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source: branches/f4grobner/monomial.lisp@ 872

Last change on this file since 872 was 872, 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 (length m))
108
109(defmacro monom-elt (m index)
110 "Return the power in the monomial M of variable number INDEX."
111 `(elt (monom-exponents ,m) ,index))
112
113(defun monom-total-degree (m &optional (start 0) (end (monom-dimension m)))
114 "Return the todal degree of a monomoal M. Optinally, a range
115of variables may be specified with arguments START and END."
116 (reduce #'+ m :start start :end end))
117
118(defun monom-sugar (m &aux (start 0) (end (monom-dimension m)))
119 "Return the sugar of a monomial M. Optinally, a range
120of variables may be specified with arguments START and END."
121 (monom-total-degree m start end))
122
123(defun monom-div (m1 m2 &aux (result (copy-structure m1)))
124 "Divide monomial M1 by monomial M2."
125 (map-into result #'- m1 m2))
126
127(defun monom-mul (m1 m2 &aux (result (copy-structure m1)))
128 "Multiply monomial M1 by monomial M2."
129 (map-into result #'+ m1 m2))
130
131(defun monom-divides-p (m1 m2)
132 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
133 (every #'<= (monom-exponents m1) (monom-exponents 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 (every #'(lambda (x y z) (declare (type exponent x y z)) (<= x (max y z)))
138 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) (<= (max x y) (max z w)))
144 m1 m2 m3 m4))
145
146
147(defun monom-lcm-equal-monom-lcm-p (m1 m2 m3 m4)
148 "Returns T if monomial MONOM-LCM(M1,M2) equals MONOM-LCM(M3,M4), NIL otherwise."
149 (every #'(lambda (x y z w) (= (max x y) (max z w)))
150 m1 m2 m3 m4))
151
152
153(defun monom-divisible-by-p (m1 m2)
154 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
155 (every #'>= m1 m2))
156
157(defun monom-rel-prime-p (m1 m2)
158 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
159 (every #'(lambda (x y) (declare (type exponent x y)) (zerop (min x y))) m1 m2))
160
161(defun monom-equal-p (m1 m2)
162 "Returns T if two monomials M1 and M2 are equal."
163 (every #'= (monom-exponents m1) (monom-exponents m2)))
164
165(defun monom-lcm (m1 m2 &aux (result (copy-sequence m1)))
166 "Returns least common multiple of monomials M1 and M2."
167 (map-into result #'max m1 m2))
168
169(defun monom-gcd (m1 m2 &aux (result (copy-sequence m1)))
170 "Returns greatest common divisor of monomials M1 and M2."
171 (map-into result #'min m1 m2))
172
173(defun monom-depends-p (m k)
174 "Return T if the monomial M depends on variable number K."
175 (plusp (monom-elt m k)))
176
177(defmacro monom-map (fun m &rest ml &aux (result `(copy-sequence ,m)))
178 `(map-into ,result ,fun ,m ,@ml))
179
180(defmacro monom-append (m1 m2)
181 `(concatenate 'vector ,m1 ,m2))
182
183(defmacro monom-contract (k m)
184 `(setf ,m (subseq ,m ,k)))
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