close Warning: Can't synchronize with repository "(default)" (The repository directory has changed, you should resynchronize the repository with: trac-admin $ENV repository resync '(default)'). Look in the Trac log for more information.

source: branches/f4grobner/termlist.lisp@ 787

Last change on this file since 787 was 787, checked in by Marek Rychlik, 9 years ago

* empty log message *
File size: 7.3 KB
Line 
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(defpackage "TERMLIST"
23 (:use :cl :monomial :ring :ring-and-order :term)
24 (:export "TERMLIST-SUGAR"
25 "TERMLIST-CONTRACT"
26 "TERMLIST-EXTEND"
27 "TERMLIST-ADD-VARIABLES"
28 "TERMLIST-LT"
29 "TERMLIST-LM"
30 "TERMLIST-LC"
31 "SCALAR-MUL"
32 "SCALAR-TIMES-TERMLIST"
33 "TERM-MUL-LST"
34 "TERMLIST-TIMES-TERM"
35 "TERM-TIMES-TERMLIST"
36 "MONOM-TIMES-TERM"
37 "MONOM-TIMES-TERMLIST"
38 "TERMLIST-UMINUS"
39 "TERMLIST-ADD"
40 "TERMLIST-SUB"
41 "TERMLIST-MUL"
42 "TERMLIST-UNIT"
43 "TERMLIST-EXPT"))
44
45(in-package :termlist)
46
47(defun termlist-sugar (p &aux (sugar -1))
48 (declare (fixnum sugar))
49 (dolist (term p sugar)
50 (setf sugar (max sugar (term-sugar term)))))
51
52(defun termlist-contract (p &optional (k 1))
53 "Eliminate first K variables from a polynomial P."
54 (mapcar #'(lambda (term) (make-term (monom-contract k (term-monom term))
55 (term-coeff term)))
56 p))
57
58(defun termlist-extend (p &optional (m (make-monom 1 :initial-element 0)))
59 "Extend every monomial in a polynomial P by inserting at the
60beginning of every monomial the list of powers M."
61 (mapcar #'(lambda (term) (make-term (monom-append m (term-monom term))
62 (term-coeff term)))
63 p))
64
65(defun termlist-add-variables (p n)
66 "Add N variables to a polynomial P by inserting zero powers
67at the beginning of each monomial."
68 (declare (fixnum n))
69 (mapcar #'(lambda (term)
70 (make-term (monom-append (make-monom n :initial-element 0)
71 (term-monom term))
72 (term-coeff term)))
73 p))
74
75
76;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
77;;
78;; Low-level polynomial arithmetic done on
79;; lists of terms
80;;
81;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
82
83(defmacro termlist-lt (p) `(car ,p))
84(defun termlist-lm (p) (term-monom (termlist-lt p)))
85(defun termlist-lc (p) (term-coeff (termlist-lt p)))
86
87(define-modify-macro scalar-mul (c) coeff-mul)
88
89(defun scalar-times-termlist (ring c p)
90 "Multiply scalar C by a polynomial P. This function works
91even if there are divisors of 0."
92 (declare (ring ring))
93 (mapcan
94 #'(lambda (term)
95 (let ((c1 (funcall (ring-mul ring) c (term-coeff term))))
96 (unless (funcall (ring-zerop ring) c1)
97 (list (make-term (term-monom term) c1)))))
98 p))
99
100
101(defun term-mul-lst (ring term1 term2)
102 "A special version of term multiplication. Returns (LIST TERM) where
103TERM is the product of the terms TERM1 TERM2, or NIL when the product
104is 0. This definition takes care of divisors of 0 in the coefficient
105ring."
106 (declare (ring ring))
107 (let ((c (funcall (ring-mul ring) (term-coeff term1) (term-coeff term2))))
108 (unless (funcall (ring-zerop ring) c)
109 (list (make-term (monom-mul (term-monom term1) (term-monom term2)) c)))))
110
111(defun term-times-termlist (ring term f)
112 (declare (type ring ring))
113 (mapcan #'(lambda (term-f) (term-mul-lst ring term term-f)) f))
114
115(defun termlist-times-term (ring f term)
116 (declare (ring ring))
117 (mapcan #'(lambda (term-f) (term-mul-lst ring term-f term)) f))
118
119(defun monom-times-term (m term)
120 (make-term (monom-mul m (term-monom term)) (term-coeff term)))
121
122(defun monom-times-termlist (m f)
123 (cond
124 ((null f) nil)
125 (t
126 (mapcar #'(lambda (x) (monom-times-term m x)) f))))
127
128(defun termlist-uminus (ring f)
129 (declare (ring ring))
130 (mapcar #'(lambda (x)
131 (make-term :monom (term-monom x)
132 :coeff (funcall (ring-uminus ring) (term-coeff x))))
133 f))
134
135(defun termlist-add (ring p q)
136 (declare (type list p q) (ring-and-order ring))
137 (do (r)
138 ((cond
139 ((endp p)
140 (setf r (revappend r q)) t)
141 ((endp q)
142 (setf r (revappend r p)) t)
143 (t
144 (multiple-value-bind
145 (lm-greater lm-equal)
146 (funcall (ring-and-order-order ring) (termlist-lm p) (termlist-lm q))
147 (cond
148 (lm-equal
149 (let ((s (funcall (ring-add ring) (termlist-lc p) (termlist-lc q))))
150 (unless (funcall (ring-zerop ring) s) ;check for cancellation
151 (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
152 (setf p (cdr p) q (cdr q))))
153 (lm-greater
154 (setf r (cons (car p) r)
155 p (cdr p)))
156 (t (setf r (cons (car q) r)
157 q (cdr q)))))
158 nil))
159 r)))
160
161(defun termlist-sub (ring p q)
162 (declare (type list p q) (ring-and-order ring))
163 (do (r)
164 ((cond
165 ((endp p)
166 (setf r (revappend r (termlist-uminus ring q)))
167 t)
168 ((endp q)
169 (setf r (revappend r p))
170 t)
171 (t
172 (multiple-value-bind
173 (mgreater mequal)
174 (funcall (ring-and-order-order ring) (termlist-lm p) (termlist-lm q))
175 (cond
176 (mequal
177 (let ((s (funcall (ring-sub ring) (termlist-lc p) (termlist-lc q))))
178 (unless (funcall (ring-zerop ring) s) ;check for cancellation
179 (setf r (cons (make-term :monom (termlist-lm p) :coeff s) r)))
180 (setf p (cdr p) q (cdr q))))
181 (mgreater
182 (setf r (cons (car p) r)
183 p (cdr p)))
184 (t (setf r (cons (make-term :monom (termlist-lm q)
185 :coeff (funcall (ring-uminus ring) (termlist-lc q))) r)
186 q (cdr q)))))
187 nil))
188 r)))
189
190;; Multiplication of polynomials
191;; Non-destructive version
192(defun termlist-mul (ring p q)
193 (declare (ring ring))
194 (cond ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
195 ;; If p=p0+p1 and q=q0+q1 then pq=p0q0+p0q1+p1q
196 ((endp (cdr p))
197 (term-times-termlist ring (car p) q))
198 ((endp (cdr q))
199 (termlist-times-term ring p (car q)))
200 (t
201 (let ((head (term-mul-lst ring (termlist-lt p) (termlist-lt q)))
202 (tail (termlist-add ring (term-times-termlist ring (car p) (cdr q))
203 (termlist-mul ring (cdr p) q))))
204 (cond ((null head) tail)
205 ((null tail) head)
206 (t (nconc head tail)))))))
207
208(defun termlist-unit (ring dimension)
209 (declare (fixnum dimension) (ring ring))
210 (list (make-term :ring ring :dimension dimension)))
211
212
213(defun termlist-expt (ring poly n &aux (dim (monom-dimension (termlist-lm poly))))
214 (declare (type fixnum n dim) (ring ring))
215 (cond
216 ((minusp n) (error "termlist-expt: Negative exponent."))
217 ((endp poly) (if (zerop n) (termlist-unit ring dim) nil))
218 (t
219 (do ((k 1 (ash k 1))
220 (q poly (termlist-mul ring q q)) ;keep squaring
221 (p (termlist-unit ring dim) (if (not (zerop (logand k n))) (termlist-mul ring p q) p)))
222 ((> k n) p)
223 (declare (fixnum k))))))
Note: See TracBrowser for help on using the repository browser.