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source: branches/f4grobner/order.lisp@ 81

Last change on this file since 81 was 80, checked in by Marek Rychlik, 9 years ago

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[80]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
[49]23;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
24;;
25;; Implementations of various admissible monomial orders
26;;
27;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
28
29;; pure lexicographic
30(defun lex> (p q &optional (start 0) (end (monom-dimension p)))
31 "Return T if P>Q with respect to lexicographic order, otherwise NIL.
32The second returned value is T if P=Q, otherwise it is NIL."
33 (declare (type monom p q) (type fixnum start end))
34 (do ((i start (1+ i)))
35 ((>= i end) (values nil t))
36 (declare (type fixnum i))
37 (cond
38 ((> (monom-elt p i) (monom-elt q i))
39 (return-from lex> (values t nil)))
40 ((< (monom-elt p i) (monom-elt q i))
41 (return-from lex> (values nil nil))))))
42
43;; total degree order , ties broken by lexicographic
44(defun grlex> (p q &optional (start 0) (end (monom-dimension p)))
45 "Return T if P>Q with respect to graded lexicographic order, otherwise NIL.
46The second returned value is T if P=Q, otherwise it is NIL."
47 (declare (type monom p q) (type fixnum start end))
48 (let ((d1 (monom-total-degree p start end))
49 (d2 (monom-total-degree q start end)))
50 (cond
51 ((> d1 d2) (values t nil))
52 ((< d1 d2) (values nil nil))
53 (t
54 (lex> p q start end)))))
55
56
57;; total degree, ties broken by reverse lexicographic
58(defun grevlex> (p q &optional (start 0) (end (monom-dimension p)))
59 "Return T if P>Q with respect to graded reverse lexicographic order,
60NIL otherwise. The second returned value is T if P=Q, otherwise it is NIL."
61 (declare (type monom p q) (type fixnum start end))
62 (let ((d1 (monom-total-degree p start end))
63 (d2 (monom-total-degree q start end)))
64 (cond
65 ((> d1 d2) (values t nil))
66 ((< d1 d2) (values nil nil))
67 (t
68 (revlex> p q start end)))))
69
70
71;; reverse lexicographic
72(defun revlex> (p q &optional (start 0) (end (monom-dimension p)))
73 "Return T if P>Q with respect to reverse lexicographic order, NIL
74otherwise. The second returned value is T if P=Q, otherwise it is
75NIL. This is not and admissible monomial order because some sets do
76not have a minimal element. This order is useful in constructing other
77orders."
78 (declare (type monom p q) (type fixnum start end))
79 (do ((i (1- end) (1- i)))
80 ((< i start) (values nil t))
81 (declare (type fixnum i))
82 (cond
83 ((< (monom-elt p i) (monom-elt q i))
84 (return-from revlex> (values t nil)))
85 ((> (monom-elt p i) (monom-elt q i))
86 (return-from revlex> (values nil nil))))))
87
88
89(defun invlex> (p q &optional (start 0) (end (monom-dimension p)))
90 "Return T if P>Q with respect to inverse lexicographic order, NIL otherwise
91The second returned value is T if P=Q, otherwise it is NIL."
92 (declare (type monom p q) (type fixnum start end))
93 (do ((i (1- end) (1- i)))
94 ((< i start) (values nil t))
95 (declare (type fixnum i))
96 (cond
97 ((> (monom-elt p i) (monom-elt q i))
98 (return-from invlex> (values t nil)))
99 ((< (monom-elt p i) (monom-elt q i))
100 (return-from invlex> (values nil nil))))))
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