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source: branches/f4grobner/monom.lisp@ 3442

Last change on this file since 3442 was 3442, 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(defmethod monom-dimension (m)
128 (length (monom-exponents ,m)))
129
130(defmethod monom-equalp (m1 m2)
131 "Returns T iff monomials M1 and M2 have identical
132EXPONENTS."
133 `(equalp (monom-exponents ,m1) (monom-exponents ,m2)))
134
135(defmethod monom-elt (m index)
136 "Return the power in the monomial M of variable number INDEX."
137 (with-slots (exponents)
138 m
139 (elt exponents index)))
140
141(defmethod (setf monom-elt) (new-value m index)
142 "Return the power in the monomial M of variable number INDEX."
143 (with-slots (exponents)
144 m
145 (setf (elt exponents index) new-value)))
146
147(defmethod monom-total-degree (m &optional (start 0) (end (monom-dimension m)))
148 "Return the todal degree of a monomoal M. Optinally, a range
149of variables may be specified with arguments START and END."
150 (declare (type fixnum start end))
151 (with-slots (exponents)
152 m
153 (reduce #'+ exponents :start start :end end)))
154
155
156(defmethod monom-sugar (m &aux (start 0) (end (monom-dimension m)))
157 "Return the sugar of a monomial M. Optinally, a range
158of variables may be specified with arguments START and END."
159 (declare (type fixnum start end))
160 (monom-total-degree m start end))
161
162(defmethod monom-multiply-by ((self monom) (other monom))
163 (with-slots ((exponents1 exponents))
164 self
165 (with-slots ((exponents2 exponents))
166 other
167 (unless (= (length exponents1) (length exponents2))
168 (error "Incompatible dimensions"))
169 (map-into exponents1 #'+ exponents1 exponents2)))
170 self)
171
172(defmethod divide-by ((self monom) (other monom))
173 (with-slots ((exponents1 exponents))
174 self
175 (with-slots ((exponents2 exponents))
176 other
177 (unless (= (length exponents1) (length exponents2))
178 (error "divide-by: Incompatible dimensions."))
179 (unless (every #'>= exponents1 exponents2)
180 (error "divide-by: Negative power would result."))
181 (map-into exponents1 #'- exponents1 exponents2)))
182 self)
183
184(defmethod monom-copy-instance ((object monom) &rest initargs &key &allow-other-keys)
185 "An :AROUNT method for COPY-INSTANCE. The primary method is a shallow copy,
186 while for monomials we typically need a fresh copy of the
187 exponents."
188 (declare (ignore object initargs))
189 (let ((copy (call-next-method)))
190 (setf (monom-exponents copy) (copy-seq (monom-exponents copy)))
191 copy))
192
193(defmethod monom-multiply-2 ((m1 monom) (m2 monom))
194 "Non-destructively multiply monomial M1 by M2."
195 (multiply-by (copy-instance m1) (copy-instance m2)))
196
197(defmethod monom-multiply ((numerator monom) &rest denominators)
198 "Non-destructively divide monomial NUMERATOR by product of DENOMINATORS."
199 (divide-by (copy-instance numerator) (reduce #'monom-multiply-2 denominators)))
200
201(defmethod monom-divides-p ((m1 monom) (m2 monom))
202 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
203 (with-slots ((exponents1 exponents))
204 m1
205 (with-slots ((exponents2 exponents))
206 m2
207 (every #'<= exponents1 exponents2))))
208
209
210(defmethod monom-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
211 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
212 (every #'(lambda (x y z) (<= x (max y z)))
213 m1 m2 m3))
214
215
216(defmethod monom-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
217 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
218 (declare (type monom m1 m2 m3 m4))
219 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
220 m1 m2 m3 m4))
221
222(defmethod monom-lcm-equal-lcm-p (m1 m2 m3 m4)
223 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
224 (with-slots ((exponents1 exponents))
225 m1
226 (with-slots ((exponents2 exponents))
227 m2
228 (with-slots ((exponents3 exponents))
229 m3
230 (with-slots ((exponents4 exponents))
231 m4
232 (every
233 #'(lambda (x y z w) (= (max x y) (max z w)))
234 exponents1 exponents2 exponents3 exponents4))))))
235
236(defmethod monom-divisible-by-p ((m1 monom) (m2 monom))
237 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
238 (with-slots ((exponents1 exponents))
239 m1
240 (with-slots ((exponents2 exponents))
241 m2
242 (every #'>= exponents1 exponents2))))
243
244(defmethod monom-rel-prime-p ((m1 monom) (m2 monom))
245 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
246 (with-slots ((exponents1 exponents))
247 m1
248 (with-slots ((exponents2 exponents))
249 m2
250 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
251
252
253(defmethod monom-lcm ((m1 monom) (m2 monom))
254 "Returns least common multiple of monomials M1 and M2."
255 (with-slots ((exponents1 exponents))
256 m1
257 (with-slots ((exponents2 exponents))
258 m2
259 (let* ((exponents (copy-seq exponents1)))
260 (map-into exponents #'max exponents1 exponents2)
261 (make-instance 'monom :exponents exponents)))))
262
263
264(defmethod monom-gcd ((m1 monom) (m2 monom))
265 "Returns greatest common divisor of monomials M1 and M2."
266 (with-slots ((exponents1 exponents))
267 m1
268 (with-slots ((exponents2 exponents))
269 m2
270 (let* ((exponents (copy-seq exponents1)))
271 (map-into exponents #'min exponents1 exponents2)
272 (make-instance 'monom :exponents exponents)))))
273
274(defmethod monom-depends-p ((m monom) k)
275 "Return T if the monomial M depends on variable number K."
276 (declare (type fixnum k))
277 (with-slots (exponents)
278 m
279 (plusp (elt exponents k))))
280
281(defmethod monom-left-tensor-product-by ((self monom) (other monom))
282 (with-slots ((exponents1 exponents))
283 self
284 (with-slots ((exponents2 exponents))
285 other
286 (setf exponents1 (concatenate 'vector exponents2 exponents1))))
287 self)
288
289(defmethod monom-right-tensor-product-by ((self monom) (other monom))
290 (with-slots ((exponents1 exponents))
291 self
292 (with-slots ((exponents2 exponents))
293 other
294 (setf exponents1 (concatenate 'vector exponents1 exponents2))))
295 self)
296
297(defmethod monom-left-contract ((self monom) k)
298 "Drop the first K variables in monomial M."
299 (declare (fixnum k))
300 (with-slots (exponents)
301 self
302 (setf exponents (subseq exponents k)))
303 self)
304
305(defun make-monom-variable (nvars pos &optional (power 1)
306 &aux (m (make-instance 'monom :dimension nvars)))
307 "Construct a monomial in the polynomial ring
308RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
309which represents a single variable. It assumes number of variables
310NVARS and the variable is at position POS. Optionally, the variable
311may appear raised to power POWER. "
312 (declare (type fixnum nvars pos power) (type monom m))
313 (with-slots (exponents)
314 m
315 (setf (elt exponents pos) power)
316 m))
317
318(defmethod monom->list ((m monom))
319 "A human-readable representation of a monomial M as a list of exponents."
320 (coerce (monom-exponents m) 'list))
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