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source: branches/f4grobner/monom.lisp@ 3459

Last change on this file since 3459 was 3456, checked in by Marek Rychlik, 9 years ago

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[1201]1;;; -*- Mode: Lisp -*-
[81]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
[1610]22(defpackage "MONOM"
[3446]23 (:use :cl :copy)
[422]24 (:export "MONOM"
[423]25 "EXPONENT"
[2781]26 "MONOM-DIMENSION"
27 "MONOM-EXPONENTS"
[3442]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
[2524]52 (:documentation
53 "This package implements basic operations on monomials.
54DATA STRUCTURES: Conceptually, monomials can be represented as lists:
[81]55
[2524]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
[1610]68(in-package :monom)
[48]69
[1925]70(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
[1923]71
[48]72(deftype exponent ()
73 "Type of exponent in a monomial."
74 'fixnum)
75
[2022]76(defclass monom ()
[3312]77 ((exponents :initarg :exponents :accessor monom-exponents
[3054]78 :documentation "The powers of the variables."))
[3289]79 ;; default-initargs are not needed, they are handled by SHARED-INITIALIZE
80 ;;(:default-initargs :dimension 'foo :exponents 'bar :exponent 'baz)
[2779]81 (:documentation
82 "Implements a monomial, i.e. a product of powers
83of variables, like X*Y^2."))
[880]84
[2245]85(defmethod print-object ((self monom) stream)
[3196]86 (print-unreadable-object (self stream :type t :identity t)
[3313]87 (with-accessors ((exponents monom-exponents))
[3216]88 self
[3313]89 (format stream "EXPONENTS=~A"
90 exponents))))
[2027]91
[3299]92(defmethod initialize-instance :after ((self monom)
[3297]93 &key
94 (dimension 0 dimension-supplied-p)
95 (exponents nil exponents-supplied-p)
[3318]96 (exponent 0)
[3297]97 &allow-other-keys
[2390]98 )
[3329]99 "The following INITIALIZE-INSTANCE method allows instance initialization
100of a MONOM in a style similar to MAKE-ARRAY, e.g.:
[3328]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)>
[3329]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.
[3328]110"
[3315]111 (cond
112 (exponents-supplied-p
[3327]113 (when (and dimension-supplied-p
114 (/= dimension (length exponents)))
115 (error "EXPONENTS (~A) must have supplied length DIMENSION (~A)"
116 exponents dimension))
[3315]117 (let ((dim (length exponents)))
118 (setf (slot-value self 'exponents) (make-array dim :initial-contents exponents))))
[3321]119 (dimension-supplied-p
[3315]120 ;; when all exponents are to be identical
[3321]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."))))
[3293]126
[3443]127(defgeneric monom-dimension (m)
128 (:method ((m monom))
129 (length (monom-exponents m))))
[3317]130
[3443]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))))
[2547]135
[3443]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))))
[48]143
[3443]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
[3453]149 (setf (elt exponents index) new-value))))
[2023]150
[3450]151(defgeneric monom-total-degree (m &optional start end)
[3449]152 (:documentation "Return the todal degree of a monomoal M. Optinally, a range
153of variables may be specified with arguments START and END.")
154 (:method ((m monom) &optional (start 0) (end (monom-dimension m)))
155 (declare (type fixnum start end))
156 (with-slots (exponents)
157 m
158 (reduce #'+ exponents :start start :end end))))
[48]159
[3451]160(defgeneric monom-sugar (m &optional start end)
[3446]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)))
[48]166
[3446]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))
[2069]177
[3456]178(defgeneric monom-divide-by (self other)
[3446]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))
[2818]190
[3448]191(defmethod copy-instance :around ((object monom) &rest initargs &key &allow-other-keys)
192 "An :AROUND method of COPY-INSTANCE. It replaces
193exponents with a fresh copy of the sequence."
[3446]194 (declare (ignore object initargs))
195 (let ((copy (call-next-method)))
196 (setf (monom-exponents copy) (copy-seq (monom-exponents copy)))
[3453]197 copy))
[2950]198
[3442]199(defmethod monom-multiply-2 ((m1 monom) (m2 monom))
[2816]200 "Non-destructively multiply monomial M1 by M2."
[3454]201 (monom-multiply-by (copy-instance m1) (copy-instance m2)))
[2816]202
[3442]203(defmethod monom-multiply ((numerator monom) &rest denominators)
[3416]204 "Non-destructively divide monomial NUMERATOR by product of DENOMINATORS."
[3455]205 (monom-divide-by (copy-instance numerator) (reduce #'monom-multiply-2 denominators)))
[48]206
[3441]207(defmethod monom-divides-p ((m1 monom) (m2 monom))
[48]208 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
[2039]209 (with-slots ((exponents1 exponents))
210 m1
211 (with-slots ((exponents2 exponents))
212 m2
213 (every #'<= exponents1 exponents2))))
[48]214
[2075]215
[3441]216(defmethod monom-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
[2055]217 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
[875]218 (every #'(lambda (x y z) (<= x (max y z)))
[869]219 m1 m2 m3))
[48]220
[2049]221
[3441]222(defmethod monom-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
[48]223 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
[1890]224 (declare (type monom m1 m2 m3 m4))
[869]225 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
226 m1 m2 m3 m4))
227
[3441]228(defmethod monom-lcm-equal-lcm-p (m1 m2 m3 m4)
[2075]229 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
[2171]230 (with-slots ((exponents1 exponents))
[2076]231 m1
[2171]232 (with-slots ((exponents2 exponents))
[2076]233 m2
[2171]234 (with-slots ((exponents3 exponents))
[2076]235 m3
[2171]236 (with-slots ((exponents4 exponents))
[2076]237 m4
[2077]238 (every
239 #'(lambda (x y z w) (= (max x y) (max z w)))
240 exponents1 exponents2 exponents3 exponents4))))))
[48]241
[3441]242(defmethod monom-divisible-by-p ((m1 monom) (m2 monom))
[48]243 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
[2171]244 (with-slots ((exponents1 exponents))
[2144]245 m1
[2171]246 (with-slots ((exponents2 exponents))
[2144]247 m2
248 (every #'>= exponents1 exponents2))))
[2078]249
[3441]250(defmethod monom-rel-prime-p ((m1 monom) (m2 monom))
[48]251 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
[2171]252 (with-slots ((exponents1 exponents))
[2078]253 m1
[2171]254 (with-slots ((exponents2 exponents))
[2078]255 m2
[2154]256 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
[48]257
[2076]258
[3441]259(defmethod monom-lcm ((m1 monom) (m2 monom))
[48]260 "Returns least common multiple of monomials M1 and M2."
[3322]261 (with-slots ((exponents1 exponents))
[2082]262 m1
[2171]263 (with-slots ((exponents2 exponents))
[2082]264 m2
[3324]265 (let* ((exponents (copy-seq exponents1)))
[2082]266 (map-into exponents #'max exponents1 exponents2)
[3322]267 (make-instance 'monom :exponents exponents)))))
[48]268
[2080]269
[3441]270(defmethod monom-gcd ((m1 monom) (m2 monom))
[48]271 "Returns greatest common divisor of monomials M1 and M2."
[3322]272 (with-slots ((exponents1 exponents))
[2082]273 m1
[2171]274 (with-slots ((exponents2 exponents))
[2082]275 m2
[3322]276 (let* ((exponents (copy-seq exponents1)))
[2082]277 (map-into exponents #'min exponents1 exponents2)
[3322]278 (make-instance 'monom :exponents exponents)))))
[48]279
[3441]280(defmethod monom-depends-p ((m monom) k)
[48]281 "Return T if the monomial M depends on variable number K."
[2083]282 (declare (type fixnum k))
283 (with-slots (exponents)
284 m
[2154]285 (plusp (elt exponents k))))
[48]286
[3441]287(defmethod monom-left-tensor-product-by ((self monom) (other monom))
[3323]288 (with-slots ((exponents1 exponents))
[3020]289 self
[3323]290 (with-slots ((exponents2 exponents))
[3020]291 other
[3323]292 (setf exponents1 (concatenate 'vector exponents2 exponents1))))
[3036]293 self)
[48]294
[3441]295(defmethod monom-right-tensor-product-by ((self monom) (other monom))
[3323]296 (with-slots ((exponents1 exponents))
[3026]297 self
[3323]298 (with-slots ((exponents2 exponents))
[3026]299 other
[3323]300 (setf exponents1 (concatenate 'vector exponents1 exponents2))))
[3036]301 self)
[3026]302
[3441]303(defmethod monom-left-contract ((self monom) k)
[1638]304 "Drop the first K variables in monomial M."
[2085]305 (declare (fixnum k))
[3323]306 (with-slots (exponents)
[3040]307 self
[3323]308 (setf exponents (subseq exponents k)))
[3039]309 self)
[886]310
311(defun make-monom-variable (nvars pos &optional (power 1)
[2218]312 &aux (m (make-instance 'monom :dimension nvars)))
[886]313 "Construct a monomial in the polynomial ring
314RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
315which represents a single variable. It assumes number of variables
316NVARS and the variable is at position POS. Optionally, the variable
317may appear raised to power POWER. "
[1924]318 (declare (type fixnum nvars pos power) (type monom m))
[2089]319 (with-slots (exponents)
320 m
[2154]321 (setf (elt exponents pos) power)
[2089]322 m))
[1151]323
[3441]324(defmethod monom->list ((m monom))
[1152]325 "A human-readable representation of a monomial M as a list of exponents."
[2779]326 (coerce (monom-exponents m) 'list))
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