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source: branches/f4grobner/monom.lisp@ 2317

Last change on this file since 2317 was 2314, 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
[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))
[2268]61 (:default-initargs :dimension nil :exponents nil :exponent nil))
[880]62
[2245]63(defmethod print-object ((self monom) stream)
64 (format stream "#<MONOM DIMENSION=~A EXPONENTS=~A>"
65 (slot-value self 'dimension)
66 (slot-value self 'exponents)))
[2027]67
[2309]68#|
69;; Debug calls to initialize-instance
[2298]70(defmethod initialize-instance :around ((self monom)
[2281]71 &rest
72 args
73 &key
74 &allow-other-keys)
[2296]75 (format t "MONOM::INITIALIZE-INSTANCE called with:~&ARGS: ~W.~%" args)
[2297]76 (call-next-method)
77 )
[2309]78|#
[2278]79
[2282]80(defmethod initialize-instance ((self monom)
81 ;;&rest args
82 &key
83 dimension
84 exponents
85 exponent
86 &allow-other-keys
87 )
[2269]88 (let* ((new-dimension (cond (dimension dimension)
89 (exponents
[2261]90 (length exponents))
91 (t
[2269]92 (error "DIMENSION or EXPONENTS must not be NIL"))))
[2261]93 (new-exponents (cond
94 ;; when exponents are supplied
[2269]95 (exponents
96 (make-array (list new-dimension) :initial-contents exponents))
[2261]97 ;; when all exponents are to be identical
[2269]98 (exponent
[2261]99 (make-array (list new-dimension) :initial-element exponent
100 :element-type 'exponent))
101 ;; otherwise, all exponents are zero
102 (t
[2262]103 (make-array (list new-dimension) :element-type 'exponent :initial-element 0)))))
[2267]104 (setf (slot-value self 'dimension) new-dimension
[2294]105 (slot-value self 'exponents) new-exponents)))
[717]106
[2221]107
[2225]108
[48]109;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
110;;
111;; Operations on monomials
112;;
113;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
114
[2143]115(defmethod r-dimension ((m monom))
[2126]116 (monom-dimension m))
[745]117
[2143]118(defmethod r-elt ((m monom) index)
[48]119 "Return the power in the monomial M of variable number INDEX."
[2023]120 (with-slots (exponents)
121 m
[2154]122 (elt exponents index)))
[48]123
[2160]124(defmethod (setf r-elt) (new-value (m monom) index)
[2023]125 "Return the power in the monomial M of variable number INDEX."
126 (with-slots (exponents)
127 m
[2154]128 (setf (elt exponents index) new-value)))
[2023]129
[2149]130(defmethod r-total-degree ((m monom) &optional (start 0) (end (r-dimension m)))
[48]131 "Return the todal degree of a monomoal M. Optinally, a range
132of variables may be specified with arguments START and END."
[2023]133 (declare (type fixnum start end))
134 (with-slots (exponents)
135 m
[2154]136 (reduce #'+ exponents :start start :end end)))
[48]137
[2064]138
[2149]139(defmethod r-sugar ((m monom) &aux (start 0) (end (r-dimension m)))
[48]140 "Return the sugar of a monomial M. Optinally, a range
141of variables may be specified with arguments START and END."
[2032]142 (declare (type fixnum start end))
[2155]143 (r-total-degree m start end))
[48]144
[2144]145(defmethod r* ((m1 monom) (m2 monom))
[2072]146 "Multiply monomial M1 by monomial M2."
[2195]147 (with-slots ((exponents1 exponents) dimension)
[2038]148 m1
[2170]149 (with-slots ((exponents2 exponents))
[2038]150 m2
[2167]151 (let* ((exponents (copy-seq exponents1)))
[2154]152 (map-into exponents #'+ exponents1 exponents2)
[2195]153 (make-instance 'monom :dimension dimension :exponents exponents)))))
[2038]154
[2069]155
156
[2144]157(defmethod r/ ((m1 monom) (m2 monom))
[1896]158 "Divide monomial M1 by monomial M2."
[2313]159 (with-slots ((exponents1 exponents) (dimension1 dimension))
[2034]160 m1
[2037]161 (with-slots ((exponents2 exponents))
[2034]162 m2
163 (let* ((exponents (copy-seq exponents1))
[2314]164 (dimension dimension1))
[2154]165 (map-into exponents #'- exponents1 exponents2)
[2195]166 (make-instance 'monom :dimension dimension :exponents exponents)))))
[48]167
[2144]168(defmethod r-divides-p ((m1 monom) (m2 monom))
[48]169 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
[2039]170 (with-slots ((exponents1 exponents))
171 m1
172 (with-slots ((exponents2 exponents))
173 m2
174 (every #'<= exponents1 exponents2))))
[48]175
[2075]176
[2144]177(defmethod r-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom))
[2055]178 "Returns T if monomial M1 divides LCM(M2,M3), NIL otherwise."
[875]179 (every #'(lambda (x y z) (<= x (max y z)))
[869]180 m1 m2 m3))
[48]181
[2049]182
[2144]183(defmethod r-lcm-divides-lcm-p ((m1 monom) (m2 monom) (m3 monom) (m4 monom))
[48]184 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
[1890]185 (declare (type monom m1 m2 m3 m4))
[869]186 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
187 m1 m2 m3 m4))
188
[2144]189(defmethod r-lcm-equal-lcm-p (m1 m2 m3 m4)
[2075]190 "Returns T if monomial LCM(M1,M2) equals LCM(M3,M4), NIL otherwise."
[2171]191 (with-slots ((exponents1 exponents))
[2076]192 m1
[2171]193 (with-slots ((exponents2 exponents))
[2076]194 m2
[2171]195 (with-slots ((exponents3 exponents))
[2076]196 m3
[2171]197 (with-slots ((exponents4 exponents))
[2076]198 m4
[2077]199 (every
200 #'(lambda (x y z w) (= (max x y) (max z w)))
201 exponents1 exponents2 exponents3 exponents4))))))
[48]202
[2144]203(defmethod r-divisible-by-p ((m1 monom) (m2 monom))
[48]204 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
[2171]205 (with-slots ((exponents1 exponents))
[2144]206 m1
[2171]207 (with-slots ((exponents2 exponents))
[2144]208 m2
209 (every #'>= exponents1 exponents2))))
[2078]210
[2146]211(defmethod r-rel-prime-p ((m1 monom) (m2 monom))
[48]212 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
[2171]213 (with-slots ((exponents1 exponents))
[2078]214 m1
[2171]215 (with-slots ((exponents2 exponents))
[2078]216 m2
[2154]217 (every #'(lambda (x y) (zerop (min x y))) exponents1 exponents2))))
[48]218
[2076]219
[2163]220(defmethod r-equalp ((m1 monom) (m2 monom))
[48]221 "Returns T if two monomials M1 and M2 are equal."
[2171]222 (with-slots ((exponents1 exponents))
[2079]223 m1
[2171]224 (with-slots ((exponents2 exponents))
[2079]225 m2
226 (every #'= exponents1 exponents2))))
[48]227
[2146]228(defmethod r-lcm ((m1 monom) (m2 monom))
[48]229 "Returns least common multiple of monomials M1 and M2."
[2171]230 (with-slots ((exponents1 exponents))
[2082]231 m1
[2171]232 (with-slots ((exponents2 exponents))
[2082]233 m2
234 (let* ((exponents (copy-seq exponents1))
[2195]235 (dimension (reduce #'+ exponents)))
[2082]236 (map-into exponents #'max exponents1 exponents2)
[2200]237 (make-instance 'monom :dimension dimension :exponents exponents)))))
[48]238
[2080]239
[2146]240(defmethod r-gcd ((m1 monom) (m2 monom))
[48]241 "Returns greatest common divisor of monomials M1 and M2."
[2171]242 (with-slots ((exponents1 exponents))
[2082]243 m1
[2171]244 (with-slots ((exponents2 exponents))
[2082]245 m2
246 (let* ((exponents (copy-seq exponents1))
[2195]247 (dimension (reduce #'+ exponents)))
[2082]248 (map-into exponents #'min exponents1 exponents2)
[2197]249 (make-instance 'monom :dimension dimension :exponents exponents)))))
[48]250
[2146]251(defmethod r-depends-p ((m monom) k)
[48]252 "Return T if the monomial M depends on variable number K."
[2083]253 (declare (type fixnum k))
254 (with-slots (exponents)
255 m
[2154]256 (plusp (elt exponents k))))
[48]257
[2146]258(defmethod r-tensor-product ((m1 monom) (m2 monom)
[2195]259 &aux (dimension (+ (r-dimension m1) (r-dimension m2))))
260 (declare (fixnum dimension))
[2171]261 (with-slots ((exponents1 exponents))
[2087]262 m1
[2171]263 (with-slots ((exponents2 exponents))
[2087]264 m2
[2147]265 (make-instance 'monom
[2195]266 :dimension dimension
[2147]267 :exponents (concatenate 'vector exponents1 exponents2)))))
[48]268
[2148]269(defmethod r-contract ((m monom) k)
[1638]270 "Drop the first K variables in monomial M."
[2085]271 (declare (fixnum k))
[2196]272 (with-slots (dimension exponents)
[2085]273 m
[2197]274 (setf dimension (- dimension k)
[2085]275 exponents (subseq exponents k))))
[886]276
277(defun make-monom-variable (nvars pos &optional (power 1)
[2218]278 &aux (m (make-instance 'monom :dimension nvars)))
[886]279 "Construct a monomial in the polynomial ring
280RING[X[0],X[1],X[2],...X[NVARS-1]] over the (unspecified) ring RING
281which represents a single variable. It assumes number of variables
282NVARS and the variable is at position POS. Optionally, the variable
283may appear raised to power POWER. "
[1924]284 (declare (type fixnum nvars pos power) (type monom m))
[2089]285 (with-slots (exponents)
286 m
[2154]287 (setf (elt exponents pos) power)
[2089]288 m))
[1151]289
[2150]290(defmethod r->list ((m monom))
[1152]291 "A human-readable representation of a monomial M as a list of exponents."
[2148]292 (coerce (monom-exponents m) 'list))
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