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source: branches/f4grobner/monomial.lisp@ 742

Last change on this file since 742 was 742, checked in by Marek Rychlik, 9 years ago

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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
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
41(defpackage "MONOMIAL"
42 (:use :cl)
43 (:export "MONOM"
44 "EXPONENT"
45 "MAKE-MONOM"
46 "MONOM-ELT"
47 "MONOM-DIMENSION"
48 "MONOM-TOTAL-DEGREE"
49 "MONOM-SUGAR"
50 "MONOM-DIV"
51 "MONOM-MUL"
52 "MONOM-DIVIDES-P"
53 "MONOM-DIVIDES-MONOM-LCM-P"
54 "MONOM-LCM-DIVIDES-MONOM-LCM-P"
55 "MONOM-LCM-EQUAL-MONOM-LCM-P"
56 "MONOM-DIVISIBLE-BY-P"
57 "MONOM-REL-PRIME-P"
58 "MONOM-EQUAL-P"
59 "MONOM-LCM"
60 "MONOM-GCD"
61 "MONOM-DEPENDS-P"
62 "MONOM-MAP"
63 "MONOM-APPEND"
64 "MONOM-CONTRACT"
65 "MONOM-EXPONENTS"))
66
67(in-package :monomial)
68
69(deftype exponent ()
70 "Type of exponent in a monomial."
71 'fixnum)
72
73(defstruct (monom
74 ;; BOA constructor
75 (:constructor make-monom (dimension
76 &key
77 (initial-contents #() initial-contents-supplied-p)
78 (initial-element #() initial-element-supplied-p)
79 (exponents (cond
80 (initial-contents-supplied-p
81 (make-array (list dimension) :initial-contents initial-contents
82 :element-type 'exponent))
83 (initial-element-supplied-p
84 (make-array (list dimension) :initial-element initial-element
85 :element-type 'exponent))
86 (t (make-array (list dimension) :element-type 'exponent :initial-element 0)))))))
87 (dimension 0 :type fixnum)
88 (exponents nil :type (vector exponent *)))
89
90;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
91;;
92;; Operations on monomials
93;;
94;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
95
96(defmacro monom-elt (m index)
97 "Return the power in the monomial M of variable number INDEX."
98 `(elt (monom-exponents ,m) ,index))
99
100(defun monom-total-degree (m &optional (start 0) (end (length (monom-exponents m))))
101 "Return the todal degree of a monomoal M. Optinally, a range
102of variables may be specified with arguments START and END."
103 (declare (type monom m) (fixnum start end))
104 (reduce #'+ (monom-exponents m) :start start :end end))
105
106(defun monom-sugar (m &aux (start 0) (end (length m)))
107 "Return the sugar of a monomial M. Optinally, a range
108of variables may be specified with arguments START and END."
109 (declare (type monom m) (fixnum start end))
110 (monom-total-degree (monom-exponents m) start end))
111
112(defun monom-div (m1 m2 &aux (result (copy-structure m1)))
113 "Divide monomial M1 by monomial M2."
114 (declare (type monom m1 m2))
115 (map-into (monom-exponents result) #'- (monom-exponents m1) (monom-exponents m2))
116 result)
117
118(defun monom-mul (m1 m2 &aux (result (copy-structure m1)))
119 "Multiply monomial M1 by monomial M2."
120 (declare (type monom m1 m2 result))
121 (map-into (monom-exponents result) #'+ (monom-exponents m1) (monom-exponents m2))
122 result)
123
124(defun monom-divides-p (m1 m2)
125 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
126 (declare (type monom m1 m2))
127 (every #'<= (monom-exponents m1) (monom-exponents m2)))
128
129(defun monom-divides-monom-lcm-p (m1 m2 m3)
130 "Returns T if monomial M1 divides MONOM-LCM(M2,M3), NIL otherwise."
131 (declare (type monom m1 m2 m3))
132 (every #'(lambda (x y z) (declare (type exponent x y z)) (<= x (max y z)))
133 (monom-exponents m1)
134 (monom-exponents m2)
135 (monom-exponents m3)))
136
137(defun monom-lcm-divides-monom-lcm-p (m1 m2 m3 m4)
138 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
139 (declare (type monom m1 m2 m3 m4))
140 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (<= (max x y) (max z w)))
141 (monom-exponents m1)
142 (monom-exponents m2)
143 (monom-exponents m3)
144 (monom-exponents m4)))
145
146(defun monom-lcm-equal-monom-lcm-p (m1 m2 m3 m4)
147 "Returns T if monomial MONOM-LCM(M1,M2) equals MONOM-LCM(M3,M4), NIL otherwise."
148 (declare (type monom m1 m2 m3 m4))
149 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (= (max x y) (max z w)))
150 (monom-exponents m1)
151 (monom-exponents m2)
152 (monom-exponents m3)
153 (monom-exponents m4)))
154
155(defun monom-divisible-by-p (m1 m2)
156 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
157 (declare (type monom m1 m2))
158 (every #'>= (monom-exponents m1) (monom-exponents m2)))
159
160(defun monom-rel-prime-p (m1 m2)
161 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
162 (declare (type monom m1 m2))
163 (every #'(lambda (x y) (declare (type exponent x y)) (zerop (min x y)))
164 (monom-exponents m1)
165 (monom-exponents m2)))
166
167(defun monom-equal-p (m1 m2)
168 "Returns T if two monomials M1 and M2 are equal."
169 (declare (type monom m1 m2))
170 (every #'= (monom-exponents m1) (monom-exponents m2)))
171
172(defun monom-lcm (m1 m2 &aux (result (copy-structure m1)))
173 "Returns least common multiple of monomials M1 and M2."
174 (declare (type monom m1 m2))
175 (map-into (monom-exponents result) #'max
176 (monom-exponents m1)
177 (monom-exponents m2))
178 result)
179
180(defun monom-gcd (m1 m2 &aux (result (copy-structure m1)))
181 "Returns greatest common divisor of monomials M1 and M2."
182 (declare (type monom m1 m2))
183 (map-into (monom-exponents result) #'min (monom-exponents m1) (monom-exponents m2))
184 result)
185
186(defun monom-depends-p (m k)
187 "Return T if the monomial M depends on variable number K."
188 (declare (type monom m) (fixnum k))
189 (plusp (monom-elt m k)))
190
191(defmacro monom-map (fun m &rest ml &aux (result `(copy-structure ,m)))
192 `(map-into (monom-exponents ,result) ,fun ,m ,@ml))
193
194(defmacro monom-append (m1 m2)
195 `(make-monom (list (+ (monom-dimension ,m1)
196 (monom-dimension ,m2)))
197 :initial-contents (concatenate 'monom (monom-exponents ,m1) (monom-exponents ,m2))))
198
199(defmacro monom-contract (k m)
200 `(setf (monom-exponents ,m) (subseq (monom-exponents ,m) ,k)))
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