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source: branches/f4grobner/monomial.lisp@ 869

Last change on this file since 869 was 869, 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 ;; NOTE: having a non-default constructor inhibits reading via #S(...)
76 (:constructor make-monom (&key
77 (dimension nil dimension-suppied-p)
78 (initial-exponents nil initial-exponents-supplied-p)
79 (initial-exponent nil initial-exponent-supplied-p)
80 &aux
81 (dim (cond (dimension-suppied-p dimension)
82 (initial-exponents-supplied-p (length initial-exponents))
83 (t (error "You must provide DIMENSION nor INITIAL-EXPONENTS"))))
84 (exponents (cond
85 ;; when exponents are supplied
86 (initial-exponents-supplied-p
87 (make-array (list dim) :initial-contents initial-exponents
88 :element-type 'exponent))
89 ;; when all exponents are to be identical
90 (initial-exponent-supplied-p
91 (make-array (list dim) :initial-element initial-exponent
92 :element-type 'exponent))
93 ;; otherwise, all exponents are zero
94 (t
95 (make-array (list dim) :element-type 'exponent :initial-element 0))))))
96 )
97 (exponents nil :type (vector exponent *)))
98
99
100;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
101;;
102;; Operations on monomials
103;;
104;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
105
106(defun monom-dimension (m)
107 (declare (type monom m))
108 (length (monom-exponents m)))
109
110(defmacro monom-elt (m index)
111 "Return the power in the monomial M of variable number INDEX."
112 `(elt (monom-exponents ,m) ,index))
113
114(defun monom-total-degree (m &optional (start 0) (end (monom-dimension m)))
115 "Return the todal degree of a monomoal M. Optinally, a range
116of variables may be specified with arguments START and END."
117 (declare (type monom m) (fixnum start end))
118 (reduce #'+ (monom-exponents m) :start start :end end))
119
120(defun monom-sugar (m &aux (start 0) (end (monom-dimension m)))
121 "Return the sugar of a monomial M. Optinally, a range
122of variables may be specified with arguments START and END."
123 (declare (type monom m) (fixnum start end))
124 (monom-total-degree m start end))
125
126(defun monom-div (m1 m2 &aux (result (copy-structure m1)))
127 "Divide monomial M1 by monomial M2."
128 (declare (type monom m1 m2))
129 (map-into (monom-exponents result) #'- (monom-exponents m1) (monom-exponents m2))
130 result)
131
132(defun monom-mul (m1 m2 &aux (result (copy-structure m1)))
133 "Multiply monomial M1 by monomial M2."
134 (declare (type monom m1 m2 result))
135 (map-into (monom-exponents result) #'+ (monom-exponents m1) (monom-exponents m2))
136 result)
137
138(defun monom-divides-p (m1 m2)
139 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
140 (every #'<= (monom-exponents m1) (monom-exponents m2)))
141
142(defun monom-divides-monom-lcm-p (m1 m2 m3)
143 "Returns T if monomial M1 divides MONOM-LCM(M2,M3), NIL otherwise."
144 (every #'(lambda (x y z) (declare (type exponent x y z)) (<= x (max y z)))
145 m1 m2 m3))
146
147(defun monom-lcm-divides-monom-lcm-p (m1 m2 m3 m4)
148 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
149 (declare (type monom m1 m2 m3 m4))
150 (every #'(lambda (x y z w) (<= (max x y) (max z w)))
151 m1 m2 m3 m4))
152
153
154(defun monom-lcm-equal-monom-lcm-p (m1 m2 m3 m4)
155 "Returns T if monomial MONOM-LCM(M1,M2) equals MONOM-LCM(M3,M4), NIL otherwise."
156 (every #'(lambda (x y z w) (= (max x y) (max z w)))
157 m1 m2 m3 m4))
158
159
160(defun monom-divisible-by-p (m1 m2)
161 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
162 (every #'>= m1 m2))
163
164(defun monom-rel-prime-p (m1 m2)
165 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
166 (every #'(lambda (x y) (declare (type exponent x y)) (zerop (min x y))) m1 m2))
167
168(defun monom-equal-p (m1 m2)
169 "Returns T if two monomials M1 and M2 are equal."
170 (every #'= (monom-exponents m1) (monom-exponents m2)))
171
172(defun monom-lcm (m1 m2 &aux (result (copy-sequence m1)))
173 "Returns least common multiple of monomials M1 and M2."
174 (map-into result #'max m1 m2))
175
176(defun monom-gcd (m1 m2 &aux (result (copy-sequence m1)))
177 "Returns greatest common divisor of monomials M1 and M2."
178 (map-into result #'min m1 m2))
179
180(defun monom-depends-p (m k)
181 "Return T if the monomial M depends on variable number K."
182 (plusp (monom-elt m k)))
183
184(defmacro monom-map (fun m &rest ml &aux (result `(copy-sequence ,m)))
185 `(map-into ,result ,fun ,m ,@ml))
186
187(defmacro monom-append (m1 m2)
188 `(concatenate 'vector ,m1 ,m2))
189
190(defmacro monom-contract (k m)
191 `(setf ,m (subseq ,m ,k)))
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