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source: branches/f4grobner/monomial.lisp@ 724

Last change on this file since 724 was 724, 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 (:constructor make-monom (&optional dim (exponents (make-array (list dim) :element-type 'exponent)))))
75 (dim 0 :type fixnum)
76 (exponents #() :type (vector 'exponent *)))
77
78
79
80#|
81
82;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
83;;
84;; Operations on monomials
85;;
86;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
87
88(defmacro monom-elt (m index)
89 "Return the power in the monomial M of variable number INDEX."
90 `(elt ,m ,index))
91
92(defun monom-dimension (m)
93 "Return the number of variables in the monomial M."
94 (length m))
95
96(defun monom-total-degree (m &optional (start 0) (end (length m)))
97 "Return the todal degree of a monomoal M. Optinally, a range
98of variables may be specified with arguments START and END."
99 (declare (type monom m) (fixnum start end))
100 (reduce #'+ m :start start :end end))
101
102(defun monom-sugar (m &aux (start 0) (end (length m)))
103 "Return the sugar of a monomial M. Optinally, a range
104of variables may be specified with arguments START and END."
105 (declare (type monom m) (fixnum start end))
106 (monom-total-degree m start end))
107
108(defun monom-div (m1 m2 &aux (result (copy-seq m1)))
109 "Divide monomial M1 by monomial M2."
110 (declare (type monom m1 m2 result))
111 (map-into result #'- m1 m2))
112
113(defun monom-mul (m1 m2 &aux (result (copy-seq m1)))
114 "Multiply monomial M1 by monomial M2."
115 (declare (type monom m1 m2 result))
116 (map-into result #'+ m1 m2))
117
118(defun monom-divides-p (m1 m2)
119 "Returns T if monomial M1 divides monomial M2, NIL otherwise."
120 (declare (type monom m1 m2))
121 (every #'<= m1 m2))
122
123(defun monom-divides-monom-lcm-p (m1 m2 m3)
124 "Returns T if monomial M1 divides MONOM-LCM(M2,M3), NIL otherwise."
125 (declare (type monom m1 m2 m3))
126 (every #'(lambda (x y z) (declare (type exponent x y z)) (<= x (max y z))) m1 m2 m3))
127
128(defun monom-lcm-divides-monom-lcm-p (m1 m2 m3 m4)
129 "Returns T if monomial MONOM-LCM(M1,M2) divides MONOM-LCM(M3,M4), NIL otherwise."
130 (declare (type monom m1 m2 m3 m4))
131 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (<= (max x y) (max z w))) m1 m2 m3 m4))
132
133(defun monom-lcm-equal-monom-lcm-p (m1 m2 m3 m4)
134 "Returns T if monomial MONOM-LCM(M1,M2) equals MONOM-LCM(M3,M4), NIL otherwise."
135 (declare (type monom m1 m2 m3 m4))
136 (every #'(lambda (x y z w) (declare (type exponent x y z w)) (= (max x y) (max z w))) m1 m2 m3 m4))
137
138(defun monom-divisible-by-p (m1 m2)
139 "Returns T if monomial M1 is divisible by monomial M2, NIL otherwise."
140 (declare (type monom m1 m2))
141 (every #'>= m1 m2))
142
143(defun monom-rel-prime-p (m1 m2)
144 "Returns T if two monomials M1 and M2 are relatively prime (disjoint)."
145 (declare (type monom m1 m2))
146 (every #'(lambda (x y) (declare (type exponent x y)) (zerop (min x y))) m1 m2))
147
148(defun monom-equal-p (m1 m2)
149 "Returns T if two monomials M1 and M2 are equal."
150 (declare (type monom m1 m2))
151 (every #'= m1 m2))
152
153(defun monom-lcm (m1 m2 &aux (result (copy-seq m1)))
154 "Returns least common multiple of monomials M1 and M2."
155 (declare (type monom m1 m2))
156 (map-into result #'max m1 m2))
157
158(defun monom-gcd (m1 m2 &aux (result (copy-seq m1)))
159 "Returns greatest common divisor of monomials M1 and M2."
160 (declare (type monom m1 m2))
161 (map-into result #'min m1 m2))
162
163(defun monom-depends-p (m k)
164 "Return T if the monomial M depends on variable number K."
165 (declare (type monom m) (fixnum k))
166 (plusp (elt m k)))
167
168(defmacro monom-map (fun m &rest ml &aux (result `(copy-seq ,m)))
169 `(map-into ,result ,fun ,m ,@ml))
170
171(defmacro monom-append (m1 m2)
172 `(concatenate 'monom ,m1 ,m2))
173
174(defmacro monom-contract (k m)
175 `(subseq ,m ,k))
176
177(defun monom-exponents (m)
178 (declare (type monom m))
179 (coerce m 'list))
180|#
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