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source: branches/f4grobner/monom.lisp@ 2220

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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
[418]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;;
[714]37;; Monom x*y^2 ---> (1 2)
[418]38;;
39;;----------------------------------------------------------------
40
[1610]41(defpackage "MONOM"
[2025]42 (:use :cl :ring)
[422]43 (:export "MONOM"
[423]44 "EXPONENT"
[2124]45 "MAKE-MONOM"
[2125]46 "MONOM-DIMENSION"
[2124]47 "MONOM-EXPONENTS"
48 "MAKE-MONOM-VARIABLE"))
[81]49
[1610]50(in-package :monom)
[48]51
[1925]52(proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
[1923]53
[48]54(deftype exponent ()
55 "Type of exponent in a monomial."
56 'fixnum)
57
[2022]58(defclass monom ()
[2193]59 ((dimension :initarg :dimension :accessor monom-dimension)
[2125]60 (exponents :initarg :exponents :accessor monom-exponents))
[2197]61 (:default-initargs :dimension 0 :exponents nil))
[880]62
[2028]63(defmethod print-object ((m monom) stream)
[2036]64 (princ (slot-value m 'exponents) stream))
[2027]65
[2220]66(defmethod initialize-instance :after ((self monom) &rest args &key)
67 (format t "INITIALIZE-INSTANCE-INSTANCE called with SELF ~A, args ~A.~%"
68 self args)
[2219]69 (call-next-method))
[2220]70
[2219]71
[2220]72(defmethod make-instance :around ((self monom)
[2216]73 &key
74 (dimension nil dimension-suppied-p)
75 (exponents nil exponents-supplied-p)
76 (exponent nil exponent-supplied-p))
[2199]77 "A constructor (factory) of monomials. If DIMENSION is given, a
78sequence of DIMENSION elements of type EXPONENT is constructed, where
[2204]79individual elements are the value of EXPONENT, which defaults
[2199]80to 0. Alternatively, all elements may be specified as a list
[2204]81EXPONENTS."
[2216]82 (format t "MAKE-INSTANCE called with DIMENSION ~A(~A), EXPONENTS ~A(~A), EXPONENT ~A(~A).~%"
[2215]83 dimension dimension-suppied-p
[2214]84 exponents exponents-supplied-p
85 exponent exponent-supplied-p)
[2215]86 #|
[2213]87 (let ((new-dimension (cond (dimension-suppied-p dimension)
88 (exponents-supplied-p
89 (length exponents))
90 (t
91 (error "You must provide DIMENSION or EXPONENTS"))))
92 (new-exponents (cond
93 ;; when exponents are supplied
94 (exponents-supplied-p
95 (make-array (list dimension) :initial-contents exponents
96 :element-type 'exponent))
97 ;; when all exponents are to be identical
98 (exponent-supplied-p
99 (make-array (list dimension) :initial-element exponent
100 :element-type 'exponent))
101 ;; otherwise, all exponents are zero
102 (t
103 (make-array (list dimension) :element-type 'exponent :initial-element 0)))))
[2215]104 |#
[2218]105 (call-next-method :dimension dimension :exponents exponents))
[717]106
[48]107;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
108;;
109;; Operations on monomials
110;;
111;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
112
[2143]113(defmethod r-dimension ((m monom))
[2126]114 (monom-dimension m))
[745]115
[2143]116(defmethod r-elt ((m monom) index)
[48]117 "Return the power in the monomial M of variable number INDEX."
[2023]118 (with-slots (exponents)
119 m
[2154]120 (elt exponents index)))
[48]121
[2160]122(defmethod (setf r-elt) (new-value (m monom) index)
[2023]123 "Return the power in the monomial M of variable number INDEX."
124 (with-slots (exponents)
125 m
[2154]126 (setf (elt exponents index) new-value)))
[2023]127
[2149]128(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
[48]129 "Return the todal degree of a monomoal M. Optinally, a range
130of variables may be specified with arguments START and END."
[2023]131 (declare (type fixnum start end))
132 (with-slots (exponents)
133 m
[2154]134 (reduce #'+ exponents :start start :end end)))
[48]135
[2064]136
[2149]137(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
[48]138 "Return the sugar of a monomial M. Optinally, a range
139of variables may be specified with arguments START and END."
[2032]140 (declare (type fixnum start end))
[2155]141 (r-total-degree m start end))
[48]142
[2144]143(defmethod r* ((m1 monom) (m2 monom))
[2072]144 "Multiply monomial M1 by monomial M2."
[2195]145 (with-slots ((exponents1 exponents) dimension)
[2038]146 m1
[2170]147 (with-slots ((exponents2 exponents))
[2038]148 m2
[2167]149 (let* ((exponents (copy-seq exponents1)))
[2154]150 (map-into exponents #'+ exponents1 exponents2)
[2195]151 (make-instance 'monom :dimension dimension :exponents exponents)))))
[2038]152
[2069]153
154
[2144]155(defmethod r/ ((m1 monom) (m2 monom))
[1896]156 "Divide monomial M1 by monomial M2."
[2037]157 (with-slots ((exponents1 exponents))
[2034]158 m1
[2037]159 (with-slots ((exponents2 exponents))
[2034]160 m2
161 (let* ((exponents (copy-seq exponents1))
[2195]162 (dimension (reduce #'+ exponents)))
[2154]163 (map-into exponents #'- exponents1 exponents2)
[2195]164 (make-instance 'monom :dimension dimension :exponents exponents)))))
[48]165
[2144]166(defmethod r-divides-p ((m1 monom) (m2 monom))
[48]167 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
[2039]168 (with-slots ((exponents1 exponents))
169 m1
170 (with-slots ((exponents2 exponents))
171 m2
172 (every #'<= exponents1 exponents2))))
[48]173
[2075]174
[2144]175(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
[2055]176 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
[875]177 (every #'(lambda (x y z) (<= x (max y z)))
[869]178 m1 m2 m3))
[48]179
[2049]180
[2144]181(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
[48]182 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
[1890]183 (declare (type monom m1 m2 m3 m4))
[869]184 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
185 m1 m2 m3 m4))
186
[2144]187(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
[2075]188 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
[2171]189 (with-slots ((exponents1 exponents))
[2076]190 m1
[2171]191 (with-slots ((exponents2 exponents))
[2076]192 m2
[2171]193 (with-slots ((exponents3 exponents))
[2076]194 m3
[2171]195 (with-slots ((exponents4 exponents))
[2076]196 m4
[2077]197 (every
198 #'(lambda (x y z w) (= (max x y) (max z w)))
199 exponents1 exponents2 exponents3 exponents4))))))
[48]200
[2144]201(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
[48]202 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
[2171]203 (with-slots ((exponents1 exponents))
[2144]204 m1
[2171]205 (with-slots ((exponents2 exponents))
[2144]206 m2
207 (every #'>= exponents1 exponents2))))
[2078]208
[2146]209(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
[48]210 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
[2171]211 (with-slots ((exponents1 exponents))
[2078]212 m1
[2171]213 (with-slots ((exponents2 exponents))
[2078]214 m2
[2154]215 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
[48]216
[2076]217
[2163]218(defmethod r-equalp ((m1 monom) (m2 monom))
[48]219 "Returns T if two monomials M1 and M2 are equal."
[2171]220 (with-slots ((exponents1 exponents))
[2079]221 m1
[2171]222 (with-slots ((exponents2 exponents))
[2079]223 m2
224 (every #'= exponents1 exponents2))))
[48]225
[2146]226(defmethod r-lcm ((m1 monom) (m2 monom))
[48]227 "Returns least common multiple of monomials M1 and M2."
[2171]228 (with-slots ((exponents1 exponents))
[2082]229 m1
[2171]230 (with-slots ((exponents2 exponents))
[2082]231 m2
232 (let* ((exponents (copy-seq exponents1))
[2195]233 (dimension (reduce #'+ exponents)))
[2082]234 (map-into exponents #'max exponents1 exponents2)
[2200]235 (make-instance 'monom :dimension dimension :exponents exponents)))))
[48]236
[2080]237
[2146]238(defmethod r-gcd ((m1 monom) (m2 monom))
[48]239 "Returns greatest common divisor of monomials M1 and M2."
[2171]240 (with-slots ((exponents1 exponents))
[2082]241 m1
[2171]242 (with-slots ((exponents2 exponents))
[2082]243 m2
244 (let* ((exponents (copy-seq exponents1))
[2195]245 (dimension (reduce #'+ exponents)))
[2082]246 (map-into exponents #'min exponents1 exponents2)
[2197]247 (make-instance 'monom :dimension dimension :exponents exponents)))))
[48]248
[2146]249(defmethod r-depends-p ((m monom) k)
[48]250 "Return T if the monomial M depends on variable number K."
[2083]251 (declare (type fixnum k))
252 (with-slots (exponents)
253 m
[2154]254 (plusp (elt exponents k))))
[48]255
[2146]256(defmethod r-tensor-product ((m1 monom) (m2 monom)
[2195]257 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
258 (declare (fixnum dimension))
[2171]259 (with-slots ((exponents1 exponents))
[2087]260 m1
[2171]261 (with-slots ((exponents2 exponents))
[2087]262 m2
[2147]263 (make-instance 'monom
[2195]264 :dimension dimension
[2147]265 :exponents (concatenate 'vector exponents1 exponents2)))))
[48]266
[2148]267(defmethod r-contract ((m monom) k)
[1638]268 "Drop the first K variables in monomial M."
[2085]269 (declare (fixnum k))
[2196]270 (with-slots (dimension exponents)
[2085]271 m
[2197]272 (setf dimension (- dimension k)
[2085]273 exponents (subseq exponents k))))
[886]274
275(defun make-monom-variable (nvars pos &optional (power 1)
[2218]276 &aux (m (make-instance 'monom :dimension nvars)))
[886]277 "Construct a monomial in the polynomial ring
278RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
279which represents a single variable. It assumes number of variables
280NVARS and the variable is at position POS. Optionally, the variable
281may appear raised to power POWER. "
[1924]282 (declare (type fixnum nvars pos power) (type monom m))
[2089]283 (with-slots (exponents)
284 m
[2154]285 (setf (elt exponents pos) power)
[2089]286 m))
[1151]287
[2150]288(defmethod r->list ((m monom))
[1152]289 "A human-readable representation of a monomial M as a list of exponents."
[2148]290 (coerce (monom-exponents m) 'list))
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