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source: branches/f4grobner/monomial.lisp@ 472

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[81]1;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
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;;
37;; Monom x*y^2 ---> #(1 2)
38;;
39;;----------------------------------------------------------------
40
[394]41(defpackage "MONOMIAL"
[395]42 (:use :cl)
[422]43 (:export "MONOM"
[423]44 "EXPONENT"
[422]45 "MAKE-MONOM"
[396]46 "MONOM-ELT"
47 "MONOM-DIMENSION"
48 "MONOM-TOTAL-DEGREE"
49 "MONOM-SUGAR"
50 "MONOM-DIV"
51 "MONOM-MUL"
52 "MONOM-DIVIDES-P"
[395]53 "MONOM-DIVIDES-MONOM-LCM-P"
54 "MONOM-LCM-DIVIDES-MONOM-LCM-P"
55 "MONOM-DIVISIBLE-BY-P"
56 "MONOM-REL-PRIME-P"
57 "MONOM-EQUAL-P"
58 "MONOM-LCM"
59 "MONOM-GCD"
60 "MONOM-MAP"
61 "MONOM-APPEND"
62 "MONOM-CONTRACT"
63 "MONOM-EXPONENTS"))
[81]64
[419]65(in-package :monomial)
[48]66
67(deftype exponent ()
68 "Type of exponent in a monomial."
69 'fixnum)
70
71(deftype monom (&optional dim)
72 "Type of monomial."
73 `(simple-array exponent (,dim)))
74
75;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
76;;
77;; Construction of monomials
78;;
79;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
80
81(defmacro make-monom (dim &key (initial-contents nil initial-contents-supplied-p)
82 (initial-element 0 initial-element-supplied-p))
83 "Make a monomial with DIM variables. Additional argument
84INITIAL-CONTENTS specifies the list of powers of the consecutive
85variables. The alternative additional argument INITIAL-ELEMENT
86specifies the common power for all variables."
87 ;;(declare (fixnum dim))
88 `(make-array ,dim
89 :element-type 'exponent
90 ,@(when initial-contents-supplied-p `(:initial-contents ,initial-contents))
91 ,@(when initial-element-supplied-p `(:initial-element ,initial-element))))
92
[392]93
[48]94;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
95;;
96;; Operations on monomials
97;;
98;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
99
100(defmacro monom-elt (m index)
101 "Return the power in the monomial M of variable number INDEX."
102 `(elt ,m ,index))
103
104(defun monom-dimension (m)
105 "Return the number of variables in the monomial M."
106 (length m))
107
108(defun monom-total-degree (m &optional (start 0) (end (length m)))
109 "Return the todal degree of a monomoal M. Optinally, a range
110of variables may be specified with arguments START and END."
111 (declare (type monom m) (fixnum start end))
112 (reduce #'+ m :start start :end end))
113
114(defun monom-sugar (m &aux (start 0) (end (length m)))
115 "Return the sugar of a monomial M. Optinally, a range
116of variables may be specified with arguments START and END."
117 (declare (type monom m) (fixnum start end))
118 (monom-total-degree m start end))
119
120(defun monom-div (m1 m2 &aux (result (copy-seq m1)))
121 "Divide monomial M1 by monomial M2."
122 (declare (type monom m1 m2 result))
123 (map-into result #'- m1 m2))
124
125(defun monom-mul (m1 m2 &aux (result (copy-seq m1)))
126 "Multiply monomial M1 by monomial M2."
127 (declare (type monom m1 m2 result))
128 (map-into result #'+ m1 m2))
129
130(defun monom-divides-p (m1 m2)
131 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
132 (declare (type monom m1 m2))
133 (every #'<= m1 m2))
134
135(defun monom-divides-monom-lcm-p (m1 m2 m3)
136 "Returns T if monomial M1 divides MONOM-LCM(M2,M3), NIL otherwise."
137 (declare (type monom m1 m2 m3))
138 (every #'(lambda (x y z) (declare (type exponent x y z)) (<= x (max y z))) m1 m2 m3))
139
140(defun monom-lcm-divides-monom-lcm-p (m1 m2 m3 m4)
141 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
142 (declare (type monom m1 m2 m3 m4))
143 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (<= (max x y) (max z w))) m1 m2 m3 m4))
144
145(defun monom-lcm-equal-monom-lcm-p (m1 m2 m3 m4)
146 "Returns T if monomial MONOM-LCM(M1,M2) equals MONOM-LCM(M3,M4), NIL otherwise."
147 (declare (type monom m1 m2 m3 m4))
148 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (= (max x y) (max z w))) m1 m2 m3 m4))
149
150(defun monom-divisible-by-p (m1 m2)
151 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
152 (declare (type monom m1 m2))
153 (every #'>= m1 m2))
154
155(defun monom-rel-prime-p (m1 m2)
156 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
157 (declare (type monom m1 m2))
158 (every #'(lambda (x y) (declare (type exponent x y)) (zerop (min x y))) m1 m2))
159
160(defun monom-equal-p (m1 m2)
161 "Returns T if two monomials M1 and M2 are equal."
162 (declare (type monom m1 m2))
163 (every #'= m1 m2))
164
165(defun monom-lcm (m1 m2 &aux (result (copy-seq m1)))
166 "Returns least common multiple of monomials M1 and M2."
167 (declare (type monom m1 m2))
168 (map-into result #'max m1 m2))
169
170(defun monom-gcd (m1 m2 &aux (result (copy-seq m1)))
171 "Returns greatest common divisor of monomials M1 and M2."
172 (declare (type monom m1 m2))
173 (map-into result #'min m1 m2))
174
175(defun monom-depends-p (m k)
176 "Return T if the monomial M depends on variable number K."
177 (declare (type monom m) (fixnum k))
178 (plusp (elt m k)))
179
180(defmacro monom-map (fun m &rest ml &aux (result `(copy-seq ,m)))
181 `(map-into ,result ,fun ,m ,@ml))
182
183(defmacro monom-append (m1 m2)
184 `(concatenate 'monom ,m1 ,m2))
185
186(defmacro monom-contract (k m)
187 `(subseq ,m ,k))
188
189(defun monom-exponents (m)
190 (declare (type monom m))
191 (coerce m 'list))
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