide-by ((self monom) (other monom))
177 (with-slots ((exponents1 exponents))
178 self
179 (with-slots ((exponents2 exponents))
180 other
181 (unless (= (length exponents1) (length exponents2))
182 (error "divide-by: Incompatible dimensions."))
183 (unless (every #'>= exponents1 exponents2)
184 (error "divide-by: Negative power would result."))
185 (map-into exponents1 #'- exponents1 exponents2)))
186 self)
187
188(defmethod monom-copy-instance ((object monom) &rest initargs &key &allow-other-keys)
189 "An :AROUNT method for COPY-INSTANCE. The primary method is a shallow copy,
190 while for monomials we typically need a fresh copy of the
191 exponents."
192 (declare (ignore object initargs))
193 (let ((copy (call-next-method)))
194 (setf (monom-exponents copy) (copy-seq (monom-exponents copy)))
195 copy))
196
197(defmethod monom-multiply-2 ((m1 monom) (m2 monom))
198 "Non-destructively multiply monomial M1 by M2."
199 (multiply-by (copy-instance m1) (copy-instance m2)))
200
201(defmethod monom-multiply ((numerator monom) &rest denominators)
202 "Non-destructively divide monomial NUMERATOR by product of DENOMINATORS."
203 (divide-by (copy-instance numerator) (reduce #'monom-multiply-2 denominators)))
204
205(defmethod monom-divides-p ((m1 monom) (m2 monom))
206 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
207 (with-slots ((exponents1 exponents))
208 m1
209 (with-slots ((exponents2 exponents))
210 m2
211 (every #'<= exponents1 exponents2))))
212
213
214(defmethod monom-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
215 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
216 (every #'(lambda (x y z) (<= x (max y z)))
217 m1 m2 m3))
218
219
220(defmethod monom-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
221 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
222 (declare (type monom m1 m2 m3 m4))
223 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
224 m1 m2 m3 m4))
225
226(defmethod monom-lcm-equal-lcm-p (m1 m2 m3 m4)
227 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
228 (with-slots ((exponents1 exponents))
229 m1
230 (with-slots ((exponents2 exponents))
231 m2
232 (with-slots ((exponents3 exponents))
233 m3
234 (with-slots ((exponents4 exponents))
235 m4
236 (every
237 #'(lambda (x y z w) (= (max x y) (max z w)))
238 exponents1 exponents2 exponents3 exponents4))))))
239
240(defmethod monom-divisible-by-p ((m1 monom) (m2 monom))
241 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
242 (with-slots ((exponents1 exponents))
243 m1
244 (with-slots ((exponents2 exponents))
245 m2
246 (every #'>= exponents1 exponents2))))
247
248(defmethod monom-rel-prime-p ((m1 monom) (m2 monom))
249 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
250 (with-slots ((exponents1 exponents))
251 m1
252 (with-slots ((exponents2 exponents))
253 m2
254 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
255
256
257(defmethod monom-lcm ((m1 monom) (m2 monom))
258 "Returns least common multiple of monomials M1 and M2."
259 (with-slots ((exponents1 exponents))
260 m1
261 (with-slots ((exponents2 exponents))
262 m2
263 (let* ((exponents (copy-seq exponents1)))
264 (map-into exponents #'max exponents1 exponents2)
265 (make-instance 'monom :exponents exponents)))))
266
267
268(defmethod monom-gcd ((m1 monom) (m2 monom))
269 "Returns greatest common divisor of monomials M1 and M2."
270 (with-slots ((exponents1 exponents))
271 m1
272 (with-slots ((exponents2 exponents))
273 m2
274 (let* ((exponents (copy-seq exponents1)))
275 (map-into exponents #'min exponents1 exponents2)
276 (make-instance 'monom :exponents exponents)))))
277
278(defmethod monom-depends-p ((m monom) k)
279 "Return T if the monomial M depends on variable number K."
280 (declare (type fixnum k))
281 (with-slots (exponents)
282 m
283 (plusp (elt exponents k))))
284
285(defmethod monom-left-tensor-product-by ((self monom) (other monom))
286 (with-slots ((exponents1 exponents))
287 self
288 (with-slots ((exponents2 exponents))
289 other
290 (setf exponents1 (concatenate 'vector exponents2 exponents1))))
291 self)
292
293(defmethod monom-right-tensor-product-by ((self monom) (other monom))
294 (with-slots ((exponents1 exponents))
295 self
296 (with-slots ((exponents2 exponents))
297 other
298 (setf exponents1 (concatenate 'vector exponents1 exponents2))))
299 self)
300
301(defmethod monom-left-contract ((self monom) k)
302 "Drop the first K variables in monomial M."
303 (declare (fixnum k))
304 (with-slots (exponents)
305 self
306 (setf exponents (subseq exponents k)))
307 self)
308
309(defun make-monom-variable (nvars pos &optional (power 1)
310 &aux (m (make-instance 'monom :dimension nvars)))
311 "Construct a monomial in the polynomial ring
312RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
313which represents a single variable. It assumes number of variables
314NVARS and the variable is at position POS. Optionally, the variable
315may appear raised to power POWER. "
316 (declare (type fixnum nvars pos power) (type monom m))
317 (with-slots (exponents)
318 m
319 (setf (elt exponents pos) power)
320 m))
321
322(defmethod monom->list ((m monom))
323 "A human-readable representation of a monomial M as a list of exponents."
324 (coerce (monom-exponents m) 'list))
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