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source: branches/f4grobner/monomial.lisp@ 750

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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 (exponents nil :type (vector exponent *)))
88
89;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
90;;
91;; Operations on monomials
92;;
93;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
94
95(defun monom-dimension (m)
96 (declare (type monom m))
97 (length (monom-exponents m)))
98
99(defmacro monom-elt (m index)
100 "Return the power in the monomial M of variable number INDEX."
101 `(elt (monom-exponents ,m) ,index))
102
103(defun monom-total-degree (m &optional (start 0) (end (monom-dimension m)))
104 "Return the todal degree of a monomoal M. Optinally, a range
105of variables may be specified with arguments START and END."
106 (declare (type monom m) (fixnum start end))
107 (reduce #'+ (monom-exponents m) :start start :end end))
108
109(defun monom-sugar (m &aux (start 0) (end (monom-dimension m)))
110 "Return the sugar of a monomial M. Optinally, a range
111of variables may be specified with arguments START and END."
112 (declare (type monom m) (fixnum start end))
113 (monom-total-degree m start end))
114
115(defun monom-div (m1 m2 &aux (result (copy-structure m1)))
116 "Divide monomial M1 by monomial M2."
117 (declare (type monom m1 m2))
118 (map-into (monom-exponents result) #'- (monom-exponents m1) (monom-exponents m2))
119 result)
120
121(defun monom-mul (m1 m2 &aux (result (copy-structure m1)))
122 "Multiply monomial M1 by monomial M2."
123 (declare (type monom m1 m2 result))
124 (map-into (monom-exponents result) #'+ (monom-exponents m1) (monom-exponents m2))
125 result)
126
127(defun monom-divides-p (m1 m2)
128 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
129 (declare (type monom m1 m2))
130 (every #'<= (monom-exponents m1) (monom-exponents m2)))
131
132(defun monom-divides-monom-lcm-p (m1 m2 m3)
133 "Returns T if monomial M1 divides MONOM-LCM(M2,M3), NIL otherwise."
134 (declare (type monom m1 m2 m3))
135 (every #'(lambda (x y z) (declare (type exponent x y z)) (<= x (max y z)))
136 (monom-exponents m1)
137 (monom-exponents m2)
138 (monom-exponents 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)))
144 (monom-exponents m1)
145 (monom-exponents m2)
146 (monom-exponents m3)
147 (monom-exponents m4)))
148
149(defun monom-lcm-equal-monom-lcm-p (m1 m2 m3 m4)
150 "Returns T if monomial MONOM-LCM(M1,M2) equals MONOM-LCM(M3,M4), NIL otherwise."
151 (declare (type monom m1 m2 m3 m4))
152 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (= (max x y) (max z w)))
153 (monom-exponents m1)
154 (monom-exponents m2)
155 (monom-exponents m3)
156 (monom-exponents m4)))
157
158(defun monom-divisible-by-p (m1 m2)
159 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
160 (declare (type monom m1 m2))
161 (every #'>= (monom-exponents m1) (monom-exponents m2)))
162
163(defun monom-rel-prime-p (m1 m2)
164 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
165 (declare (type monom m1 m2))
166 (every #'(lambda (x y) (declare (type exponent x y)) (zerop (min x y)))
167 (monom-exponents m1)
168 (monom-exponents m2)))
169
170(defun monom-equal-p (m1 m2)
171 "Returns T if two monomials M1 and M2 are equal."
172 (declare (type monom m1 m2))
173 (every #'= (monom-exponents m1) (monom-exponents m2)))
174
175(defun monom-lcm (m1 m2 &aux (result (copy-structure m1)))
176 "Returns least common multiple of monomials M1 and M2."
177 (declare (type monom m1 m2))
178 (map-into (monom-exponents result) #'max
179 (monom-exponents m1)
180 (monom-exponents m2))
181 result)
182
183(defun monom-gcd (m1 m2 &aux (result (copy-structure m1)))
184 "Returns greatest common divisor of monomials M1 and M2."
185 (declare (type monom m1 m2))
186 (map-into (monom-exponents result) #'min (monom-exponents m1) (monom-exponents m2))
187 result)
188
189(defun monom-depends-p (m k)
190 "Return T if the monomial M depends on variable number K."
191 (declare (type monom m) (fixnum k))
192 (plusp (monom-elt m k)))
193
194(defmacro monom-map (fun m &rest ml &aux (result `(copy-structure ,m)))
195 `(map-into (monom-exponents ,result) ,fun ,m ,@ml))
196
197(defmacro monom-append (m1 m2)
198 `(make-monom (list (+ (monom-dimension ,m1)
199 (monom-dimension ,m2)))
200 :initial-contents (concatenate 'monom (monom-exponents ,m1) (monom-exponents ,m2))))
201
202(defmacro monom-contract (k m)
203 `(setf (monom-exponents ,m) (subseq (monom-exponents ,m) ,k)))
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